RFC9332: Dual-Queue Coupled Active Queue Management (AQM) for Low Latency, Low Loss, and Scalable Throughput (L4S)

Download in text format

Internet Engineering Task Force (IETF)                    K. De Schepper
Request for Comments: 9332                               Nokia Bell Labs
Category: Experimental                                   B. Briscoe, Ed.
ISSN: 2070-1721                                              Independent
                                                                G. White
                                                            January 2023

 Dual-Queue Coupled Active Queue Management (AQM) for Low Latency, Low
                  Loss, and Scalable Throughput (L4S)


   This specification defines a framework for coupling the Active Queue
   Management (AQM) algorithms in two queues intended for flows with
   different responses to congestion.  This provides a way for the
   Internet to transition from the scaling problems of standard TCP-
   Reno-friendly ('Classic') congestion controls to the family of
   'Scalable' congestion controls.  These are designed for consistently
   very low queuing latency, very low congestion loss, and scaling of
   per-flow throughput by using Explicit Congestion Notification (ECN)
   in a modified way.  Until the Coupled Dual Queue (DualQ), these
   Scalable L4S congestion controls could only be deployed where a
   clean-slate environment could be arranged, such as in private data

   This specification first explains how a Coupled DualQ works.  It then
   gives the normative requirements that are necessary for it to work
   well.  All this is independent of which two AQMs are used, but
   pseudocode examples of specific AQMs are given in appendices.

Status of This Memo

   This document is not an Internet Standards Track specification; it is
   published for examination, experimental implementation, and

   This document defines an Experimental Protocol for the Internet
   community.  This document is a product of the Internet Engineering
   Task Force (IETF).  It represents the consensus of the IETF
   community.  It has received public review and has been approved for
   publication by the Internet Engineering Steering Group (IESG).  Not
   all documents approved by the IESG are candidates for any level of
   Internet Standard; see Section 2 of RFC 7841.

   Information about the current status of this document, any errata,
   and how to provide feedback on it may be obtained at

Copyright Notice

   Copyright (c) 2023 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

   This document is subject to BCP 78 and the IETF Trust's Legal
   Provisions Relating to IETF Documents
   (https://trustee.ietf.org/license-info) in effect on the date of
   publication of this document.  Please review these documents
   carefully, as they describe your rights and restrictions with respect
   to this document.  Code Components extracted from this document must
   include Revised BSD License text as described in Section 4.e of the
   Trust Legal Provisions and are provided without warranty as described
   in the Revised BSD License.

Table of Contents

   1.  Introduction
     1.1.  Outline of the Problem
     1.2.  Context, Scope, and Applicability
     1.3.  Terminology
     1.4.  Features
   2.  DualQ Coupled AQM
     2.1.  Coupled AQM
     2.2.  Dual Queue
     2.3.  Traffic Classification
     2.4.  Overall DualQ Coupled AQM Structure
     2.5.  Normative Requirements for a DualQ Coupled AQM
       2.5.1.  Functional Requirements  Requirements in Unexpected Cases
       2.5.2.  Management Requirements  Configuration  Monitoring  Anomaly Detection  Deployment, Coexistence, and Scaling
   3.  IANA Considerations
   4.  Security Considerations
     4.1.  Low Delay without Requiring Per-flow Processing
     4.2.  Handling Unresponsive Flows and Overload
       4.2.1.  Unresponsive Traffic without Overload
       4.2.2.  Avoiding Short-Term Classic Starvation: Sacrifice L4S
               Throughput or Delay?
       4.2.3.  L4S ECN Saturation: Introduce Drop or Delay?  Protecting against Overload by Unresponsive
                 ECN-Capable Traffic
   5.  References
     5.1.  Normative References
     5.2.  Informative References
   Appendix A.  Example DualQ Coupled PI2 Algorithm
     A.1.  Pass #1: Core Concepts
     A.2.  Pass #2: Edge-Case Details
   Appendix B.  Example DualQ Coupled Curvy RED Algorithm
     B.1.  Curvy RED in Pseudocode
     B.2.  Efficient Implementation of Curvy RED
   Appendix C.  Choice of Coupling Factor, k
     C.1.  RTT-Dependence
     C.2.  Guidance on Controlling Throughput Equivalence
   Authors' Addresses

1.  Introduction

   This document specifies a framework for DualQ Coupled AQMs, which can
   serve as the network part of the L4S architecture [RFC9330].  A DualQ
   Coupled AQM consists of two queues: L4S and Classic.  The L4S queue
   is intended for Scalable congestion controls that can maintain very
   low queuing latency (sub-millisecond on average) and high throughput
   at the same time.  The Coupled DualQ acts like a semi-permeable
   membrane: the L4S queue isolates the sub-millisecond average queuing
   delay of L4S from Classic latency, while the coupling between the
   queues pools the capacity between both queues so that ad hoc numbers
   of capacity-seeking applications all sharing the same capacity can
   have roughly equivalent throughput per flow, whichever queue they
   use.  The DualQ achieves this indirectly, without having to inspect
   transport-layer flow identifiers and without compromising the
   performance of the Classic traffic, relative to a single queue.  The
   DualQ design has low complexity and requires no configuration for the
   public Internet.

1.1.  Outline of the Problem

   Latency is becoming the critical performance factor for many (perhaps
   most) applications on the public Internet, e.g., interactive web, web
   services, voice, conversational video, interactive video, interactive
   remote presence, instant messaging, online gaming, remote desktop,
   cloud-based applications, and video-assisted remote control of
   machinery and industrial processes.  Once access network bitrates
   reach levels now common in the developed world, further increases
   offer diminishing returns unless latency is also addressed
   [Dukkipati06].  In the last decade or so, much has been done to
   reduce propagation time by placing caches or servers closer to users.
   However, queuing remains a major intermittent component of latency.

   Previously, very low latency has only been available for a few
   selected low-rate applications, that confine their sending rate
   within a specially carved-off portion of capacity, which is
   prioritized over other traffic, e.g., Diffserv Expedited Forwarding
   (EF) [RFC3246].  Up to now, it has not been possible to allow any
   number of low-latency, high throughput applications to seek to fully
   utilize available capacity, because the capacity-seeking process
   itself causes too much queuing delay.

   To reduce this queuing delay caused by the capacity-seeking process,
   changes either to the network alone or to end systems alone are in
   progress.  L4S involves a recognition that both approaches are
   yielding diminishing returns:

   *  Recent state-of-the-art AQM in the network, e.g., Flow Queue CoDel
      [RFC8290], Proportional Integral controller Enhanced (PIE)
      [RFC8033], and Adaptive Random Early Detection (ARED) [ARED01]),
      has reduced queuing delay for all traffic, not just a select few
      applications.  However, no matter how good the AQM, the capacity-
      seeking (sawtoothing) rate of TCP-like congestion controls
      represents a lower limit that will cause either the queuing delay
      to vary or the link to be underutilized.  These AQMs are tuned to
      allow a typical capacity-seeking TCP-Reno-friendly flow to induce
      an average queue that roughly doubles the base round-trip time
      (RTT), adding 5-15 ms of queuing on average for a mix of long-
      running flows and web traffic (cf. 500 microseconds with L4S for
      the same traffic mix [L4Seval22]).  However, for many
      applications, low delay is not useful unless it is consistently
      low.  With these AQMs, 99th percentile queuing delay is 20-30 ms
      (cf. 2 ms with the same traffic over L4S).

   *  Similarly, recent research into using end-to-end congestion
      control without needing an AQM in the network (e.g., Bottleneck
      Bandwidth and Round-trip propagation time (BBR) [BBR-CC]) seems to
      have hit a similar queuing delay floor of about 20 ms on average,
      but there are also regular 25 ms delay spikes due to bandwidth
      probes and 60 ms spikes due to flow-starts.

   L4S learns from the experience of Data Center TCP (DCTCP) [RFC8257],
   which shows the power of complementary changes both in the network
   and on end systems.  DCTCP teaches us that two small but radical
   changes to congestion control are needed to cut the two major
   outstanding causes of queuing delay variability:

   1.  Far smaller rate variations (sawteeth) than Reno-friendly
       congestion controls.

   2.  A shift of smoothing and hence smoothing delay from network to

   Without the former, a 'Classic' (e.g., Reno-friendly) flow's RTT
   varies between roughly 1 and 2 times the base RTT between the
   machines in question.  Without the latter, a 'Classic' flow's
   response to changing events is delayed by a worst-case
   (transcontinental) RTT, which could be hundreds of times the actual
   smoothing delay needed for the RTT of typical traffic from localized
   Content Delivery Networks (CDNs).

   These changes are the two main features of the family of so-called
   'Scalable' congestion controls (which include DCTCP, Prague, and
   Self-Clocked Rate Adaptation for Multimedia (SCReAM)).  Both of these
   changes only reduce delay in combination with a complementary change
   in the network, and they are both only feasible with ECN, not drop,
   for the signalling:

   1.  The smaller sawteeth allow an extremely shallow ECN packet-
       marking threshold in the queue.

   2.  No smoothing in the network means that every fluctuation of the
       queue is signalled immediately.

   Without ECN, either of these would lead to very high loss levels.  In
   contrast, with ECN, the resulting high marking levels are just
   signals, not impairments.  (Note that BBRv2 [BBRv2] combines the best
   of both worlds -- it works as a Scalable congestion control when ECN
   is available, but it also aims to minimize delay when ECN is absent.)

   However, until now, Scalable congestion controls (like DCTCP) did not
   coexist well in a shared ECN-capable queue with existing Classic
   (e.g., Reno [RFC5681] or CUBIC [RFC8312]) congestion controls --
   Scalable controls are so aggressive that these 'Classic' algorithms
   would drive themselves to a small capacity share.  Therefore, until
   now, L4S controls could only be deployed where a clean-slate
   environment could be arranged, such as in private data centres (hence
   the name DCTCP).

   One way to solve the problem of coexistence between Scalable and
   Classic flows is to use a per-flow-queuing (FQ) approach such as FQ-
   CoDel [RFC8290].  It classifies packets by flow identifier into
   separate queues in order to isolate sparse flows from the higher
   latency in the queues assigned to heavier flows.  However, if a
   Classic flow needs both low delay and high throughput, having a queue
   to itself does not isolate it from the harm it causes to itself.
   Also FQ approaches need to inspect flow identifiers, which is not
   always practical.

   In summary, Scalable congestion controls address the root cause of
   the latency, loss and scaling problems with Classic congestion
   controls.  Both FQ and DualQ AQMs can be enablers for this smooth
   low-latency scalable behaviour.  The DualQ approach is particularly
   useful because identifying flows is sometimes not practical or

1.2.  Context, Scope, and Applicability

   L4S involves complementary changes in the network and on end systems:

      A DualQ Coupled AQM (defined in the present document) or a
      modification to flow queue AQMs (described in paragraph "b" in
      Section 4.2 of the L4S architecture [RFC9330]).

   End system:
      A Scalable congestion control (defined in Section 4 of the L4S ECN
      protocol spec [RFC9331]).

   Packet identifier:
      The network and end-system parts of L4S can be deployed
      incrementally, because they both identify L4S packets using the
      experimentally assigned ECN codepoints in the IP header: ECT(1)
      and CE [RFC8311] [RFC9331].

   DCTCP [RFC8257] is an example of a Scalable congestion control for
   controlled environments that has been deployed for some time in
   Linux, Windows, and FreeBSD operating systems.  During the progress
   of this document through the IETF, a number of other Scalable
   congestion controls were implemented, e.g., Prague over TCP and QUIC
   [PRAGUE-CC] [PragueLinux], BBRv2 [BBRv2] [BBR-CC], and the L4S
   variant of SCReAM for real-time media [SCReAM-L4S] [RFC8298].

   The focus of this specification is to enable deployment of the
   network part of the L4S service.  Then, without any management
   intervention, applications can exploit this new network capability as
   the applications or their operating systems migrate to Scalable
   congestion controls, which can then evolve _while_ their benefits are
   being enjoyed by everyone on the Internet.

   The DualQ Coupled AQM framework can incorporate any AQM designed for
   a single queue that generates a statistical or deterministic mark/
   drop probability driven by the queue dynamics.  Pseudocode examples
   of two different DualQ Coupled AQMs are given in the appendices.  In
   many cases the framework simplifies the basic control algorithm and
   requires little extra processing.  Therefore, it is believed the
   Coupled AQM would be applicable and easy to deploy in all types of
   buffers such as buffers in cost-reduced mass-market residential
   equipment; buffers in end-system stacks; buffers in carrier-scale
   equipment including remote access servers, routers, firewalls, and
   Ethernet switches; buffers in network interface cards; buffers in
   virtualized network appliances, hypervisors; and so on.

   For the public Internet, nearly all the benefit will typically be
   achieved by deploying the Coupled AQM into either end of the access
   link between a 'site' and the Internet, which is invariably the
   bottleneck (see Section 6.4 of [RFC9330] about deployment, which also
   defines the term 'site' to mean a home, an office, a campus, or
   mobile user equipment).

   Latency is not the only concern of L4S:

   *  The 'Low Loss' part of the name denotes that L4S generally
      achieves zero congestion loss (which would otherwise cause
      retransmission delays), due to its use of ECN.

   *  The 'Scalable throughput' part of the name denotes that the per-
      flow throughput of Scalable congestion controls should scale
      indefinitely, avoiding the imminent scaling problems with 'TCP-
      Friendly' congestion control algorithms [RFC3649].

   The former is clearly in scope of this AQM document.  However, the
   latter is an outcome of the end-system behaviour and is therefore
   outside the scope of this AQM document, even though the AQM is an

   The overall L4S architecture [RFC9330] gives more detail, including
   on wider deployment aspects such as backwards compatibility of
   Scalable congestion controls in bottlenecks where a DualQ Coupled AQM
   has not been deployed.  The supporting papers [L4Seval22],
   [DualPI2Linux], [PI2], and [PI2param] give the full rationale for the
   AQM design, both discursively and in more precise mathematical form,
   as well as the results of performance evaluations.  The main results
   have been validated independently when using the Prague congestion
   control [Boru20] (experiments are run using Prague and DCTCP, but
   only the former is relevant for validation, because Prague fixes a
   number of problems with the Linux DCTCP code that make it unsuitable
   for the public Internet).

1.3.  Terminology

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "OPTIONAL" in this document are to be interpreted as described in
   BCP 14 [RFC2119] [RFC8174] when, and only when, they appear in all
   capitals, as shown here.

   The DualQ Coupled AQM uses two queues for two services:

   Classic Service/Queue:  The Classic service is intended for all the
      congestion control behaviours that coexist with Reno [RFC5681]
      (e.g., Reno itself, CUBIC [RFC8312], and TFRC [RFC5348]).  The
      term 'Classic queue' means a queue providing the Classic service.

   Low Latency, Low Loss, and Scalable throughput (L4S) Service/
   Queue:  The 'L4S' service is intended for traffic from Scalable
      congestion control algorithms, such as the Prague congestion
      control [PRAGUE-CC], which was derived from Data Center TCP
      [RFC8257].  The L4S service is for more general traffic than just
      Prague -- it allows the set of congestion controls with similar
      scaling properties to Prague to evolve, such as the examples
      listed below (Relentless, SCReAM, etc.).  The term 'L4S queue'
      means a queue providing the L4S service.

   Classic Congestion Control:  A congestion control behaviour that can
      coexist with standard Reno [RFC5681] without causing significantly
      negative impact on its flow rate [RFC5033].  With Classic
      congestion controls, such as Reno or CUBIC, because flow rate has
      scaled since TCP congestion control was first designed in 1988, it
      now takes hundreds of round trips (and growing) to recover after a
      congestion signal (whether a loss or an ECN mark) as shown in the
      examples in Section 5.1 of the L4S architecture [RFC9330] and in
      [RFC3649].  Therefore, control of queuing and utilization becomes
      very slack, and the slightest disturbances (e.g., from new flows
      starting) prevent a high rate from being attained.

   Scalable Congestion Control:  A congestion control where the average
      time from one congestion signal to the next (the recovery time)
      remains invariant as flow rate scales, all other factors being
      equal.  This maintains the same degree of control over queuing and
      utilization whatever the flow rate, as well as ensuring that high
      throughput is robust to disturbances.  For instance, DCTCP
      averages 2 congestion signals per round trip, whatever the flow
      rate, as do other recently developed Scalable congestion controls,
      e.g., Relentless TCP [RELENTLESS], Prague [PRAGUE-CC]
      [PragueLinux], BBRv2 [BBRv2] [BBR-CC], and the L4S variant of
      SCReAM for real-time media [SCReAM-L4S] [RFC8298].  For the public
      Internet, a Scalable transport has to comply with the requirements
      in Section 4 of [RFC9331] (a.k.a. the 'Prague L4S requirements').

