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Versions: (draft-briscoe-tsvwg-aqm-dualq-coupled) 00 01 02 03 04 05 06 07 08 09 10

Transport Area working group (tsvwg)                      K. De Schepper
Internet-Draft                                           Nokia Bell Labs
Intended status: Experimental                            B. Briscoe, Ed.
Expires: January 9, 2020                                        G. White
                                                               CableLabs
                                                            July 8, 2019


  DualQ Coupled AQMs for Low Latency, Low Loss and Scalable Throughput
                                 (L4S)
                 draft-ietf-tsvwg-aqm-dualq-coupled-10

Abstract

   The Low Latency Low Loss Scalable Throughput (L4S) architecture
   allows data flows over the public Internet to achieve consistent
   ultra-low queuing latency, generally zero congestion loss and scaling
   of per-flow throughput without the scaling problems of traditional
   TCP.  To achieve this, L4S data flows have to use one of the family
   of 'Scalable' congestion controls (Data Centre TCP and TCP Prague are
   examples) and a form of Explicit Congestion Notification (ECN) with
   modified behaviour.  However, until now, Scalable congestion controls
   did not co-exist with existing TCP Reno/Cubic traffic --- Scalable
   controls are so aggressive that 'Classic' TCP algorithms 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).
   This specification defines `DualQ Coupled Active Queue Management
   (AQM)', which enables these Scalable congestion controls to safely
   co-exist with Classic Internet traffic.

   Analytical study and implementation testing of the Coupled AQM have
   shown that Scalable and Classic flows competing under similar
   conditions run at roughly the same rate.  It achieves this
   indirectly, without having to inspect transport layer flow
   identifiers.  When tested in a residential broadband setting, DCTCP
   also achieves sub-millisecond average queuing delay and zero
   congestion loss under a wide range of mixes of DCTCP and `Classic'
   broadband Internet traffic, without compromising the performance of
   the Classic traffic.  The solution also reduces network complexity
   and requires no configuration for the public Internet.

Status of This Memo

   This Internet-Draft is submitted in full conformance with the
   provisions of BCP 78 and BCP 79.





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Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   3
     1.1.  Outline of the Problem  . . . . . . . . . . . . . . . . .   3
     1.2.  Scope . . . . . . . . . . . . . . . . . . . . . . . . . .   5
     1.3.  Terminology . . . . . . . . . . . . . . . . . . . . . . .   7
     1.4.  Features  . . . . . . . . . . . . . . . . . . . . . . . .   8
   2.  DualQ Coupled AQM . . . . . . . . . . . . . . . . . . . . . .   9
     2.1.  Coupled AQM . . . . . . . . . . . . . . . . . . . . . . .   9
     2.2.  Dual Queue  . . . . . . . . . . . . . . . . . . . . . . .  10
     2.3.  Traffic Classification  . . . . . . . . . . . . . . . . .  11
     2.4.  Overall DualQ Coupled AQM Structure . . . . . . . . . . .  11
     2.5.  Normative Requirements for a DualQ Coupled AQM  . . . . .  14
       2.5.1.  Functional Requirements . . . . . . . . . . . . . . .  14
         2.5.1.1.  Requirements in Unexpected Cases  . . . . . . . .  15
       2.5.2.  Management Requirements . . . . . . . . . . . . . . .  16
         2.5.2.1.  Configuration . . . . . . . . . . . . . . . . . .  16
         2.5.2.2.  Monitoring  . . . . . . . . . . . . . . . . . . .  18
         2.5.2.3.  Anomaly Detection . . . . . . . . . . . . . . . .  18
         2.5.2.4.  Deployment, Coexistence and Scaling . . . . . . .  19
   3.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  19



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   4.  Security Considerations . . . . . . . . . . . . . . . . . . .  19
     4.1.  Overload Handling . . . . . . . . . . . . . . . . . . . .  19
       4.1.1.  Avoiding Classic Starvation: Sacrifice L4S Throughput
               or Delay? . . . . . . . . . . . . . . . . . . . . . .  20
       4.1.2.  Congestion Signal Saturation: Introduce L4S Drop or
               Delay?  . . . . . . . . . . . . . . . . . . . . . . .  21
       4.1.3.  Protecting against