   C:  Abbreviation for Classic, e.g., when used as a subscript.

   L:  Abbreviation for L4S, e.g., when used as a subscript.

      The terms Classic or L4S can also qualify other nouns, such as
      'codepoint', 'identifier', 'classification', 'packet', and 'flow'.
      For example, an L4S packet means a packet with an L4S identifier
      sent from an L4S congestion control.

      Both Classic and L4S services can cope with a proportion of
      unresponsive or less-responsive traffic as well but, in the L4S
      case, its rate has to be smooth enough or low enough to not build
      a queue (e.g., DNS, Voice over IP (VoIP), game sync datagrams,
      etc.).  The DualQ Coupled AQM behaviour is defined to be similar
      to a single First-In, First-Out (FIFO) queue with respect to
      unresponsive and overload traffic.

   Reno-friendly:  The subset of Classic traffic that is friendly to the
      standard Reno congestion control defined for TCP in [RFC5681].
      The TFRC spec [RFC5348] indirectly implies that 'friendly' is
      defined as "generally within a factor of two of the sending rate
      of a TCP flow under the same conditions".  'Reno-friendly' is used
      here in place of 'TCP-friendly', given the latter has become
      imprecise, because the TCP protocol is now used with so many
      different congestion control behaviours, and Reno is used in non-
      TCP transports, such as QUIC [RFC9000].

   DualQ or DualQ AQM:  Used loosely as shorthand for a Dual-Queue
      Coupled AQM, where the context makes 'Coupled AQM' obvious.

   Classic ECN:  The original Explicit Congestion Notification (ECN)
      protocol [RFC3168] that requires ECN signals to be treated as
      equivalent to drops, both when generated in the network and when
      responded to by the sender.

      For L4S, the names used for the four codepoints of the 2-bit IP-
      ECN field are unchanged from those defined in the ECN spec
      [RFC3168], i.e., Not-ECT, ECT(0), ECT(1), and CE, where ECT stands
      for ECN-Capable Transport and CE stands for Congestion
      Experienced.  A packet marked with the CE codepoint is termed
      'ECN-marked' or sometimes just 'marked' where the context makes
      ECN obvious.

1.4.  Features

   The AQM couples marking and/or dropping from the Classic queue to the
   L4S queue in such a way that a flow will get roughly the same
   throughput whichever it uses.  Therefore, both queues can feed into
   the full capacity of a link, and no rates need to be configured for
   the queues.  The L4S queue enables Scalable congestion controls like
   DCTCP or Prague to give very low and consistently low latency,
   without compromising the performance of competing 'Classic' Internet

   Thousands of tests have been conducted in a typical fixed residential
   broadband setting.  Experiments used a range of base round-trip
   delays up to 100 ms and link rates up to 200 Mb/s between the data
   centre and home network, with varying amounts of background traffic
   in both queues.  For every L4S packet, the AQM kept the average
   queuing delay below 1 ms (or 2 packets where serialization delay
   exceeded 1 ms on slower links), with the 99th percentile being no
   worse than 2 ms.  No losses at all were introduced by the L4S AQM.
   Details of the extensive experiments are available in [L4Seval22] and
   [DualPI2Linux].  Subjective testing using very demanding high-
   bandwidth low-latency applications over a single shared access link
   is also described in [L4Sdemo16] and summarized in Section 6.1 of the
   L4S architecture [RFC9330].

   In all these experiments, the host was connected to the home network
   by fixed Ethernet, in order to quantify the queuing delay that can be
   achieved by a user who cares about delay.  It should be emphasized
   that L4S support at the bottleneck link cannot 'undelay' bursts
   introduced by another link on the path, for instance by legacy Wi-Fi
   equipment.  However, if L4S support is added to the queue feeding the
   _outgoing_ WAN link of a home gateway, it would be counterproductive
   not to also reduce the burstiness of the _incoming_ Wi-Fi.  Also,
   trials of Wi-Fi equipment with an L4S DualQ Coupled AQM on the
   _outgoing_ Wi-Fi interface are in progress, and early results of an
   L4S DualQ Coupled AQM in a 5G radio access network testbed with
   emulated outdoor cell edge radio fading are given in [L4S_5G].

   Unlike Diffserv EF, the L4S queue does not have to be limited to a
   small proportion of the link capacity in order to achieve low delay.
   The L4S queue can be filled with a heavy load of capacity-seeking
   flows (Prague, BBRv2, etc.) and still achieve low delay.  The L4S
   queue does not rely on the presence of other traffic in the Classic
   queue that can be 'overtaken'.  It gives low latency to L4S traffic
   whether or not there is Classic traffic.  The tail latency of traffic
   served by the Classic AQM is sometimes a little better, sometimes a
   little worse, when a proportion of the traffic is L4S.

   The two queues are only necessary because:

   *  The large variations (sawteeth) of Classic flows need roughly a
      base RTT of queuing delay to ensure full utilization.

   *  Scalable flows do not need a queue to keep utilization high, but
      they cannot keep latency consistently low if they are mixed with
      Classic traffic.

   The L4S queue has latency priority within sub-round-trip timescales,
   but over longer periods the coupling from the Classic to the L4S AQM
   (explained below) ensures that it does not have bandwidth priority
   over the Classic queue.

2.  DualQ Coupled AQM

   There are two main aspects to the DualQ Coupled AQM approach:

   1.  The Coupled AQM that addresses throughput equivalence between
       Classic (e.g., Reno or CUBIC) flows and L4S flows (that satisfy
       the Prague L4S requirements).

   2.  The Dual-Queue structure that provides latency separation for L4S
       flows to isolate them from the typically large Classic queue.

2.1.  Coupled AQM

   In the 1990s, the 'TCP formula' was derived for the relationship
   between the steady-state congestion window, cwnd, and the drop
   probability, p of standard Reno congestion control [RFC5681].  To a
   first-order approximation, the steady-state cwnd of Reno is inversely
   proportional to the square root of p.

   The design focuses on Reno as the worst case, because if it does no
   harm to Reno, it will not harm CUBIC or any traffic designed to be
   friendly to Reno.  TCP CUBIC implements a Reno-friendly mode, which
   is relevant for typical RTTs under 20 ms as long as the throughput of
   a single flow is less than about 350 Mb/s.  In such cases, it can be
   assumed that CUBIC traffic behaves similarly to Reno.  The term
   'Classic' will be used for the collection of Reno-friendly traffic
   including CUBIC and potentially other experimental congestion
   controls intended not to significantly impact the flow rate of Reno.

   A supporting paper [PI2] includes the derivation of the equivalent
   rate equation for DCTCP, for which cwnd is inversely proportional to
   p (not the square root), where in this case p is the ECN-marking
   probability.  DCTCP is not the only congestion control that behaves
   like this, so the term 'Scalable' will be used for all similar
   congestion control behaviours (see examples in Section 1.2).  The
   term 'L4S' is used for traffic driven by a Scalable congestion
   control that also complies with the additional 'Prague L4S
   requirements' [RFC9331].

   For safe coexistence, under stationary conditions, a Scalable flow
   has to run at roughly the same rate as a Reno TCP flow (all other
   factors being equal).  So the drop or marking probability for Classic
   traffic, p_C, has to be distinct from the marking probability for L4S
   traffic, p_L.  The original ECN spec [RFC3168] required these
   probabilities to be the same, but [RFC8311] updates [RFC3168] to
   enable experiments in which these probabilities are different.

   Also, to remain stable, Classic sources need the network to smooth
   p_C so it changes relatively slowly.  It is hard for a network node
   to know the RTTs of all the flows, so a Classic AQM adds a _worst-
   case_ RTT of smoothing delay (about 100-200 ms).  In contrast, L4S
   shifts responsibility for smoothing ECN feedback to the sender, which
   only delays its response by its _own_ RTT, as well as allowing a more
   immediate response if necessary.

   The Coupled AQM achieves safe coexistence by making the Classic drop
   probability p_C proportional to the square of the coupled L4S
   probability p_CL. p_CL is an input to the instantaneous L4S marking
   probability p_L, but it changes as slowly as p_C.  This makes the
   Reno flow rate roughly equal the DCTCP flow rate, because the
   squaring of p_CL counterbalances the square root of p_C in the 'TCP
   formula' of Classic Reno congestion control.

   Stating this as a formula, the relation between Classic drop
   probability, p_C, and the coupled L4S probability p_CL needs to take
   the following form:

       p_C = ( p_CL / k )^2,                 (1)

   where k is the constant of proportionality, which is termed the
   'coupling factor'.

2.2.  Dual Queue

   Classic traffic needs to build a large queue to prevent
   underutilization.  Therefore, a separate queue is provided for L4S
   traffic, and it is scheduled with priority over the Classic queue.
   Priority is conditional to prevent starvation of Classic traffic in
   certain conditions (see Section 2.4).

   Nonetheless, coupled marking ensures that giving priority to L4S
   traffic still leaves the right amount of spare scheduling time for
   Classic flows to each get equivalent throughput to DCTCP flows (all
   other factors, such as RTT, being equal).

2.3.  Traffic Classification

   Both the Coupled AQM and DualQ mechanisms need an identifier to
   distinguish L4S (L) and Classic (C) packets.  Then the coupling
   algorithm can achieve coexistence without having to inspect flow
   identifiers, because it can apply the appropriate marking or dropping
   probability to all flows of each type.  A separate specification
   [RFC9331] requires the network to treat the ECT(1) and CE codepoints
   of the ECN field as this identifier.  An additional process document
   has proved necessary to make the ECT(1) codepoint available for
   experimentation [RFC8311].

   For policy reasons, an operator might choose to steer certain packets
   (e.g., from certain flows or with certain addresses) out of the L
   queue, even though they identify themselves as L4S by their ECN
   codepoints.  In such cases, the L4S ECN protocol [RFC9331] states
   that the device "MUST NOT alter the end-to-end L4S ECN identifier" so
   that it is preserved end to end.  The aim is that each operator can
   choose how it treats L4S traffic locally, but an individual operator
   does not alter the identification of L4S packets, which would prevent
   other operators downstream from making their own choices on how to
   treat L4S traffic.

   In addition, an operator could use other identifiers to classify
   certain additional packet types into the L queue that it deems will
   not risk harm to the L4S service, for instance, addresses of specific
   applications or hosts; specific Diffserv codepoints such as EF,
   Voice-Admit, or the Non-Queue-Building (NQB) per-hop behaviour; or
   certain protocols (e.g., ARP and DNS) (see Section 5.4.1 of
   [RFC9331].  Note that [RFC9331] states that "a network node MUST NOT
   change Not-ECT or ECT(0) in the IP-ECN field into an L4S identifier."
   Thus, the L queue is not solely an L4S queue; it can be considered
   more generally as a low-latency queue.

2.4.  Overall DualQ Coupled AQM Structure

   Figure 1 shows the overall structure that any DualQ Coupled AQM is
   likely to have.  This schematic is intended to aid understanding of
   the current designs of DualQ Coupled AQMs.  However, it is not
   intended to preclude other innovative ways of satisfying the
   normative requirements in Section 2.5 that minimally define a DualQ
   Coupled AQM.  Also, the schematic only illustrates operation under
   normally expected circumstances; behaviour under overload or with
   operator-specific classifiers is deferred to Section

   The classifier on the left separates incoming traffic between the two
   queues (L and C).  Each queue has its own AQM that determines the
   likelihood of marking or dropping (p_L and p_C).  In [PI2], it has
   been proved that it is preferable to control load with a linear
   controller, then square the output before applying it as a drop
   probability to Reno-friendly traffic (because Reno congestion control
   decreases its load proportional to the square root of the increase in
   drop).  So, the AQM for Classic traffic needs to be implemented in
   two stages: i) a base stage that outputs an internal probability p'
   (pronounced 'p-prime') and ii) a squaring stage that outputs p_C,

       p_C = (p')^2.                         (2)

   Substituting for p_C in equation (1) gives

       p' = p_CL / k.

   So the slow-moving input to ECN marking in the L queue (the coupled
   L4S probability) is

       p_CL = k*p'.                          (3)

   The actual ECN-marking probability p_L that is applied to the L queue
   needs to track the immediate L queue delay under L-only congestion
   conditions, as well as track p_CL under coupled congestion
   conditions.  So the L queue uses a 'Native AQM' that calculates a
   probability p'_L as a function of the instantaneous L queue delay.
   And given the L queue has conditional priority over the C queue,
   whenever the L queue grows, the AQM ought to apply marking
   probability p'_L, but p_L ought to not fall below p_CL.  This

       p_L = max(p'_L, p_CL),                (4)

   which has also been found to work very well in practice.

   The two transformations of p' in equations (2) and (3) implement the
   required coupling given in equation (1) earlier.

   The constant of proportionality or coupling factor, k, in equation
   (1) determines the ratio between the congestion probabilities (loss
   or marking) experienced by L4S and Classic traffic.  Thus, k
   indirectly determines the ratio between L4S and Classic flow rates,
   because flows (assuming they are responsive) adjust their rate in
   response to congestion probability.  Appendix C.2 gives guidance on
   the choice of k and its effect on relative flow rates.

                                  | |    ,------.
                    L4S (L) queue | |===>| ECN  |
                       ,'| _______|_|    |marker|\
                     <'  |         |     `------'\\
                      //`'         v        ^ p_L \\
                     //       ,-------.     |      \\
                    //        |Native |p'_L |       \\,.
                   //         |  L4S  |--->(MAX)    <  |   ___
      ,----------.//          |  AQM  |     ^ p_CL   `\|.'Cond-`.
      |  IP-ECN  |/           `-------'     |          / itional \
   ==>|Classifier|            ,-------.   (k*p')       [ priority]==>
      |          |\           |  Base |     |          \scheduler/
      `----------'\\          |  AQM  |---->:        ,'|`-.___.-'
                   \\         |       |p'   |      <'  |
                    \\        `-------'   (p'^2)    //`'
                     \\            ^        |      //
                      \\,.         |        v p_C //
                      <  | _________     .------.//
                       `\|   |      |    | Drop |/
                 Classic (C) |queue |===>|/mark |
                           __|______|    `------'

   Legend: ===> traffic flow
           ---> control dependency

                   Figure 1: DualQ Coupled AQM Schematic

   After the AQMs have applied their dropping or marking, the scheduler
   forwards their packets to the link.  Even though the scheduler gives
   priority to the L queue, it is not as strong as the coupling from the
   C queue.  This is because, as the C queue grows, the 'Base AQM'
   applies more congestion signals to L traffic (as well as to C).  As L
   flows reduce their rate in response, they use less than the
   scheduling share for L traffic.  So, because the scheduler is work
   preserving, it schedules any C traffic in the gaps.

   Giving priority to the L queue has the benefit of very low L queue
   delay, because the L queue is kept empty whenever L traffic is
   controlled by the coupling.  Also, there only has to be a coupling in
   one direction -- from Classic to L4S.  Priority has to be conditional
   in some way to prevent the C queue from being starved in the short
   term (see Section 4.2.2) to give C traffic a means to push in, as
   explained next.  With normal responsive L traffic, the coupled ECN
   marking gives C traffic the ability to push back against even strict
   priority, by congestion marking the L traffic to make it yield some
   space.  However, if there is just a small finite set of C packets
   (e.g., a DNS request or an initial window of data), some Classic AQMs
   will not induce enough ECN marking in the L queue, no matter how long
   the small set of C packets waits.  Then, if the L queue happens to
   remain busy, the C traffic would never get a scheduling opportunity
   from a strict priority scheduler.  Ideally, the Classic AQM would be
   designed to increase the coupled marking the longer that C packets
   have been waiting, but this is not always practical -- hence the need
   for L priority to be conditional.  Giving a small weight or limited
   waiting time for C traffic improves response times for short Classic
   messages, such as DNS requests, and improves Classic flow startup
   because immediate capacity is available.

   Example DualQ Coupled AQM algorithms called 'DualPI2' and 'Curvy RED'
   are given in Appendices A and B.  Either example AQM can be used to
   couple packet marking and dropping across a DualQ:

   *  DualPI2 uses a Proportional Integral (PI) controller as the Base
      AQM.  Indeed, this Base AQM with just the squared output and no
      L4S queue can be used as a drop-in replacement for PIE [RFC8033],
      in which case it is just called PI2 [PI2].  PI2 is a principled
      simplification of PIE that is both more responsive and more stable
      in the face of dynamically varying load.

   *  Curvy RED is derived from RED [RED], except its configuration
      parameters are delay-based to make them insensitive to link rate,
      and it requires fewer operations per packet than RED.  However,
      DualPI2 is more responsive and stable over a wider range of RTTs
      than Curvy RED.  As a consequence, at the time of writing, DualPI2
      has attracted more development and evaluation attention than Curvy
      RED, leaving the Curvy RED design not so fully evaluated.

   Both AQMs regulate their queue against targets configured in units of
   time rather than bytes.  As already explained, this ensures
   configuration can be invariant for different drain rates.  With AQMs
   in a DualQ structure this is particularly important because the drain
   rate of each queue can vary rapidly as flows for the two queues
   arrive and depart, even if the combined link rate is constant.

   It would be possible to control the queues with other alternative
   AQMs, as long as the normative requirements (those expressed in
   capitals) in Section 2.5 are observed.

   The two queues could optionally be part of a larger queuing
   hierarchy, such as the initial example ideas in [L4S-DIFFSERV].

2.5.  Normative Requirements for a DualQ Coupled AQM

   The following requirements are intended to capture only the essential
   aspects of a DualQ Coupled AQM.  They are intended to be independent
   of the particular AQMs implemented for each queue but to still define
   the DualQ framework built around those AQMs.

2.5.1.  Functional Requirements

   A DualQ Coupled AQM implementation MUST comply with the prerequisite
   L4S behaviours for any L4S network node (not just a DualQ) as
   specified in Section 5 of [RFC9331].  These primarily concern
   classification and re-marking as briefly summarized earlier in
   Section 2.3.  But Section 5.5 of [RFC9331] also gives guidance on
   reducing the burstiness of the link technology underlying any L4S

   A DualQ Coupled AQM implementation MUST utilize two queues, each with
   an AQM algorithm.

   The AQM algorithm for the low-latency (L) queue MUST be able to apply
   ECN marking to ECN-capable packets.

   The scheduler draining the two queues MUST give L4S packets priority
   over Classic, although priority MUST be bounded in order not to
   starve Classic traffic (see Section 4.2.2).  The scheduler SHOULD be
   work-conserving, or otherwise close to work-conserving.  This is
   because Classic traffic needs to be able to efficiently fill any
   space left by L4S traffic even though the scheduler would otherwise
   allocate it to L4S.

   [RFC9331] defines the meaning of an ECN marking on L4S traffic,
   relative to drop of Classic traffic.  In order to ensure coexistence
   of Classic and Scalable L4S traffic, it says, "the likelihood that
   the AQM drops a Not-ECT Classic packet (p_C) MUST be roughly
   proportional to the square of the likelihood that it would have
   marked it if it had been an L4S packet (p_L)."  The term 'likelihood'
   is used to allow for marking and dropping to be either probabilistic
   or deterministic.

   For the current specification, this translates into the following
   requirement.  A DualQ Coupled AQM MUST apply ECN marking to traffic
   in the L queue that is no lower than that derived from the likelihood
   of drop (or ECN marking) in the Classic queue using equation (1).

   The constant of proportionality, k, in equation (1) determines the
   relative flow rates of Classic and L4S flows when the AQM concerned
   is the bottleneck (all other factors being equal).  The L4S ECN
   protocol [RFC9331] says, "The constant of proportionality (k) does
   not have to be standardised for interoperability, but a value of 2 is

   Assuming Scalable congestion controls for the Internet will be as
   aggressive as DCTCP, this will ensure their congestion window will be
   roughly the same as that of a Standards Track TCP Reno congestion
   control (Reno) [RFC5681] and other Reno-friendly controls, such as
   TCP CUBIC in its Reno-friendly mode.

   The choice of k is a matter of operator policy, and operators MAY
   choose a different value using the guidelines in Appendix C.2.

   If multiple customers or users share capacity at a bottleneck (e.g.,
   in the Internet access link of a campus network), the operator's
   choice of k will determine capacity sharing between the flows of
   different customers.  However, on the public Internet, access network
   operators typically isolate customers from each other with some form
   of Layer 2 multiplexing (OFDM(A) in DOCSIS 3.1, CDMA in 3G, and SC-
   FDMA in LTE) or Layer 3 scheduling (Weighted Round Robin (WRR) for
   DSL) rather than relying on host congestion controls to share
   capacity between customers [RFC0970].  In such cases, the choice of k
   will solely affect relative flow rates within each customer's access
   capacity, not between customers.  Also, k will not affect relative
   flow rates at any times when all flows are Classic or all flows are
   L4S, and it will not affect the relative throughput of small flows.  Requirements in Unexpected Cases

   The flexibility to allow operator-specific classifiers (Section 2.3)
   leads to the need to specify what the AQM in each queue ought to do
   with packets that do not carry the ECN field expected for that queue.
   It is expected that the AQM in each queue will inspect the ECN field
   to determine what sort of congestion notification to signal, then it
   will decide whether to apply congestion notification to this
   particular packet, as follows:

   *  If a packet that does not carry an ECT(1) or a CE codepoint is
      classified into the L queue, then:

      -  if the packet is ECT(0), the L AQM SHOULD apply CE marking
         using a probability appropriate to Classic congestion control
         and appropriate to the target delay in the L queue

      -  if the packet is Not-ECT, the appropriate action depends on
         whether some other function is protecting the L queue from
         misbehaving flows (e.g., per-flow queue protection
         [DOCSIS-Q-PROT] or latency policing):

         o  if separate queue protection is provided, the L AQM SHOULD
            ignore the packet and forward it unchanged, meaning it
            should not calculate whether to apply congestion
            notification, and it should neither drop nor CE mark the
            packet (for instance, the operator might classify EF traffic
            that is unresponsive to drop into the L queue, alongside
            responsive L4S-ECN traffic)

         o  if separate queue protection is not provided, the L AQM
            SHOULD apply drop using a drop probability appropriate to
            Classic congestion control and to the target delay in the L

   *  If a packet that carries an ECT(1) codepoint is classified into
      the C queue:

      -  the C AQM SHOULD apply CE marking using the Coupled AQM
         probability p_CL (= k*p').

   The above requirements are worded as "SHOULD"s, because operator-
   specific classifiers are for flexibility, by definition.  Therefore,
   alternative actions might be appropriate in the operator's specific
   circumstances.  An example would be where the operator knows that
   certain legacy traffic set to one codepoint actually has a congestion
   response associated with another codepoint.

   If the DualQ Coupled AQM has detected overload, it MUST introduce
   Classic drop to both types of ECN-capable traffic until the overload
   episode has subsided.  Introducing drop if ECN marking is
   persistently high is recommended in Section 7 of the ECN spec
   [RFC3168] and in Section 4.2.1 of the AQM Recommendations [RFC7567].

2.5.2.  Management Requirements  Configuration

   By default, a DualQ Coupled AQM SHOULD NOT need any configuration for
   use at a bottleneck on the public Internet [RFC7567].  The following
   parameters MAY be operator-configurable, e.g., to tune for non-
   Internet settings:

   *  Optional packet classifier(s) to use in addition to the ECN field
      (see Section 2.3).

   *  Expected typical RTT, which can be used to determine the queuing
      delay of the Classic AQM at its operating point, in order to
      prevent typical lone flows from underutilizing capacity.  For

      -  for the PI2 algorithm (Appendix A), the queuing delay target is
         dependent on the typical RTT.

      -  for the Curvy RED algorithm (Appendix B), the queuing delay at
         the desired operating point of the curvy ramp is configured to
         encompass a typical RTT.

      -  if another Classic AQM was used, it would be likely to need an
         operating point for the queue based on the typical RTT, and if
         so, it SHOULD be expressed in units of time.

      An operating point that is manually calculated might be directly
      configurable instead, e.g., for links with large numbers of flows
      where underutilization by a single flow would be unlikely.

   *  Expected maximum RTT, which can be used to set the stability
      parameter(s) of the Classic AQM.  For example:

      -  for the PI2 algorithm (Appendix A), the gain parameters of the
         PI algorithm depend on the maximum RTT.

      -  for the Curvy RED algorithm (Appendix B), the smoothing
         parameter is chosen to filter out transients in the queue
         within a maximum RTT.

      Any stability parameter that is manually calculated assuming a
      maximum RTT might be directly configurable instead.

   *  Coupling factor, k (see Appendix C.2).

   *  A limit to the conditional priority of L4S.  This is scheduler-
      dependent, but it SHOULD be expressed as a relation between the
      max delay of a C packet and an L packet.  For example:

      -  for a WRR scheduler, a weight ratio between L and C of w:1
         means that the maximum delay of a C packet is w times that of
         an L packet.

      -  for a time-shifted FIFO (TS-FIFO) scheduler (see
         Section 4.2.2), a time-shift of tshift means that the maximum
         delay to a C packet is tshift greater than that of an L packet.
         tshift could be expressed as a multiple of the typical RTT
         rather than as an absolute delay.

   *  The maximum Classic ECN-marking probability, p_Cmax, before
      introducing drop.  Monitoring

   An experimental DualQ Coupled AQM SHOULD allow the operator to
   monitor each of the following operational statistics on demand, per
   queue and per configurable sample interval, for performance
   monitoring and perhaps also for accounting in some cases:

   *  bits forwarded, from which utilization can be calculated;

   *  total packets in the three categories: arrived, presented to the
      AQM, and forwarded.  The difference between the first two will
      measure any non-AQM tail discard.  The difference between the last
      two will measure proactive AQM discard;

   *  ECN packets marked, non-ECN packets dropped, and ECN packets
      dropped, which can be combined with the three total packet counts
      above to calculate marking and dropping probabilities; and

   *  queue delay (not including serialization delay of the head packet
      or medium acquisition delay) -- see further notes below.

      Unlike the other statistics, queue delay cannot be captured in a
      simple accumulating counter.  Therefore, the type of queue delay
      statistics produced (mean, percentiles, etc.) will depend on
      implementation constraints.  To facilitate comparative evaluation
      of different implementations and approaches, an implementation
      SHOULD allow mean and 99th percentile queue delay to be derived
      (per queue per sample interval).  A relatively simple way to do
      this would be to store a coarse-grained histogram of queue delay.
      This could be done with a small number of bins with configurable
      edges that represent contiguous ranges of queue delay.  Then, over
      a sample interval, each bin would accumulate a count of the number
      of packets that had fallen within each range.  The maximum queue
      delay per queue per interval MAY also be recorded, to aid
      diagnosis of faults and anomalous events.  Anomaly Detection

   An experimental DualQ Coupled AQM SHOULD asynchronously report the
   following data about anomalous conditions:

   *  Start time and duration of overload state.

      A hysteresis mechanism SHOULD be used to prevent flapping in and
      out of overload causing an event storm.  For instance, exiting
      from overload state could trigger one report but also latch a
      timer.  Then, during that time, if the AQM enters and exits
      overload state any number of times, the duration in overload state
      is accumulated, but no new report is generated until the first
      time the AQM is out of overload once the timer has expired.  Deployment, Coexistence, and Scaling

   [RFC5706] suggests that deployment, coexistence, and scaling should
   also be covered as management requirements.  The raison d'etre of the
   DualQ Coupled AQM is to enable deployment and coexistence of Scalable
   congestion controls (as incremental replacements for today's Reno-
   friendly controls that do not scale with bandwidth-delay product).
   Therefore, there is no need to repeat these motivating issues here
   given they are already explained in the Introduction and detailed in
   the L4S architecture [RFC9330].

   The descriptions of specific DualQ Coupled AQM algorithms in the
   appendices cover scaling of their configuration parameters, e.g.,
   with respect to RTT and sampling frequency.

3.  IANA Considerations

   This document has no IANA actions.

4.  Security Considerations

4.1.  Low Delay without Requiring Per-flow Processing

   The L4S architecture [RFC9330] compares the DualQ and FQ approaches
   to L4S.  The privacy considerations section in that document
   motivates the DualQ on the grounds that users who want to encrypt
   application flow identifiers, e.g., in IPsec or other encrypted VPN
   tunnels, don't have to sacrifice low delay ([RFC8404] encourages
   avoidance of such privacy compromises).

   The security considerations section of the L4S architecture [RFC9330]
   also includes subsections on policing of relative flow rates
   (Section 8.1) and on policing of flows that cause excessive queuing
   delay (Section 8.2).  It explains that the interests of users do not
   collide in the same way for delay as they do for bandwidth.  For
   someone to get more of the bandwidth of a shared link, someone else
   necessarily gets less (a 'zero-sum game'), whereas queuing delay can
   be reduced for everyone, without any need for someone else to lose
   out.  It also explains that, on the current Internet, scheduling
   usually enforces separation of bandwidth between 'sites' (e.g.,
   households, businesses, or mobile users), but it is not common to
   need to schedule or police the bandwidth used by individual
   application flows.

   By the above arguments, per-flow rate policing might not be
   necessary, and in trusted environments (e.g., private data centres),
   it is certainly unlikely to be needed.  Therefore, because it is hard
   to avoid complexity and unintended side effects with per-flow rate
   policing, it needs to be separable from a basic AQM, as an option,
   under policy control.  On this basis, the DualQ Coupled AQM provides
   low delay without prejudging the question of per-flow rate policing.

   Nonetheless, the interests of users or flows might conflict, e.g., in
   case of accident or malice.  Then per-flow rate control could be
   necessary.  If per-flow rate control is needed, it can be provided as
   a modular addition to a DualQ.  And similarly, if protection against
   excessive queue delay is needed, a per-flow queue protection option
   can be added to a DualQ (e.g., [DOCSIS-Q-PROT]).

4.2.  Handling Unresponsive Flows and Overload

   In the absence of any per-flow control, it is important that the
   basic DualQ Coupled AQM gives unresponsive flows no more throughput
   advantage than a single-queue AQM would, and that it at least handles
   overload situations.  Overload means that incoming load significantly
   or persistently exceeds output capacity, but it is not intended to be
   a precise term -- significant and persistent are matters of degree.

   A trade-off needs to be made between complexity and the risk of
   either traffic class harming the other.  In overloaded conditions,
   the higher priority L4S service will have to sacrifice some aspect of
   its performance.  Depending on the degree of overload, alternative
   solutions may relax a different factor: for example, throughput,
   delay, or drop.  These choices need to be made either by the
   developer or by operator policy, rather than by the IETF.  Subsequent
   subsections discuss handling different degrees of overload:

   *  Unresponsive flows (L and/or C) but not overloaded, i.e., the sum
      of unresponsive load before adding any responsive traffic is below

         This case is handled by the regular Coupled DualQ (Section 2.1)
         but not discussed there.  So below, Section 4.2.1 explains the
         design goal and how it is achieved in practice.

   *  Unresponsive flows (L and/or C) causing persistent overload, i.e.,
      the sum of unresponsive load even before adding any responsive
      traffic persistently exceeds capacity.

         This case is not covered by the regular Coupled DualQ mechanism
         (Section 2.1), but the last paragraph in Section sets
         out a requirement to handle the case where ECN-capable traffic
         could starve non-ECN-capable traffic.  Section 4.2.3 below
         discusses the general options and gives specific examples.

   *  Short-term overload that lies between the 'not overloaded' and
      'persistently overloaded' cases.

         For the period before overload is deemed persistent,
         Section 4.2.2 discusses options for more immediate mechanisms
         at the scheduler timescale.  These prevent short-term
         starvation of the C queue by making the priority of the L queue
         conditional, as required in Section 2.5.1.

4.2.1.  Unresponsive Traffic without Overload

   When one or more L flows and/or C flows are unresponsive, but their
   total load is within the link capacity so that they do not saturate
   the coupled marking (below 100%), the goal of a DualQ AQM is to
   behave no worse than a single-queue AQM.

   Tests have shown that this is indeed the case with no additional
   mechanism beyond the regular Coupled DualQ of Section 2.1 (see the
   results of 'overload experiments' in [L4Seval22]).  Perhaps
   counterintuitively, whether the unresponsive flow classifies itself
   into the L or the C queue, the DualQ system behaves as if it has
   subtracted from the overall link capacity.  Then, the coupling shares
   out the remaining capacity between any competing responsive flows (in
   either queue).  See also Section 4.2.2, which discusses scheduler-
   specific details.

4.2.2.  Avoiding Short-Term Classic Starvation: Sacrifice L4S Throughput
        or Delay?

   Priority of L4S is required to be conditional (see Sections 2.4 and
   2.5.1) to avoid short-term starvation of Classic.  Otherwise, as
   explained in Section 2.4, even a lone responsive L4S flow could
   temporarily block a small finite set of C packets (e.g., an initial
   window or DNS request).  The blockage would only be brief, but it
   could be longer for certain AQM implementations that can only
   increase the congestion signal coupled from the C queue when C
   packets are actually being dequeued.  There is then the question of
   whether to sacrifice L4S throughput or L4S delay (or some other
   policy) to make the priority conditional:

   Sacrifice L4S throughput:
      By using WRR as the conditional priority scheduler, the L4S
      service can sacrifice some throughput during overload.  This can
      be thought of as guaranteeing either a minimum throughput service
      for Classic traffic or a maximum delay for a packet at the head of
      the Classic queue.

         |  Cautionary note: a WRR scheduler can only guarantee Classic
         |  throughput if Classic sources are sending enough to use it
         |  -- congestion signals can undermine scheduling because they
         |  determine how much responsive traffic of each class arrives
         |  for scheduling in the first place.  This is why scheduling
         |  is only relied on to handle short-term starvation, until
         |  congestion signals build up and the sources react.  Even
         |  during long-term overload (discussed more fully in
         |  Section 4.2.3), it's pragmatic to discard packets from both
         |  queues, which again thins the traffic before it reaches the
         |  scheduler.  This is because a scheduler cannot be relied on
         |  to handle long-term overload since the right scheduler
         |  weight cannot be known for every scenario.

      The scheduling weight of the Classic queue should be small (e.g.,
      1/16).  In most traffic scenarios, the scheduler will not
      interfere and it will not need to, because the coupling mechanism
      and the end systems will determine the share of capacity across
      both queues as if it were a single pool.  However, if L4S traffic
      is over-aggressive or unresponsive, the scheduler weight for
      Classic traffic will at least be large enough to ensure it does
      not starve in the short term.

      Although WRR scheduling is only expected to address short-term
      overload, there are (somewhat rare) cases when WRR has an effect
      on capacity shares over longer timescales.  But its effect is
      minor, and it certainly does no harm.  Specifically, in cases
      where the ratio of L4S to Classic flows (e.g., 19:1) is greater
      than the ratio of their scheduler weights (e.g., 15:1), the L4S
      flows will get less than an equal share of the capacity, but only
      slightly.  For instance, with the example numbers given, each L4S
      flow will get (15/16)/19 = 4.9% when ideally each would get 1/20 =
      5%. In the rather specific case of an unresponsive flow taking up
      just less than the capacity set aside for L4S (e.g., 14/16 in the
      above example), using WRR could significantly reduce the capacity
      left for any responsive L4S flows.

      The scheduling weight of the Classic queue should not be too
      small, otherwise a C packet at the head of the queue could be
      excessively delayed by a continually busy L queue.  For instance,
      if the Classic weight is 1/16, the maximum that a Classic packet
      at the head of the queue can be delayed by L traffic is the
      serialization delay of 15 MTU-sized packets.

   Sacrifice L4S delay:
      The operator could choose to control overload of the Classic queue
      by allowing some delay to 'leak' across to the L4S queue.  The
      scheduler can be made to behave like a single FIFO queue with
      different service times by implementing a very simple conditional
      priority scheduler that could be called a "time-shifted FIFO" (TS-
      FIFO) (see the Modifier Earliest Deadline First (MEDF) scheduler
      [MEDF]).  This scheduler adds tshift to the queue delay of the
      next L4S packet, before comparing it with the queue delay of the
      next Classic packet, then it selects the packet with the greater
      adjusted queue delay.

      Under regular conditions, the TS-FIFO scheduler behaves just like
      a strict priority scheduler.  But under moderate or high overload,
      it prevents starvation of the Classic queue, because the time-
      shift (tshift) defines the maximum extra queuing delay of Classic
      packets relative to L4S.  This would control milder overload of
      responsive traffic by introducing delay to defer invoking the
      overload mechanisms in Section 4.2.3, particularly when close to
      the maximum congestion signal.

   The example implementations in Appendices A and B could both be
   implemented with either policy.

4.2.3.  L4S ECN Saturation: Introduce Drop or Delay?

   This section concerns persistent overload caused by unresponsive L
   and/or C flows.  To keep the throughput of both L4S and Classic flows
   roughly equal over the full load range, a different control strategy
   needs to be defined above the point where the L4S AQM persistently
   saturates to an ECN marking probability of 100%, leaving no room to
   push back the load any harder.  L4S ECN marking will saturate first
   (assuming the coupling factor k>1), even though saturation could be
   caused by the sum of unresponsive traffic in either or both queues
   exceeding the link capacity.

   The term 'unresponsive' includes cases where a flow becomes
   temporarily unresponsive, for instance, a real-time flow that takes a
   while to adapt its rate in response to congestion, or a standard Reno
   flow that is normally responsive, but above a certain congestion
   level it will not be able to reduce its congestion window below the
   allowed minimum of 2 segments [RFC5681], effectively becoming
   unresponsive.  (Note that L4S traffic ought to remain responsive
   below a window of 2 segments.  See the L4S requirements [RFC9331].)

   Saturation raises the question of whether to relieve congestion by
   introducing some drop into the L4S queue or by allowing delay to grow
   in both queues (which could eventually lead to drop due to buffer
   exhaustion anyway):

   Drop on Saturation:
      Persistent saturation can be defined by a maximum threshold for
      coupled L4S ECN marking (assuming k>1) before saturation starts to
      make the flow rates of the different traffic types diverge.  Above
      that, the drop probability of Classic traffic is applied to all
      packets of all traffic types.  Then experiments have shown that
      queuing delay can be kept at the target in any overload situation,
      including with unresponsive traffic, and no further measures are
      required (Section

   Delay on Saturation:
      When L4S marking saturates, instead of introducing L4S drop, the
      drop and marking probabilities of both queues could be capped.
      Beyond that, delay will grow either solely in the queue with
      unresponsive traffic (if WRR is used) or in both queues (if TS-
      FIFO is used).  In either case, the higher delay ought to control
      temporary high congestion.  If the overload is more persistent,
      eventually the combined DualQ will overflow and tail drop will
      control congestion.

   The example implementation in Appendix A solely applies the "drop on
   saturation" policy.  The DOCSIS specification of a DualQ Coupled AQM
   [DOCSIS3.1] also implements the 'drop on saturation' policy with a
   very shallow L buffer.  However, the addition of DOCSIS per-flow
   Queue Protection [DOCSIS-Q-PROT] turns this into 'delay on
   saturation' by redirecting some packets of the flow or flows that are
   most responsible for L queue overload into the C queue, which has a
   higher delay target.  If overload continues, this again becomes 'drop
   on saturation' as the level of drop in the C queue rises to maintain
   the target delay of the C queue.  Protecting against Overload by Unresponsive ECN-Capable

   Without a specific overload mechanism, unresponsive traffic would
   have a greater advantage if it were also ECN-capable.  The advantage
   is undetectable at normal low levels of marking.  However, it would
   become significant with the higher levels of marking typical during
   overload, when it could evade a significant degree of drop.  This is
   an issue whether the ECN-capable traffic is L4S or Classic.

   This raises the question of whether and when to introduce drop of
   ECN-capable traffic, as required by both Section 7 of the ECN spec
   [RFC3168] and Section 4.2.1 of the AQM recommendations [RFC7567].

   As an example, experiments with the DualPI2 AQM (Appendix A) have
   shown that introducing 'drop on saturation' at 100% coupled L4S
   marking addresses this problem with unresponsive ECN, and it also
   addresses the saturation problem.  At saturation, DualPI2 switches
   into overload mode, where the Base AQM is driven by the max delay of
   both queues, and it introduces probabilistic drop to both queues
   equally.  It leaves only a small range of congestion levels just
   below saturation where unresponsive traffic gains any advantage from
   using the ECN capability (relative to being unresponsive without
   ECN), and the advantage is hardly detectable (see [DualQ-Test] and
   section IV-G of [L4Seval22]).  Also, overload with an unresponsive
   ECT(1) flow gets no more bandwidth advantage than with ECT(0).

5.  References

5.1.  Normative References

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119,
              DOI 10.17487/RFC2119, March 1997,

   [RFC3168]  Ramakrishnan, K., Floyd, S., and D. Black, "The Addition
              of Explicit Congestion Notification (ECN) to IP",
              RFC 3168, DOI 10.17487/RFC3168, September 2001,

   [RFC8311]  Black, D., "Relaxing Restrictions on Explicit Congestion
              Notification (ECN) Experimentation", RFC 8311,
              DOI 10.17487/RFC8311, January 2018,

   [RFC9331]  De Schepper, K. and B. Briscoe, Ed., "The Explicit
              Congestion Notification (ECN) Protocol for Low Latency,
              Low Loss, and Scalable Throughput (L4S)", RFC 9331,
              DOI 10.17487/RFC9331, January 2023,

5.2.  Informative References

              Alizadeh, M., Javanmard, A., and B. Prabhakar, "Analysis
              of DCTCP: Stability, Convergence, and Fairness",
              SIGMETRICS '11: Proceedings of the ACM SIGMETRICS Joint
              International Conference on Measurement and Modeling of
              Computer Systems, pp. 73-84, DOI 10.1145/1993744.1993753,
              June 2011, <https://dl.acm.org/citation.cfm?id=1993753>.

              Kwon, M. and S. Fahmy, "A Comparison of Load-based and
              Queue-based Active Queue Management Algorithms", Proc.
              Int'l Soc. for Optical Engineering (SPIE), Vol. 4866, pp.
              35-46, DOI 10.1117/12.473021, 2002,

   [ARED01]   Floyd, S., Gummadi, R., and S. Shenker, "Adaptive RED: An
              Algorithm for Increasing the Robustness of RED's Active
              Queue Management", ACIRI Technical Report 301, August
              2001, <https://www.icsi.berkeley.edu/icsi/node/2032>.

   [BBR-CC]   Cardwell, N., Cheng, Y., Hassas Yeganeh, S., Swett, I.,
              and V. Jacobson, "BBR Congestion Control", Work in
              Progress, Internet-Draft, draft-cardwell-iccrg-bbr-
              congestion-control-02, 7 March 2022,

   [BBRv2]    "TCP BBR v2 Alpha/Preview Release", commit 17700ca, June
              2022, <https://github.com/google/bbr>.

   [Boru20]   Boru Oljira, D., Grinnemo, K-J., Brunstrom, A., and J.
              Taheri, "Validating the Sharing Behavior and Latency
              Characteristics of the L4S Architecture", ACM SIGCOMM
              Computer Communication Review, Vol. 50, Issue 2, pp.
              37-44, DOI 10.1145/3402413.3402419, May 2020,

              Mishra, A., Sun, X., Jain, A., Pande, S., Joshi, R., and
              B. Leong, "The Great Internet TCP Congestion Control
              Census", Proceedings of the ACM on Measurement and
              Analysis of Computing Systems, Vol. 3, Issue 3, Article
              No. 45, pp. 1-24, DOI 10.1145/3366693, December 2019,

   [CoDel]    Nichols, K. and V. Jacobson, "Controlling Queue Delay",
              ACM Queue, Vol. 10, Issue 5, May 2012,

              Briscoe, B. and K. De Schepper, "Insights from Curvy RED
              (Random Early Detection)", BT Technical Report, TR-
              TUB8-2015-003, DOI 10.48550/arXiv.1904.07339, August 2015,

              Briscoe, B., Ed. and G. White, "The DOCSIS® Queue
              Protection to Preserve Low Latency", Work in Progress,
              Internet-Draft, draft-briscoe-docsis-q-protection-06, 13
              May 2022, <https://datatracker.ietf.org/doc/html/draft-

              CableLabs, "DOCSIS 3.1 MAC and Upper Layer Protocols
              Interface Specification", CM-SP-MULPIv3.1, Data-Over-Cable
              Service Interface Specifications DOCSIS 3.1 Version I17 or
              later, January 2019, <https://specification-

              Albisser, O., De Schepper, K., Briscoe, B., Tilmans, O.,
              and H. Steen, "DUALPI2 - Low Latency, Low Loss and
              Scalable (L4S) AQM", Proceedings of Linux Netdev 0x13 ,
              March 2019, <https://www.netdevconf.org/0x13/

              Steen, H., "Destruction Testing: Ultra-Low Delay using
              Dual Queue Coupled Active Queue Management", Master's
              Thesis, Department of Informatics, University of Oslo, May

              Dukkipati, N. and N. McKeown, "Why Flow-Completion Time is
              the Right Metric for Congestion Control", ACM SIGCOMM
              Computer Communication Review, Vol. 36, Issue 1, pp.
              59-62, DOI 10.1145/1111322.1111336, January 2006,

   [Heist21]  "L4S Tests", commit e21cd91, August 2021,

              Briscoe, B., "Interactions between Low Latency, Low Loss,
              Scalable Throughput (L4S) and Differentiated Services",
              Work in Progress, Internet-Draft, draft-briscoe-tsvwg-l4s-
              diffserv-02, 4 November 2018,

              Bondarenko, O., De Schepper, K., Tsang, I., Briscoe, B.,
              Petlund, A., and C. Griwodz, "Ultra-Low Delay for All:
              Live Experience, Live Analysis", Proceedings of the 7th
              International Conference on Multimedia Systems, Article
              No. 33, pp. 1-4, DOI 10.1145/2910017.2910633, May 2016,

              De Schepper, K., Albisser, O., Tilmans, O., and B.
              Briscoe, "Dual Queue Coupled AQM: Deployable Very Low
              Queuing Delay for All", Preprint submitted to IEEE/ACM
              Transactions on Networking, DOI 10.48550/arXiv.2209.01078,
              September 2022, <https://arxiv.org/abs/2209.01078>.

   [L4S_5G]   Willars, P., Wittenmark, E., Ronkainen, H., Östberg, C.,
              Johansson, I., Strand, J., Lédl, P., and D. Schnieders,
              "Enabling time-critical applications over 5G with rate
              adaptation", Ericsson - Deutsche Telekom White Paper,
              BNEW-21:025455, May 2021, <https://www.ericsson.com/en/

              Labovitz, C., Iekel-Johnson, S., McPherson, D., Oberheide,
              J., and F. Jahanian, "Internet Inter-Domain Traffic", ACM
              SIGCOMM Computer Communication Review, Vol. 40, Issue 4,
              pp. 75-86, DOI 10.1145/1851275.1851194, August 2010,

   [LLD]      White, G., Sundaresan, K., and B. Briscoe, "Low Latency
              DOCSIS: Technology Overview", CableLabs White Paper,
              February 2019, <https://cablela.bs/low-latency-docsis-

   [MEDF]     Menth, M., Schmid, M., Heiss, H., and T. Reim, "MEDF - A
              Simple Scheduling Algorithm for Two Real-Time Transport
              Service Classes with Application in the UTRAN", Proc. IEEE
              Conference on Computer Communications (INFOCOM'03), Vol.
              2, pp. 1116-1122, DOI 10.1109/INFCOM.2003.1208948, March
              2003, <https://doi.org/10.1109/INFCOM.2003.1208948>.

   [PI2]      De Schepper, K., Bondarenko, O., Briscoe, B., and I.
              Tsang, "PI2: A Linearized AQM for both Classic and
              Scalable TCP", ACM CoNEXT'16, DOI 10.1145/2999572.2999578,
              December 2016,

   [PI2param] Briscoe, B., "PI2 Parameters", Technical Report, TR-BB-
              2021-001, arXiv:2107.01003 [cs.NI],
              DOI 10.48550/arXiv.2107.01003, July 2021,

              De Schepper, K., Tilmans, O., and B. Briscoe, "Prague
              Congestion Control", Work in Progress, Internet-Draft,
              draft-briscoe-iccrg-prague-congestion-control-01, 11 July
              2022, <https://datatracker.ietf.org/doc/html/draft-

              Briscoe, B., De Schepper, K., Albisser, O., Misund, J.,
              Tilmans, O., Kuehlewind, M., and A. Ahmed, "Implementing
              the 'TCP Prague' Requirements for L4S", Proceedings of
              Linux Netdev 0x13, March 2019,

   [RED]      Floyd, S. and V. Jacobson, "Random Early Detection
              Gateways for Congestion Avoidance", IEEE/ACM Transactions
              on Networking, Volume 1, Issue 4, pp. 397-413,
              DOI 10.1109/90.251892, August 1993,

              Mathis, M., "Relentless Congestion Control", Work in
              Progress, Internet-Draft, draft-mathis-iccrg-relentless-
              tcp-00, 4 March 2009,

   [RFC0970]  Nagle, J., "On Packet Switches With Infinite Storage",
              RFC 970, DOI 10.17487/RFC0970, December 1985,

   [RFC2914]  Floyd, S., "Congestion Control Principles", BCP 41,
              RFC 2914, DOI 10.17487/RFC2914, September 2000,

   [RFC3246]  Davie, B., Charny, A., Bennet, J.C.R., Benson, K., Le
              Boudec, J.Y., Courtney, W., Davari, S., Firoiu, V., and D.
              Stiliadis, "An Expedited Forwarding PHB (Per-Hop
              Behavior)", RFC 3246, DOI 10.17487/RFC3246, March 2002,

   [RFC3649]  Floyd, S., "HighSpeed TCP for Large Congestion Windows",
              RFC 3649, DOI 10.17487/RFC3649, December 2003,

   [RFC5033]  Floyd, S. and M. Allman, "Specifying New Congestion
              Control Algorithms", BCP 133, RFC 5033,
              DOI 10.17487/RFC5033, August 2007,

   [RFC5348]  Floyd, S., Handley, M., Padhye, J., and J. Widmer, "TCP
              Friendly Rate Control (TFRC): Protocol Specification",
              RFC 5348, DOI 10.17487/RFC5348, September 2008,

   [RFC5681]  Allman, M., Paxson, V., and E. Blanton, "TCP Congestion
              Control", RFC 5681, DOI 10.17487/RFC5681, September 2009,

   [RFC5706]  Harrington, D., "Guidelines for Considering Operations and
              Management of New Protocols and Protocol Extensions",
              RFC 5706, DOI 10.17487/RFC5706, November 2009,

   [RFC7567]  Baker, F., Ed. and G. Fairhurst, Ed., "IETF
              Recommendations Regarding Active Queue Management",
              BCP 197, RFC 7567, DOI 10.17487/RFC7567, July 2015,

   [RFC8033]  Pan, R., Natarajan, P., Baker, F., and G. White,
              "Proportional Integral Controller Enhanced (PIE): A
              Lightweight Control Scheme to Address the Bufferbloat
              Problem", RFC 8033, DOI 10.17487/RFC8033, February 2017,

   [RFC8034]  White, G. and R. Pan, "Active Queue Management (AQM) Based
              on Proportional Integral Controller Enhanced (PIE) for
              Data-Over-Cable Service Interface Specifications (DOCSIS)
              Cable Modems", RFC 8034, DOI 10.17487/RFC8034, February
              2017, <https://www.rfc-editor.org/info/rfc8034>.

   [RFC8174]  Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC
              2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,
              May 2017, <https://www.rfc-editor.org/info/rfc8174>.

   [RFC8257]  Bensley, S., Thaler, D., Balasubramanian, P., Eggert, L.,
              and G. Judd, "Data Center TCP (DCTCP): TCP Congestion
              Control for Data Centers", RFC 8257, DOI 10.17487/RFC8257,
              October 2017, <https://www.rfc-editor.org/info/rfc8257>.

   [RFC8290]  Hoeiland-Joergensen, T., McKenney, P., Taht, D., Gettys,
              J., and E. Dumazet, "The Flow Queue CoDel Packet Scheduler
              and Active Queue Management Algorithm", RFC 8290,
              DOI 10.17487/RFC8290, January 2018,

   [RFC8298]  Johansson, I. and Z. Sarker, "Self-Clocked Rate Adaptation
              for Multimedia", RFC 8298, DOI 10.17487/RFC8298, December
              2017, <https://www.rfc-editor.org/info/rfc8298>.

   [RFC8312]  Rhee, I., Xu, L., Ha, S., Zimmermann, A., Eggert, L., and
              R. Scheffenegger, "CUBIC for Fast Long-Distance Networks",
              RFC 8312, DOI 10.17487/RFC8312, February 2018,

   [RFC8404]  Moriarty, K., Ed. and A. Morton, Ed., "Effects of
              Pervasive Encryption on Operators", RFC 8404,
              DOI 10.17487/RFC8404, July 2018,

   [RFC9000]  Iyengar, J., Ed. and M. Thomson, Ed., "QUIC: A UDP-Based
              Multiplexed and Secure Transport", RFC 9000,
              DOI 10.17487/RFC9000, May 2021,

   [RFC9330]  Briscoe, B., Ed., De Schepper, K., Bagnulo, M., and G.
              White, "Low Latency, Low Loss, and Scalable Throughput
              (L4S) Internet Service: Architecture", RFC 9330,
              DOI 10.17487/RFC9330, January 2023,

              "SCReAM", commit fda6c53, June 2022,

   [SigQ-Dyn] Briscoe, B., "Rapid Signalling of Queue Dynamics",
              Technical Report, TR-BB-2017-001,
              DOI 10.48550/arXiv.1904.07044, September 2017,

Appendix A.  Example DualQ Coupled PI2 Algorithm

   As a first concrete example, the pseudocode below gives the DualPI2
   algorithm.  DualPI2 follows the structure of the DualQ Coupled AQM
   framework in Figure 1.  A simple ramp function (configured in units
   of queuing time) with unsmoothed ECN marking is used for the Native
   L4S AQM.  The ramp can also be configured as a step function.  The
   PI2 algorithm [PI2] is used for the Classic AQM.  PI2 is an improved
   variant of the PIE AQM [RFC8033].

   The pseudocode will be introduced in two passes.  The first pass
   explains the core concepts, deferring handling of edge-cases like
   overload to the second pass.  To aid comparison, line numbers are
   kept in step between the two passes by using letter suffixes where
   the longer code needs extra lines.

   All variables are assumed to be floating point in their basic units
   (size in bytes, time in seconds, rates in bytes/second, alpha and
   beta in Hz, and probabilities from 0 to 1).  Constants expressed in k
   (kilo), M (mega), G (giga), u (micro), m (milli), %, and so forth,
   are assumed to be converted to their appropriate multiple or fraction
   to represent the basic units.  A real implementation that wants to
   use integer values needs to handle appropriate scaling factors and
   allow appropriate resolution of its integer types (including
   temporary internal values during calculations).

   A full open source implementation for Linux is available at
   <https://github.com/L4STeam/sch_dualpi2_upstream> and explained in
   [DualPI2Linux].  The specification of the DualQ Coupled AQM for
   DOCSIS cable modems and cable modem termination systems (CMTSs) is
   available in [DOCSIS3.1] and explained in [LLD].

A.1.  Pass #1: Core Concepts

   The pseudocode manipulates three main structures of variables: the
   packet (pkt), the L4S queue (lq), and the Classic queue (cq).  The
   pseudocode consists of the following six functions:

   *  The initialization function dualpi2_params_init(...) (Figure 2)
      that sets parameter defaults (the API for setting non-default
      values is omitted for brevity).

   *  The enqueue function dualpi2_enqueue(lq, cq, pkt) (Figure 3).

   *  The dequeue function dualpi2_dequeue(lq, cq, pkt) (Figure 4).

   *  The recurrence function recur(q, likelihood) for de-randomized ECN
      marking (shown at the end of Figure 4).

   *  The L4S AQM function laqm(qdelay) (Figure 5) used to calculate the
      ECN-marking probability for the L4S queue.

   *  The Base AQM function that implements the PI algorithm
      dualpi2_update(lq, cq) (Figure 6) used to regularly update the
      base probability (p'), which is squared for the Classic AQM as
      well as being coupled across to the L4S queue.

   It also uses the following functions that are not shown in full here:

   *  scheduler(), which selects between the head packets of the two
      queues.  The choice of scheduler technology is discussed later.

   *  cq.byt() or lq.byt() returns the current length (a.k.a. backlog)
      of the relevant queue in bytes.

   *  cq.len() or lq.len() returns the current length of the relevant
      queue in packets.

   *  cq.time() or lq.time() returns the current queuing delay of the
      relevant queue in units of time (see Note a below).

   *  mark(pkt) and drop(pkt) for ECN marking and dropping a packet.

   In experiments so far (building on experiments with PIE) on broadband
   access links ranging from 4 Mb/s to 200 Mb/s with base RTTs from 5 ms
   to 100 ms, DualPI2 achieves good results with the default parameters
   in Figure 2.  The parameters are categorised by whether they relate
   to the PI2 AQM, the L4S AQM, or the framework coupling them together.
   Constants and variables derived from these parameters are also
   included at the end of each category.  Each parameter is explained as
   it is encountered in the walk-through of the pseudocode below, and
   the rationale for the chosen defaults are given so that sensible
   values can be used in scenarios other than the regular public

   1:  dualpi2_params_init(...) {         % Set input parameter defaults
   2:    % DualQ Coupled framework parameters
   5:    limit = MAX_LINK_RATE * 250 ms               % Dual buffer size
   3:    k = 2                                         % Coupling factor
   4:    % NOT SHOWN % scheduler-dependent weight or equival't parameter
   7:    % PI2 Classic AQM parameters
   8:    target = 15 ms                             % Queue delay target
   9:    RTT_max = 100 ms                      % Worst case RTT expected
   10:   % PI2 constants derived from above PI2 parameters
   11:   p_Cmax = min(1/k^2, 1)             % Max Classic drop/mark prob
   12:   Tupdate = min(target, RTT_max/3)        % PI sampling interval
   13:   alpha = 0.1 * Tupdate / RTT_max^2      % PI integral gain in Hz
   14:   beta = 0.3 / RTT_max               % PI proportional gain in Hz
   16:   % L4S ramp AQM parameters
   17:   minTh = 800 us        % L4S min marking threshold in time units
   18:   range = 400 us                % Range of L4S ramp in time units
   19:   Th_len = 1 pkt           % Min L4S marking threshold in packets
   20:   % L4S constants
   21:   p_Lmax = 1                               % Max L4S marking prob
   22: }

       Figure 2: Example Header Pseudocode for DualQ Coupled PI2 AQM

   The overall goal of the code is to apply the marking and dropping
   probabilities for L4S and Classic traffic (p_L and p_C).  These are
   derived from the underlying base probabilities p'_L and p' driven,
   respectively, by the traffic in the L and C queues.  The marking
   probability for the L queue (p_L) depends on both the base
   probability in its own queue (p'_L) and a probability called p_CL,
   which is coupled across from p' in the C queue (see Section 2.4 for
   the derivation of the specific equations and dependencies).

   The probabilities p_CL and p_C are derived in lines 4 and 5 of the
   dualpi2_update() function (Figure 6) then used in the
   dualpi2_dequeue() function where p_L is also derived from p_CL at
   line 6 (Figure 4).  The code walk-through below builds up to
   explaining that part of the code eventually, but it starts from
   packet arrival.

   1:  dualpi2_enqueue(lq, cq, pkt) { % Test limit and classify lq or cq
   2:    if ( lq.byt() + cq.byt() + MTU > limit)
   3:      drop(pkt)                     % drop packet if buffer is full
   4:    timestamp(pkt)     % only needed if using the sojourn technique
   5:    % Packet classifier
   6:    if ( ecn(pkt) modulo 2 == 1 )         % ECN bits = ECT(1) or CE
   7:      lq.enqueue(pkt)
   8:    else                             % ECN bits = not-ECT or ECT(0)
   9:      cq.enqueue(pkt)
   10: }

       Figure 3: Example Enqueue Pseudocode for DualQ Coupled PI2 AQM

   1:  dualpi2_dequeue(lq, cq, pkt) {     % Couples L4S & Classic queues
   2:    while ( lq.byt() + cq.byt() > 0 ) {
   3:      if ( scheduler() == lq ) {
   4:        lq.dequeue(pkt)                      % Scheduler chooses lq
   5:        p'_L = laqm(lq.time())                        % Native LAQM
   6:        p_L = max(p'_L, p_CL)                  % Combining function
   7:        if ( recur(lq, p_L) )                      % Linear marking
   8:          mark(pkt)
   9:      } else {
   10:       cq.dequeue(pkt)                      % Scheduler chooses cq
   11:       if ( recur(cq, p_C) ) {            % probability p_C = p'^2
   12:         if ( ecn(pkt) == 0 ) {           % if ECN field = not-ECT
   13:           drop(pkt)                                % squared drop
   14:           continue        % continue to the top of the while loop
   15:         }
   16:         mark(pkt)                                  % squared mark
   17:       }
   18:     }
   19:     return(pkt)                      % return the packet and stop
   20:   }
   21:   return(NULL)                             % no packet to dequeue
   22: }

   23: recur(q, likelihood) {   % Returns TRUE with a certain likelihood
   24:   q.count += likelihood
   25:   if (q.count > 1) {
   26:     q.count -= 1
   27:     return TRUE
   28:   }
   29:   return FALSE
   30: }

       Figure 4: Example Dequeue Pseudocode for DualQ Coupled PI2 AQM

   When packets arrive, a common queue limit is checked first as shown
   in line 2 of the enqueuing pseudocode in Figure 3.  This assumes a
   shared buffer for the two queues (Note b discusses the merits of
   separate buffers).  In order to avoid any bias against larger
   packets, 1 MTU of space is always allowed, and the limit is
   deliberately tested before enqueue.

   If limit is not exceeded, the packet is timestamped in line 4 (only
   if the sojourn time technique is being used to measure queue delay;
   see Note a below for alternatives).

   At lines 5-9, the packet is classified and enqueued to the Classic or
   L4S queue dependent on the least significant bit (LSB) of the ECN
   field in the IP header (line 6).  Packets with a codepoint having an
   LSB of 0 (Not-ECT and ECT(0)) will be enqueued in the Classic queue.
   Otherwise, ECT(1) and CE packets will be enqueued in the L4S queue.
   Optional additional packet classification flexibility is omitted for
   brevity (see the L4S ECN protocol [RFC9331]).

   The dequeue pseudocode (Figure 4) is repeatedly called whenever the
   lower layer is ready to forward a packet.  It schedules one packet
   for dequeuing (or zero if the queue is empty) then returns control to
   the caller so that it does not block while that packet is being
   forwarded.  While making this dequeue decision, it also makes the
   necessary AQM decisions on dropping or marking.  The alternative of
   applying the AQMs at enqueue would shift some processing from the
   critical time when each packet is dequeued.  However, it would also
   add a whole queue of delay to the control signals, making the control
   loop sloppier (for a typical RTT, it would double the Classic queue's
   feedback delay).

   All the dequeue code is contained within a large while loop so that
   if it decides to drop a packet, it will continue until it selects a
   packet to schedule.  Line 3 of the dequeue pseudocode is where the
   scheduler chooses between the L4S queue (lq) and the Classic queue
   (cq).  Detailed implementation of the scheduler is not shown (see
   discussion later).

   *  If an L4S packet is scheduled, in lines 7 and 8 the packet is ECN-
      marked with likelihood p_L.  The recur() function at the end of
      Figure 4 is used, which is preferred over random marking because
      it avoids delay due to randomization when interpreting congestion
      signals, but it still desynchronizes the sawteeth of the flows.
      Line 6 calculates p_L as the maximum of the coupled L4S
      probability p_CL and the probability from the Native L4S AQM p'_L.
      This implements the max() function shown in Figure 1 to couple the
      outputs of the two AQMs together.  Of the two probabilities input
      to p_L in line 6:

      -  p'_L is calculated per packet in line 5 by the laqm() function
         (see Figure 5), whereas

      -  p_CL is maintained by the dualpi2_update() function, which runs
         every Tupdate (Tupdate is set in line 12 of Figure 2).

   *  If a Classic packet is scheduled, lines 10 to 17 drop or mark the
      packet with probability p_C.

   The Native L4S AQM algorithm (Figure 5) is a ramp function, similar
   to the RED algorithm, but simplified as follows:

   *  The extent of the ramp is defined in units of queuing delay, not
      bytes, so that configuration remains invariant as the queue
      departure rate varies.

   *  It uses instantaneous queuing delay, which avoids the complexity
      of smoothing, but also avoids embedding a worst-case RTT of
      smoothing delay in the network (see Section 2.1).

   *  The ramp rises linearly directly from 0 to 1, not to an
      intermediate value of p'_L as RED would, because there is no need
      to keep ECN-marking probability low.

   *  Marking does not have to be randomized.  Determinism is used
      instead of randomness to reduce the delay necessary to smooth out
      the noise of randomness from the signal.

   The ramp function requires two configuration parameters, the minimum
   threshold (minTh) and the width of the ramp (range), both in units of
   queuing time, as shown in lines 17 and 18 of the initialization
   function in Figure 2.  The ramp function can be configured as a step
   (see Note c).

   Although the DCTCP paper [Alizadeh-stability] recommends an ECN-
   marking threshold of 0.17*RTT_typ, it also shows that the threshold
   can be much shallower with hardly any worse underutilization of the
   link (because the amplitude of DCTCP's sawteeth is so small).  Based
   on extensive experiments, for the public Internet the default minimum
   ECN-marking threshold (target) in Figure 2 is considered a good
   compromise, even though it is a significantly smaller fraction of

   1:  laqm(qdelay) {               % Returns Native L4S AQM probability
   2:    if (qdelay >= maxTh)
   3:      return 1
   4:    else if (qdelay > minTh)
   5:      return (qdelay - minTh)/range  % Divide could use a bit-shift
   6:    else
   7:      return 0
   8:  }

            Figure 5: Example Pseudocode for the Native L4S AQM

   1:  dualpi2_update(lq, cq) {                % Update p' every Tupdate
   2:    curq = cq.time()  % use queuing time of first-in Classic packet
   3:    p' = p' + alpha * (curq - target) + beta * (curq - prevq)
   4:    p_CL = k * p'  % Coupled L4S prob = base prob * coupling factor
   5:    p_C = p'^2                       % Classic prob = (base prob)^2
   6:    prevq = curq
   7:  }

      Figure 6: Example PI-update Pseudocode for DualQ Coupled PI2 AQM

      (Note: Clamping p' within the range [0,1] omitted for clarity --
      see below.)

   The coupled marking probability p_CL depends on the base probability
   (p'), which is kept up to date by executing the core PI algorithm in
   Figure 6 every Tupdate.

   Note that p' solely depends on the queuing time in the Classic queue.
   In line 2, the current queuing delay (curq) is evaluated from how
   long the head packet was in the Classic queue (cq).  The function
   cq.time() (not shown) subtracts the time stamped at enqueue from the
   current time (see Note a below) and implicitly takes the current
   queuing delay as 0 if the queue is empty.

   The algorithm centres on line 3, which is a classical PI controller
   that alters p' dependent on: a) the error between the current queuing
   delay (curq) and the target queuing delay (target) and b) the change
   in queuing delay since the last sample.  The name 'PI' represents the
   fact that the second factor (how fast the queue is growing) is
   Proportional to load while the first is the Integral of the load (so
   it removes any standing queue in excess of the target).

   The target parameter can be set based on local knowledge, but the aim
   is for the default to be a good compromise for anywhere in the
   intended deployment environment -- the public Internet.  According to
   [PI2param], the target queuing delay on line 8 of Figure 2 is related
   to the typical base RTT worldwide, RTT_typ, by two factors: target =
   RTT_typ * g * f.  Below, we summarize the rationale behind these
   factors and introduce a further adjustment.  The two factors ensure
   that, in a large proportion of cases (say 90%), the sawtooth
   variations in RTT of a single flow will fit within the buffer without
   underutilizing the link.  Frankly, these factors are educated
   guesses, but with the emphasis closer to 'educated' than to 'guess'
   (see [PI2param] for the full background):

   *  RTT_typ is taken as 25 ms.  This is based on an average CDN
      latency measured in each country weighted by the number of
      Internet users in that country to produce an overall weighted
      average for the Internet [PI2param].  Countries were ranked by
      number of Internet users, and once 90% of Internet users were
      covered, smaller countries were excluded to avoid small sample
      sizes that would be less representative.  Also, importantly, the
      data for the average CDN latency in China (with the largest number
      of Internet users) has been removed, because the CDN latency was a
      significant outlier and, on reflection, the experimental technique
      seemed inappropriate to the CDN market in China.

   *  g is taken as 0.38.  The factor g is a geometry factor that
      characterizes the shape of the sawteeth of prevalent Classic
      congestion controllers.  The geometry factor is the fraction of
      the amplitude of the sawtooth variability in queue delay that lies
      below the AQM's target.  For instance, at low bitrates, the
      geometry factor of standard Reno is 0.5, but at higher rates, it
      tends towards just under 1.  According to the census of congestion
      controllers conducted by Mishra et al. in Jul-Oct 2019
      [CCcensus19], most Classic TCP traffic uses CUBIC.  And, according
      to the analysis in [PI2param], if running over a PI2 AQM, a large
      proportion of this CUBIC traffic would be in its Reno-friendly
      mode, which has a geometry factor of ~0.39 (for all known
      implementations).  The rest of the CUBIC traffic would be in true
      CUBIC mode, which has a geometry factor of ~0.36.  Without
      modelling the sawtooth profiles from all the other less prevalent
      congestion controllers, we estimate a 7:3 weighted average of
      these two, resulting in an average geometry factor of 0.38.

   *  f is taken as 2.  The factor f is a safety factor that increases
      the target queue to allow for the distribution of RTT_typ around
      its mean.  Otherwise, the target queue would only avoid
      underutilization for those users below the mean.  It also provides
      a safety margin for the proportion of paths in use that span
      beyond the distance between a user and their local CDN.
      Currently, no data is available on the variance of queue delay
      around the mean in each region, so there is plenty of room for
      this guess to become more educated.

   *  [PI2param] recommends target = RTT_typ * g * f = 25 ms * 0.38 * 2
      = 19 ms.  However, a further adjustment is warranted, because
      target is moving year-on-year.  The paper is based on data
      collected in 2019, and it mentions evidence from the Speedtest
      Global Index that suggests RTT_typ reduced by 17% (fixed) or 12%
      (mobile) between 2020 and 2021.  Therefore, we recommend a default
      of target = 15 ms at the time of writing (2021).

   Operators can always use the data and discussion in [PI2param] to
   configure a more appropriate target for their environment.  For
   instance, an operator might wish to question the assumptions called
   out in that paper, such as the goal of no underutilization for a
   large majority of single flow transfers (given many large transfers
   use multiple flows to avoid the scaling limitations of Classic

   The two 'gain factors' in line 3 of Figure 6, alpha and beta,
   respectively weight how strongly each of the two elements (Integral
   and Proportional) alters p'.  They are in units of 'per second of
   delay' or Hz, because they transform differences in queuing delay
   into changes in probability (assuming probability has a value from 0
   to 1).

   Alpha and beta determine how much p' ought to change after each
   update interval (Tupdate).  For a smaller Tupdate, p' should change
   by the same amount per second but in finer more frequent steps.  So
   alpha depends on Tupdate (see line 13 of the initialization function
   in Figure 2).  It is best to update p' as frequently as possible, but
   Tupdate will probably be constrained by hardware performance.  As
   shown in line 12, the update interval should be frequent enough to
   update at least once in the time taken for the target queue to drain
   ('target') as long as it updates at least three times per maximum
   RTT.  Tupdate defaults to 16 ms in the reference Linux implementation
   because it has to be rounded to a multiple of 4 ms.  For link rates
   from 4 to 200 Mb/s and a maximum RTT of 100 ms, it has been verified
   through extensive testing that Tupdate = 16 ms (as also recommended
   in the PIE spec [RFC8033]) is sufficient.

   The choice of alpha and beta also determines the AQM's stable
   operating range.  The AQM ought to change p' as fast as possible in
   response to changes in load without overcompensating and therefore
   causing oscillations in the queue.  Therefore, the values of alpha
   and beta also depend on the RTT of the expected worst-case flow

   The maximum RTT of a PI controller (RTT_max in line 9 of Figure 2) is
   not an absolute maximum, but more instability (more queue
   variability) sets in for long-running flows with an RTT above this
   value.  The propagation delay halfway round the planet and back in
   glass fibre is 200 ms.  However, hardly any traffic traverses such
   extreme paths and, since the significant consolidation of Internet
   traffic between 2007 and 2009 [Labovitz10], a high and growing
   proportion of all Internet traffic (roughly two-thirds at the time of
   writing) has been served from CDNs or 'cloud' services distributed
   close to end users.  The Internet might change again, but for now,
   designing for a maximum RTT of 100 ms is a good compromise between
   faster queue control at low RTT and some instability on the occasions
   when a longer path is necessary.

   Recommended derivations of the gain constants alpha and beta can be
   approximated for Reno over a PI2 AQM as: alpha = 0.1 * Tupdate /
   RTT_max^2; beta = 0.3 / RTT_max, as shown in lines 13 and 14 of
   Figure 2.  These are derived from the stability analysis in [PI2].
   For the default values of Tupdate = 16 ms and RTT_max = 100 ms, they
   result in alpha = 0.16; beta = 3.2 (discrepancies are due to
   rounding).  These defaults have been verified with a wide range of
   link rates, target delays, and traffic models with mixed and similar
   RTTs, short and long flows, etc.

   In corner cases, p' can overflow the range [0,1] so the resulting
   value of p' has to be bounded (omitted from the pseudocode).  Then,
   as already explained, the coupled and Classic probabilities are
   derived from the new p' in lines 4 and 5 of Figure 6 as p_CL = k*p'
   and p_C = p'^2.

   Because the coupled L4S marking probability (p_CL) is factored up by
   k, the dynamic gain parameters alpha and beta are also inherently
   factored up by k for the L4S queue.  So, the effective gain factor
   for the L4S queue is k*alpha (with defaults alpha = 0.16 Hz and k =
   2, effective L4S alpha = 0.32 Hz).

   Unlike in PIE [RFC8033], alpha and beta do not need to be tuned every
   Tupdate dependent on p'.  Instead, in PI2, alpha and beta are
   independent of p' because the squaring applied to Classic traffic
   tunes them inherently.  This is explained in [PI2], which also
   explains why this more principled approach removes the need for most
   of the heuristics that had to be added to PIE.

   Nonetheless, an implementer might wish to add selected details to
   either AQM.  For instance, the Linux reference DualPI2 implementation
   includes the following (not shown in the pseudocode above):

   *  Classic and coupled marking or dropping (i.e., based on p_C and
      p_CL from the PI controller) is not applied to a packet if the
      aggregate queue length in bytes is < 2 MTU (prior to enqueuing the
      packet or dequeuing it, depending on whether the AQM is configured
      to be applied at enqueue or dequeue); and

   *  in the WRR scheduler, the 'credit' indicating which queue should
      transmit is only changed if there are packets in both queues
      (i.e., if there is actual resource contention).  This means that a
      properly paced L flow might never be delayed by the WRR.  The WRR
      credit is reset in favour of the L queue when the link is idle.

   An implementer might also wish to add other heuristics, e.g., burst
   protection [RFC8033] or enhanced burst protection [RFC8034].


   a.  The drain rate of the queue can vary if it is scheduled relative
       to other queues or if it accommodates fluctuations in a wireless
       medium.  To auto-adjust to changes in drain rate, the queue needs
       to be measured in time, not bytes or packets [AQMmetrics]
       [CoDel].  Queuing delay could be measured directly as the sojourn
       time (a.k.a.  service time) of the queue by storing a per-packet
       timestamp as each packet is enqueued and subtracting it from the
       system time when the packet is dequeued.  If timestamping is not
       easy to introduce with certain hardware, queuing delay could be
       predicted indirectly by dividing the size of the queue by the
       predicted departure rate, which might be known precisely for some
       link technologies (see, for example, DOCSIS PIE [RFC8034]).

       However, sojourn time is slow to detect bursts.  For instance, if
       a burst arrives at an empty queue, the sojourn time only fully
       measures the burst's delay when its last packet is dequeued, even
       though the queue has known the size of the burst since its last
       packet was enqueued -- so it could have signalled congestion
       earlier.  To remedy this, each head packet can be marked when it
       is dequeued based on the expected delay of the tail packet behind
       it, as explained below, rather than based on the head packet's
       own delay due to the packets in front of it.  "Underutilization
       with Bursty Traffic" in [Heist21] identifies a specific scenario
       where bursty traffic significantly hits utilization of the L
       queue.  If this effect proves to be more widely applicable, using
       the delay behind the head could improve performance.

       The delay behind the head can be implemented by dividing the
       backlog at dequeue by the link rate or equivalently multiplying
       the backlog by the delay per unit of backlog.  The implementation
       details will depend on whether the link rate is known; if it is
       not, a moving average of the delay per unit backlog can be
       maintained.  This delay consists of serialization as well as
       media acquisition for shared media.  So the details will depend
       strongly on the specific link technology.  This approach should
       be less sensitive to timing errors and cost less in operations
       and memory than the otherwise equivalent 'scaled sojourn time'
       metric, which is the sojourn time of a packet scaled by the ratio
       of the queue sizes when the packet departed and arrived

   b.  Line 2 of the dualpi2_enqueue() function (Figure 3) assumes an
       implementation where lq and cq share common buffer memory.  An
       alternative implementation could use separate buffers for each
       queue, in which case the arriving packet would have to be
       classified first to determine which buffer to check for available
       space.  The choice is a trade-off; a shared buffer can use less
       memory whereas separate buffers isolate the L4S queue from tail
       drop due to large bursts of Classic traffic (e.g., a Classic Reno
       TCP during slow-start over a long RTT).

   c.  There has been some concern that using the step function of DCTCP
       for the Native L4S AQM requires end systems to smooth the signal
       for an unnecessarily large number of round trips to ensure
       sufficient fidelity.  A ramp is no worse than a step in initial
       experiments with existing DCTCP.  Therefore, it is recommended
       that a ramp is configured in place of a step, which will allow
       congestion control algorithms to investigate faster smoothing

       A ramp is more general than a step, because an operator can
       effectively turn the ramp into a step function, as used by DCTCP,
       by setting the range to zero.  There will not be a divide by zero
       problem at line 5 of Figure 5 because, if minTh is equal to
       maxTh, the condition for this ramp calculation cannot arise.

A.2.  Pass #2: Edge-Case Details

   This section takes a second pass through the pseudocode to add
   details of two edge-cases: low link rate and overload.  Figure 7
   repeats the dequeue function of Figure 4, but with details of both
   edge-cases added.  Similarly, Figure 8 repeats the core PI algorithm
   of Figure 6, but with overload details added.  The initialization,
   enqueue, L4S AQM, and recur functions are unchanged.

   The link rate can be so low that it takes a single packet queue
   longer to serialize than the threshold delay at which ECN marking
   starts to be applied in the L queue.  Therefore, a minimum marking
   threshold parameter in units of packets rather than time is necessary
   (Th_len, default 1 packet in line 19 of Figure 2) to ensure that the
   ramp does not trigger excessive marking on slow links.  Where an
   implementation knows the link rate, it can set up this minimum at the
   time it is configured.  For instance, it would divide 1 MTU by the
   link rate to convert it into a serialization time, then if the lower
   threshold of the Native L AQM ramp was lower than this serialization
   time, it could increase the thresholds to shift the bottom of the
   ramp to 2 MTU.  This is the approach used in DOCSIS [DOCSIS3.1],
   because the configured link rate is dedicated to the DualQ.

   The pseudocode given here applies where the link rate is unknown,
   which is more common for software implementations that might be
   deployed in scenarios where the link is shared with other queues.  In
   lines 5a to 5d in Figure 7, the native L4S marking probability, p'_L,
   is zeroed if the queue is only 1 packet (in the default

      |  Linux implementation note: In Linux, the check that the queue
      |  exceeds Th_len before marking with the Native L4S AQM is
      |  actually at enqueue, not dequeue; otherwise, it would exempt
      |  the last packet of a burst from being marked.  The result of
      |  the check is conveyed from enqueue to the dequeue function via
      |  a boolean in the packet metadata.

   Persistent overload is deemed to have occurred when Classic drop/
   marking probability reaches p_Cmax.  Above this point, the Classic
   drop probability is applied to both the L and C queues, irrespective
   of whether any packet is ECN-capable.  ECT packets that are not
   dropped can still be ECN-marked.

   In line 11 of the initialization function (Figure 2), the maximum
   Classic drop probability p_Cmax = min(1/k^2, 1) or 1/4 for the
   default coupling factor k = 2.  In practice, 25% has been found to be
   a good threshold to preserve fairness between ECN-capable and non-
   ECN-capable traffic.  This protects the queues against both temporary
   overload from responsive flows and more persistent overload from any
   unresponsive traffic that falsely claims to be responsive to ECN.

   When the Classic ECN-marking probability reaches the p_Cmax threshold
   (1/k^2), the marking probability that is coupled to the L4S queue,
   p_CL, will always be 100% for any k (by equation (1) in Section 2.1).
   So, for readability, the constant p_Lmax is defined as 1 in line 21
   of the initialization function (Figure 2).  This is intended to
   ensure that the L4S queue starts to introduce dropping once ECN
   marking saturates at 100% and can rise no further.  The 'Prague L4S
   requirements' [RFC9331] state that when an L4S congestion control
   detects a drop, it falls back to a response that coexists with
   'Classic' Reno congestion control.  So, it is correct that when the
   L4S queue drops packets, it drops them proportional to p'^2, as if
   they are Classic packets.

   The two queues each test for overload in lines 4b and 12b of the
   dequeue function (Figure 7).  Lines 8c to 8g drop L4S packets with
   probability p'^2.  Lines 8h to 8i mark the remaining packets with
   probability p_CL.  Given p_Lmax = 1, all remaining packets will be
   marked because, to have reached the else block at line 8b, p_CL >= 1.

   Line 2a in the core PI algorithm (Figure 8) deals with overload of
   the L4S queue when there is little or no Classic traffic.  This is
   necessary, because the core PI algorithm maintains the appropriate
   drop probability to regulate overload, but it depends on the length
   of the Classic queue.  If there is little or no Classic queue, the
   naive PI-update function (Figure 6) would drop nothing, even if the
   L4S queue were overloaded -- so tail drop would have to take over
   (lines 2 and 3 of Figure 3).

   Instead, line 2a of the full PI-update function (Figure 8) ensures
   that the Base PI AQM in line 3 is driven by whichever of the two
   queue delays is greater, but line 3 still always uses the same
   Classic target (default 15 ms).  If L queue delay is greater just
   because there is little or no Classic traffic, normally it will still
   be well below the Base AQM target.  This is because L4S traffic is
   also governed by the shallow threshold of its own Native AQM (lines
   5a to 6 of the dequeue algorithm in Figure 7).  So the Base AQM will
   be driven to zero and not contribute.  However, if the L queue is
   overloaded by traffic that is unresponsive to its marking, the max()
   in line 2a of Figure 8 enables the L queue to smoothly take over
   driving the Base AQM into overload mode even if there is little or no
   Classic traffic.  Then the Base AQM will keep the L queue to the
   Classic target (default 15 ms) by shedding L packets.

   1:  dualpi2_dequeue(lq, cq, pkt) {     % Couples L4S & Classic queues
   2:    while ( lq.byt() + cq.byt() > 0 ) {
   3:      if ( scheduler() == lq ) {
   4a:       lq.dequeue(pkt)                             % L4S scheduled
   4b:       if ( p_CL < p_Lmax ) {      % Check for overload saturation
   5a:         if (lq.len()>Th_len)                   % >1 packet queued
   5b:           p'_L = laqm(lq.time())                    % Native LAQM
   5c:         else
   5d:           p'_L = 0                 % Suppress marking 1 pkt queue
   6:          p_L = max(p'_L, p_CL)                % Combining function
   7:          if ( recur(lq, p_L)                       %Linear marking
   8a:           mark(pkt)
   8b:       } else {                              % overload saturation
   8c:         if ( recur(lq, p_C) ) {          % probability p_C = p'^2
   8e:           drop(pkt)      % revert to Classic drop due to overload
   8f:           continue        % continue to the top of the while loop
   8g:         }
   8h:         if ( recur(lq, p_CL) )        % probability p_CL = k * p'
   8i:           mark(pkt)         % linear marking of remaining packets
   8j:       }
   9:      } else {
   10:       cq.dequeue(pkt)                         % Classic scheduled
   11:       if ( recur(cq, p_C) ) {            % probability p_C = p'^2
   12a:        if ( (ecn(pkt) == 0)                % ECN field = not-ECT
   12b:             OR (p_C >= p_Cmax) ) {       % Overload disables ECN
   13:           drop(pkt)                     % squared drop, redo loop
   14:           continue        % continue to the top of the while loop
   15:         }
   16:         mark(pkt)                                  % squared mark
   17:       }
   18:     }
   19:     return(pkt)                      % return the packet and stop
   20:   }
   21:   return(NULL)                             % no packet to dequeue
   22: }

       Figure 7: Example Dequeue Pseudocode for DualQ Coupled PI2 AQM
                      (Including Code for Edge-Cases)

   1:  dualpi2_update(lq, cq) {                % Update p' every Tupdate
   2a:   curq = max(cq.time(), lq.time())    % use greatest queuing time
   3:    p' = p' + alpha * (curq - target) + beta * (curq - prevq)
   4:    p_CL = p' * k  % Coupled L4S prob = base prob * coupling factor
   5:    p_C = p'^2                       % Classic prob = (base prob)^2
   6:    prevq = curq
   7:  }

      Figure 8: Example PI-update Pseudocode for DualQ Coupled PI2 AQM
                         (Including Overload Code)

   The choice of scheduler technology is critical to overload protection
   (see Section 4.2.2).

   *  A well-understood weighted scheduler such as WRR is recommended.
      As long as the scheduler weight for Classic is small (e.g., 1/16),
      its exact value is unimportant, because it does not normally
      determine capacity shares.  The weight is only important to
      prevent unresponsive L4S traffic starving Classic traffic in the
      short term (see Section 4.2.2).  This is because capacity sharing
      between the queues is normally determined by the coupled
      congestion signal, which overrides the scheduler, by making L4S
      sources leave roughly equal per-flow capacity available for
      Classic flows.

   *  Alternatively, a time-shifted FIFO (TS-FIFO) could be used.  It
      works by selecting the head packet that has waited the longest,
      biased against the Classic traffic by a time-shift of tshift.  To
      implement TS-FIFO, the scheduler() function in line 3 of the
      dequeue code would simply be implemented as the scheduler()
      function at the bottom of Figure 10 in Appendix B.  For the public
      Internet, a good value for tshift is 50 ms.  For private networks
      with smaller diameter, about 4*target would be reasonable.  TS-
      FIFO is a very simple scheduler, but complexity might need to be
      added to address some deficiencies (which is why it is not
      recommended over WRR):

      -  TS-FIFO does not fully isolate latency in the L4S queue from
         uncontrolled bursts in the Classic queue;

      -  using sojourn time for TS-FIFO is only appropriate if
         timestamping of packets is feasible; and

      -  even if timestamping is supported, the sojourn time of the head
         packet is always stale, so a more instantaneous measure of
         queue delay could be used (see Note a in Appendix A.1).

   *  A strict priority scheduler would be inappropriate as discussed in
      Section 4.2.2.

Appendix B.  Example DualQ Coupled Curvy RED Algorithm

   As another example of a DualQ Coupled AQM algorithm, the pseudocode
   below gives the Curvy-RED-based algorithm.  Although the AQM was
   designed to be efficient in integer arithmetic, to aid understanding
   it is first given using floating point arithmetic (Figure 10).  Then,
   one possible optimization for integer arithmetic is given, also in
   pseudocode (Figure 11).  To aid comparison, the line numbers are kept
   in step between the two by using letter suffixes where the longer
   code needs extra lines.

B.1.  Curvy RED in Pseudocode

   The pseudocode manipulates three main structures of variables: the
   packet (pkt), the L4S queue (lq), and the Classic queue (cq).  It is
   defined and described below in the following three functions:

   *  the initialization function cred_params_init(...) (Figure 2) that
      sets parameter defaults (the API for setting non-default values is
      omitted for brevity);

   *  the dequeue function cred_dequeue(lq, cq, pkt) (Figure 4); and

   *  the scheduling function scheduler(), which selects between the
      head packets of the two queues.

   It also uses the following functions that are either shown elsewhere
   or not shown in full here:

   *  the enqueue function, which is identical to that used for DualPI2,
      dualpi2_enqueue(lq, cq, pkt) in Figure 3;

   *  mark(pkt) and drop(pkt) for ECN marking and dropping a packet;

   *  cq.byt() or lq.byt() returns the current length (a.k.a. backlog)
      of the relevant queue in bytes; and

   *  cq.time() or lq.time() returns the current queuing delay of the
      relevant queue in units of time (see Note a in Appendix A.1).

   Because Curvy RED was evaluated before DualPI2, certain improvements
   introduced for DualPI2 were not evaluated for Curvy RED.  In the
   pseudocode below, the straightforward improvements have been added on
   the assumption they will provide similar benefits, but that has not
   been proven experimentally.  They are: i) a conditional priority
   scheduler instead of strict priority; ii) a time-based threshold for
   the Native L4S AQM; and iii) ECN support for the Classic AQM.  A
   recent evaluation has proved that a minimum ECN-marking threshold
   (minTh) greatly improves performance, so this is also included in the

   Overload protection has not been added to the Curvy RED pseudocode
   below so as not to detract from the main features.  It would be added
   in exactly the same way as in Appendix A.2 for the DualPI2
   pseudocode.  The Native L4S AQM uses a step threshold, but a ramp
   like that described for DualPI2 could be used instead.  The scheduler
   uses the simple TS-FIFO algorithm, but it could be replaced with WRR.

   The Curvy RED algorithm has not been maintained or evaluated to the
   same degree as the DualPI2 algorithm.  In initial experiments on
   broadband access links ranging from 4 Mb/s to 200 Mb/s with base RTTs
   from 5 ms to 100 ms, Curvy RED achieved good results with the default
   parameters in Figure 9.

   The parameters are categorized by whether they relate to the Classic
   AQM, the L4S AQM, or the framework coupling them together.  Constants
   and variables derived from these parameters are also included at the
   end of each category.  These are the raw input parameters for the
   algorithm.  A configuration front-end could accept more meaningful
   parameters (e.g., RTT_max and RTT_typ) and convert them into these
   raw parameters, as has been done for DualPI2 in Appendix A.  Where
   necessary, parameters are explained further in the walk-through of
   the pseudocode below.

   1:  cred_params_init(...) {            % Set input parameter defaults
   2:    % DualQ Coupled framework parameters
   3:    limit = MAX_LINK_RATE * 250 ms               % Dual buffer size
   4:    k' = 1                        % Coupling factor as a power of 2
   5:    tshift = 50 ms                % Time-shift of TS-FIFO scheduler
   6:    % Constants derived from Classic AQM parameters
   7:    k = 2^k'                    % Coupling factor from equation (1)
   7:    % Classic AQM parameters
   8:    g_C = 5            % EWMA smoothing parameter as a power of 1/2
   9:    S_C = -1          % Classic ramp scaling factor as a power of 2
   10:   minTh = 500 ms    % No Classic drop/mark below this queue delay
   11:   % Constants derived from Classic AQM parameters
   12:   gamma = 2^(-g_C)                     % EWMA smoothing parameter
   13:   range_C = 2^S_C                         % Range of Classic ramp
   15:   % L4S AQM parameters
   16:   T = 1 ms             % Queue delay threshold for Native L4S AQM
   17:   % Constants derived from above parameters
   18:   S_L = S_C - k'        % L4S ramp scaling factor as a power of 2
   19:   range_L = 2^S_L                             % Range of L4S ramp
   20: }

    Figure 9: Example Header Pseudocode for DualQ Coupled Curvy RED AQM

   1:  cred_dequeue(lq, cq, pkt) {       % Couples L4S & Classic queues
   2:    while ( lq.byt() + cq.byt() > 0 ) {
   3:      if ( scheduler() == lq ) {
   4:        lq.dequeue(pkt)                            % L4S scheduled
   5a:       p_CL = (Q_C - minTh) / range_L
   5b:       if (  ( lq.time() > T )
   5c:          OR ( p_CL > maxrand(U) ) )
   6:          mark(pkt)
   7:      } else {
   8:        cq.dequeue(pkt)                        % Classic scheduled
   9a:       Q_C = gamma * cq.time() + (1-gamma) * Q_C % Classic Q EWMA
   10a:      sqrt_p_C = (Q_C - minTh) / range_C
   10b:      if ( sqrt_p_C > maxrand(2*U) ) {
   11:         if ( (ecn(pkt) == 0)  {            % ECN field = not-ECT
   12:           drop(pkt)                    % Squared drop, redo loop
   13:           continue       % continue to the top of the while loop
   14:         }
   15:         mark(pkt)
   16:       }
   17:     }
   18:     return(pkt)                % return the packet and stop here
   19:   }
   20:   return(NULL)                            % no packet to dequeue
   21: }

   22: maxrand(u) {                % return the max of u random numbers
   23:   maxr=0
   24:   while (u-- > 0)
   25:     maxr = max(maxr, rand())                   % 0 <= rand() < 1
   26:   return(maxr)
   27: }

   28: scheduler() {
   29:   if ( lq.time() + tshift >= cq.time() )
   30:     return lq;
   31:   else
   32:     return cq;
   33: }

   Figure 10: Example Dequeue Pseudocode for DualQ Coupled Curvy RED AQM

   The dequeue pseudocode (Figure 10) is repeatedly called whenever the
   lower layer is ready to forward a packet.  It schedules one packet
   for dequeuing (or zero if the queue is empty) then returns control to
   the caller so that it does not block while that packet is being
   forwarded.  While making this dequeue decision, it also makes the
   necessary AQM decisions on dropping or marking.  The alternative of
   applying the AQMs at enqueue would shift some processing from the
   critical time when each packet is dequeued.  However, it would also
   add a whole queue of delay to the control signals, making the control
   loop very sloppy.

   The code is written assuming the AQMs are applied on dequeue (Note
   1).  All the dequeue code is contained within a large while loop so
   that if it decides to drop a packet, it will continue until it
   selects a packet to schedule.  If both queues are empty, the routine
   returns NULL at line 20.  Line 3 of the dequeue pseudocode is where
   the conditional priority scheduler chooses between the L4S queue (lq)
   and the Classic queue (cq).  The TS-FIFO scheduler is shown at lines
   28-33, which would be suitable if simplicity is paramount (see Note

   Within each queue, the decision whether to forward, drop, or mark is
   taken as follows (to simplify the explanation, it is assumed that U =

      If the test at line 3 determines there is an L4S packet to
      dequeue, the tests at lines 5b and 5c determine whether to mark
      it.  The first is a simple test of whether the L4S queue delay
      (lq.time()) is greater than a step threshold T (Note 3).  The
      second test is similar to the random ECN marking in RED but with
      the following differences: i) marking depends on queuing time, not
      bytes, in order to scale for any link rate without being
      reconfigured; ii) marking of the L4S queue depends on a logical OR
      of two tests: one against its own queuing time and one against the
      queuing time of the _other_ (Classic) queue; iii) the tests are
      against the instantaneous queuing time of the L4S queue but
      against a smoothed average of the other (Classic) queue; and iv)
      the queue is compared with the maximum of U random numbers (but if
      U = 1, this is the same as the single random number used in RED).

      Specifically, in line 5a, the coupled marking probability p_CL is
      set to the amount by which the averaged Classic queuing delay Q_C
      exceeds the minimum queuing delay threshold (minTh), all divided
      by the L4S scaling parameter range_L. range_L represents the
      queuing delay (in seconds) added to minTh at which marking
      probability would hit 100%. Then, in line 5c (if U = 1), the
      result is compared with a uniformly distributed random number
      between 0 and 1, which ensures that, over range_L, marking
      probability will linearly increase with queuing time.

      If the scheduler at line 3 chooses to dequeue a Classic packet and
      jumps to line 7, the test at line 10b determines whether to drop
      or mark it.  But before that, line 9a updates Q_C, which is an
      exponentially weighted moving average (Note 4) of the queuing time
      of the Classic queue, where cq.time() is the current instantaneous
      queuing time of the packet at the head of the Classic queue (zero
      if empty), and gamma is the exponentially weighted moving average
      (EWMA) constant (default 1/32; see line 12 of the initialization

      Lines 10a and 10b implement the Classic AQM.  In line 10a, the
      averaged queuing time Q_C is divided by the Classic scaling
      parameter range_C, in the same way that queuing time was scaled
      for L4S marking.  This scaled queuing time will be squared to
      compute Classic drop probability.  So, before it is squared, it is
      effectively the square root of the drop probability; hence, it is
      given the variable name sqrt_p_C.  The squaring is done by
      comparing it with the maximum out of two random numbers (assuming
      U = 1).  Comparing it with the maximum out of two is the same as
      the logical 'AND' of two tests, which ensures drop probability
      rises with the square of queuing time.

   The AQM functions in each queue (lines 5c and 10b) are two cases of a
   new generalization of RED called 'Curvy RED', motivated as follows.
   When the performance of this AQM was compared with FQ-CoDel and PIE,
   their goal of holding queuing delay to a fixed target seemed
   misguided [CRED_Insights].  As the number of flows increases, if the
   AQM does not allow host congestion controllers to increase queuing
   delay, it has to introduce abnormally high levels of loss.  Then loss
   rather than queuing becomes the dominant cause of delay for short
   flows, due to timeouts and tail losses.

   Curvy RED constrains delay with a softened target that allows some
   increase in delay as load increases.  This is achieved by increasing
   drop probability on a convex curve relative to queue growth (the
   square curve in the Classic queue, if U = 1).  Like RED, the curve
   hugs the zero axis while the queue is shallow.  Then, as load
   increases, it introduces a growing barrier to higher delay.  But,
   unlike RED, it requires only two parameters, not three.  The
   disadvantage of Curvy RED (compared to a PI controller, for example)
   is that it is not adapted to a wide range of RTTs.  Curvy RED can be
   used as is when the RTT range to be supported is limited; otherwise,
   an adaptation mechanism is needed.

   From our limited experiments with Curvy RED so far, recommended
   values of these parameters are: S_C = -1; g_C = 5; T = 5 * MTU at the
   link rate (about 1 ms at 60 Mb/s) for the range of base RTTs typical
   on the public Internet.  [CRED_Insights] explains why these
   parameters are applicable whatever rate link this AQM implementation
   is deployed on and how the parameters would need to be adjusted for a
   scenario with a different range of RTTs (e.g., a data centre).  The
   setting of k depends on policy (see Section 2.5 and Appendix C.2,
   respectively, for its recommended setting and guidance on

   There is also a cUrviness parameter, U, which is a small positive
   integer.  It is likely to take the same hard-coded value for all
   implementations, once experiments have determined a good value.  Only
   U = 1 has been used in experiments so far, but results might be even
   better with U = 2 or higher.


   1.  The alternative of applying the AQMs at enqueue would shift some
       processing from the critical time when each packet is dequeued.
       However, it would also add a whole queue of delay to the control
       signals, making the control loop sloppier (for a typical RTT, it
       would double the Classic queue's feedback delay).  On a platform
       where packet timestamping is feasible, e.g., Linux, it is also
       easiest to apply the AQMs at dequeue, because that is where
       queuing time is also measured.

   2.  WRR better isolates the L4S queue from large delay bursts in the
       Classic queue, but it is slightly less simple than TS-FIFO.  If
       WRR were used, a low default Classic weight (e.g., 1/16) would
       need to be configured in place of the time-shift in line 5 of the
       initialization function (Figure 9).

   3.  A step function is shown for simplicity.  A ramp function (see
       Figure 5 and the discussion around it in Appendix A.1) is
       recommended, because it is more general than a step and has the
       potential to enable L4S congestion controls to converge more

   4.  An EWMA is only one possible way to filter bursts; other more
       adaptive smoothing methods could be valid, and it might be
       appropriate to decrease the EWMA faster than it increases, e.g.,
       by using the minimum of the smoothed and instantaneous queue
       delays, min(Q_C, qc.time()).

B.2.  Efficient Implementation of Curvy RED

   Although code optimization depends on the platform, the following
   notes explain where the design of Curvy RED was particularly
   motivated by efficient implementation.

   The Classic AQM at line 10b in Figure 10 calls maxrand(2*U), which
   gives twice as much curviness as the call to maxrand(U) in the
   marking function at line 5c.  This is the trick that implements the
   square rule in equation (1) (Section 2.1).  This is based on the fact
   that, given a number X from 1 to 6, the probability that two dice
   throws will both be less than X is the square of the probability that
   one throw will be less than X.  So, when U = 1, the L4S marking
   function is linear and the Classic dropping function is squared.  If
   U = 2, L4S would be a square function and Classic would be quartic.
   And so on.

   The maxrand(u) function in lines 22-27 simply generates u random
   numbers and returns the maximum.  Typically, maxrand(u) could be run
   in parallel out of band.  For instance, if U = 1, the Classic queue
   would require the maximum of two random numbers.  So, instead of
   calling maxrand(2*U) in-band, the maximum of every pair of values
   from a pseudorandom number generator could be generated out of band
   and held in a buffer ready for the Classic queue to consume.

   1:  cred_dequeue(lq, cq, pkt) {       % Couples L4S & Classic queues
   2:    while ( lq.byt() + cq.byt() > 0 ) {
   3:      if ( scheduler() == lq ) {
   4:        lq.dequeue(pkt)                            % L4S scheduled
   5:        if ((lq.time() > T) OR (Q_C >> (S_L-2) > maxrand(U)))
   6:          mark(pkt)
   7:      } else {
   8:        cq.dequeue(pkt)                        % Classic scheduled
   9:        Q_C += (qc.ns() - Q_C) >> g_C             % Classic Q EWMA
   10:       if ( (Q_C >> (S_C-2) ) > maxrand(2*U) ) {
   11:         if ( (ecn(pkt) == 0)  {            % ECN field = not-ECT
   12:           drop(pkt)                    % Squared drop, redo loop
   13:           continue       % continue to the top of the while loop
   14:         }
   15:         mark(pkt)
   16:       }
   17:     }
   18:     return(pkt)                % return the packet and stop here
   19:   }
   20:   return(NULL)                            % no packet to dequeue
   21: }

     Figure 11: Optimised Example Dequeue Pseudocode for DualQ Coupled
                        AQM using Integer Arithmetic

   The two ranges, range_L and range_C, are expressed as powers of 2 so
   that division can be implemented as a right bit-shift (>>) in lines 5
   and 10 of the integer variant of the pseudocode (Figure 11).

   For the integer variant of the pseudocode, an integer version of the
   rand() function used at line 25 of the maxrand() function in
   Figure 10 would be arranged to return an integer in the range 0 <=
   maxrand() < 2^32 (not shown).  This would scale up all the floating
   point probabilities in the range [0,1] by 2^32.

   Queuing delays are also scaled up by 2^32, but in two stages: i) in
   line 9, queuing time qc.ns() is returned in integer nanoseconds,
   making the value about 2^30 times larger than when the units were
   seconds, and then ii) in lines 5 and 10, an adjustment of -2 to the
   right bit-shift multiplies the result by 2^2, to complete the scaling
   by 2^32.

   In line 8 of the initialization function, the EWMA constant gamma is
   represented as an integer power of 2, g_C, so that in line 9 of the
   integer code (Figure 11), the division needed to weight the moving
   average can be implemented by a right bit-shift (>> g_C).

Appendix C.  Choice of Coupling Factor, k

C.1.  RTT-Dependence

   Where Classic flows compete for the same capacity, their relative
   flow rates depend not only on the congestion probability but also on
   their end-to-end RTT (= base RTT + queue delay).  The rates of Reno
   [RFC5681] flows competing over an AQM are roughly inversely
   proportional to their RTTs.  CUBIC exhibits similar RTT-dependence
   when in Reno-friendly mode, but it is less RTT-dependent otherwise.

   Until the early experiments with the DualQ Coupled AQM, the
   importance of the reasonably large Classic queue in mitigating RTT-
   dependence when the base RTT is low had not been appreciated.
   Appendix A.1.6 of the L4S ECN Protocol [RFC9331] uses numerical
   examples to explain why bloated buffers had concealed the RTT-
   dependence of Classic congestion controls before that time.  Then, it
   explains why, the more that queuing delays have reduced, the more
   that RTT-dependence has surfaced as a potential starvation problem
   for long RTT flows, when competing against very short RTT flows.

   Given that congestion control on end systems is voluntary, there is
   no reason why it has to be voluntarily RTT-dependent.  The RTT-
   dependence of existing Classic traffic cannot be 'undeployed'.
   Therefore, [RFC9331] requires L4S congestion controls to be
   significantly less RTT-dependent than the standard Reno congestion
   control [RFC5681], at least at low RTT.  Then RTT-dependence ought to
   be no worse than it is with appropriately sized Classic buffers.
   Following this approach means there is no need for network devices to
   address RTT-dependence, although there would be no harm if they did,
   which per-flow queuing inherently does.

C.2.  Guidance on Controlling Throughput Equivalence

   The coupling factor, k, determines the balance between L4S and
   Classic flow rates (see Section and equation (1) in
   Section 2.1).

   For the public Internet, a coupling factor of k = 2 is recommended
   and justified below.  For scenarios other than the public Internet, a
   good coupling factor can be derived by plugging the appropriate
   numbers into the same working.

   To summarize the maths below, from equation (7) it can be seen that
   choosing k = 1.64 would theoretically make L4S throughput roughly the
   same as Classic, _if their actual end-to-end RTTs were the same_.
   However, even if the base RTTs are the same, the actual RTTs are
   unlikely to be the same, because Classic traffic needs a fairly large
   queue to avoid underutilization and excess drop, whereas L4S does

   Therefore, to determine the appropriate coupling factor policy, the
   operator needs to decide at what base RTT it wants L4S and Classic
   flows to have roughly equal throughput, once the effect of the
   additional Classic queue on Classic throughput has been taken into
   account.  With this approach, a network operator can determine a good
   coupling factor without knowing the precise L4S algorithm for
   reducing RTT-dependence -- or even in the absence of any algorithm.

   The following additional terminology will be used, with appropriate

   r:  Packet rate [pkt/s]

   R:  RTT [s/round]

   p:  ECN-marking probability []

   On the Classic side, we consider Reno as the most sensitive and
   therefore worst-case Classic congestion control.  We will also
   consider CUBIC in its Reno-friendly mode ('CReno') as the most
   prevalent congestion control, according to the references and
   analysis in [PI2param].  In either case, the Classic packet rate in
   steady state is given by the well-known square root formula for Reno
   congestion control:

       r_C = 1.22 / (R_C * p_C^0.5)          (5)

   On the L4S side, we consider the Prague congestion control
   [PRAGUE-CC] as the reference for steady-state dependence on
   congestion.  Prague conforms to the same equation as DCTCP, but we do
   not use the equation derived in the DCTCP paper, which is only
   appropriate for step marking.  The coupled marking, p_CL, is the
   appropriate one when considering throughput equivalence with Classic
   flows.  Unlike step marking, coupled markings are inherently spaced
   out, so we use the formula for DCTCP packet rate with probabilistic
   marking derived in Appendix A of [PI2].  We use the equation without
   RTT-independence enabled, which will be explained later.

       r_L = 2 / (R_L * p_CL)                (6)

   For packet rate equivalence, we equate the two packet rates and
   rearrange the equation into the same form as equation (1) (copied
   from Section 2.1) so the two can be equated and simplified to produce
   a formula for a theoretical coupling factor, which we shall call k*:

       r_c = r_L
   =>  p_C = (p_CL/1.64 * R_L/R_C)^2.

       p_C = ( p_CL / k )^2.                 (1)

       k* = 1.64 * (R_C / R_L).              (7)

   We say that this coupling factor is theoretical, because it is in
   terms of two RTTs, which raises two practical questions: i) for
   multiple flows with different RTTs, the RTT for each traffic class
   would have to be derived from the RTTs of all the flows in that class
   (actually the harmonic mean would be needed) and ii) a network node
   cannot easily know the RTT of the flows anyway.

   RTT-dependence is caused by window-based congestion control, so it
   ought to be reversed there, not in the network.  Therefore, we use a
   fixed coupling factor in the network and reduce RTT-dependence in L4S
   senders.  We cannot expect Classic senders to all be updated to
   reduce their RTT-dependence.  But solely addressing the problem in
   L4S senders at least makes RTT-dependence no worse -- not just
   between L4S senders, but also between L4S and Classic senders.

   Throughput equivalence is defined for flows under comparable
   conditions, including with the same base RTT [RFC2914].  So if we
   assume the same base RTT, R_b, for comparable flows, we can put both
   R_C and R_L in terms of R_b.

   We can approximate the L4S RTT to be hardly greater than the base
   RTT, i.e., R_L ~= R_b.  And we can replace R_C with (R_b + q_C),
   where the Classic queue, q_C, depends on the target queue delay that
   the operator has configured for the Classic AQM.

   Taking PI2 as an example Classic AQM, it seems that we could just
   take R_C = R_b + target (recommended 15 ms by default in
   Appendix A.1).  However, target is roughly the queue depth reached by
   the tips of the sawteeth of a congestion control, not the average
   [PI2param].  That is R_max = R_b + target.

   The position of the average in relation to the max depends on the
   amplitude and geometry of the sawteeth.  We consider two examples:
   Reno [RFC5681], as the most sensitive worst case, and CUBIC [RFC8312]
   in its Reno-friendly mode ('CReno') as the most prevalent congestion
   control algorithm on the Internet according to the references in
   [PI2param].  Both are Additive Increase Multiplicative Decrease
   (AIMD), so we will generalize using b as the multiplicative decrease
   factor (b_r = 0.5 for Reno, b_c = 0.7 for CReno).  Then

     R_C  = (R_max + b*R_max) / 2
          = R_max * (1+b)/2.

   R_reno = 0.75 * (R_b + target);    R_creno = 0.85 * (R_b + target).

   Plugging all this into equation (7), at any particular base RTT, R_b,
   we get a fixed coupling factor for each:

   k_reno = 1.64*0.75*(R_b+target)/R_b
          = 1.23*(1 + target/R_b);    k_creno = 1.39 * (1 + target/R_b).

   An operator can then choose the base RTT at which it wants throughput
   to be equivalent.  For instance, if we recommend that the operator
   chooses R_b = 25 ms, as a typical base RTT between Internet users and
   CDNs [PI2param], then these coupling factors become:

   k_reno = 1.23 * (1 + 15/25)        k_creno  = 1.39 * (1 + 15/25)
          = 1.97                               = 2.22
          ~= 2.                                ~= 2.                 (9)

   The approximation is relevant to any of the above example DualQ
   Coupled algorithms, which use a coupling factor that is an integer
   power of 2 to aid efficient implementation.  It also fits best for
   the worst case (Reno).

   To check the outcome of this coupling factor, we can express the
   ratio of L4S to Classic throughput by substituting from their rate
   equations (5) and (6), then also substituting for p_C in terms of
   p_CL using equation (1) with k = 2 as just determined for the

   r_L / r_C  = 2 (R_C * p_C^0.5) / 1.22 (R_L * p_CL)
              = (R_C * p_CL) / (1.22 * R_L * p_CL)
              = R_C / (1.22 * R_L).                                 (10)

   As an example, we can then consider single competing CReno and Prague
   flows, by expressing both their RTTs in (10) in terms of their base
   RTTs, R_bC and R_bL.  So R_C is replaced by equation (8) for CReno.
   And R_L is replaced by the max() function below, which represents the
   effective RTT of the current Prague congestion control [PRAGUE-CC] in
   its (default) RTT-independent mode, because it sets a floor to the
   effective RTT that it uses for additive increase:

   r_L / r_C ~= 0.85 * (R_bC + target) / (1.22 * max(R_bL, R_typ))
             ~= (R_bC + target) / (1.4 * max(R_bL, R_typ)).

   It can be seen that, for base RTTs below target (15 ms), both the
   numerator and the denominator plateau, which has the desired effect
   of limiting RTT-dependence.

   At the start of the above derivations, an explanation was promised
   for why the L4S throughput equation in equation (6) did not need to
   model RTT-independence.  This is because we only use one point -- at
   the typical base RTT where the operator chooses to calculate the
   coupling factor.  Then throughput equivalence will at least hold at
   that chosen point.  Nonetheless, assuming Prague senders implement
   RTT-independence over a range of RTTs below this, the throughput
   equivalence will then extend over that range as well.

   Congestion control designers can choose different ways to reduce RTT-
   dependence.  And each operator can make a policy choice to decide on
   a different base RTT, and therefore a different k, at which it wants
   throughput equivalence.  Nonetheless, for the Internet, it makes
   sense to choose what is believed to be the typical RTT most users
   experience, because a Classic AQM's target queuing delay is also
   derived from a typical RTT for the Internet.

   As a non-Internet example, for localized traffic from a particular
   ISP's data centre, using the measured RTTs, it was calculated that a
   value of k = 8 would achieve throughput equivalence, and experiments
   verified the formula very closely.

   But, for a typical mix of RTTs across the general Internet, a value
   of k = 2 is recommended as a good workable compromise.


   Thanks to Anil Agarwal, Sowmini Varadhan, Gabi Bracha, Nicolas Kuhn,
   Greg Skinner, Tom Henderson, David Pullen, Mirja Kühlewind, Gorry
   Fairhurst, Pete Heist, Ermin Sakic, and Martin Duke for detailed
   review comments, particularly of the appendices, and suggestions on
   how to make the explanations clearer.  Thanks also to Tom Henderson
   for insight on the choice of schedulers and queue delay measurement
   techniques.  And thanks to the area reviewers Christer Holmberg, Lars
   Eggert, and Roman Danyliw.

   The early contributions of Koen De Schepper, Bob Briscoe, Olga
   Bondarenko, and Inton Tsang were partly funded by the European
   Community under its Seventh Framework Programme through the Reducing
   Internet Transport Latency (RITE) project (ICT-317700).
   Contributions of Koen De Schepper and Olivier Tilmans were also
   partly funded by the 5Growth and DAEMON EU H2020 projects.  Bob
   Briscoe's contribution was also partly funded by the Comcast
   Innovation Fund and the Research Council of Norway through the TimeIn
   project.  The views expressed here are solely those of the authors.


   The following contributed implementations and evaluations that
   validated and helped to improve this specification:

   Olga Albisser <olga@albisser.org> of Simula Research Lab, Norway
   (Olga Bondarenko during early draft versions) implemented the
   prototype DualPI2 AQM for Linux with Koen De Schepper and conducted
   extensive evaluations as well as implementing the live performance
   visualization GUI [L4Sdemo16].

   Olivier Tilmans <olivier.tilmans@nokia-bell-labs.com> of Nokia Bell
   Labs, Belgium prepared and maintains the Linux implementation of
   DualPI2 for upstreaming.

   Shravya K.S. wrote a model for the ns-3 simulator based on draft-
   ietf-tsvwg-aqm-dualq-coupled-01 (a draft version of this document).
   Based on this initial work, Tom Henderson <tomh@tomh.org> updated
   that earlier model and created a model for the DualQ variant
   specified as part of the Low Latency DOCSIS specification, as well as
   conducting extensive evaluations.

   Ing Jyh (Inton) Tsang of Nokia, Belgium built the End-to-End Data
   Centre to the Home broadband testbed on which DualQ Coupled AQM
   implementations were tested.

Authors' Addresses

   Koen De Schepper
   Nokia Bell Labs
   Email: koen.de_schepper@nokia.com
   URI:   https://www.bell-labs.com/about/researcher-profiles/

   Bob Briscoe (editor)
   United Kingdom
   Email: ietf@bobbriscoe.net
   URI:   https://bobbriscoe.net/

   Greg White
   Louisville, CO
   United States of America
   Email: G.White@CableLabs.com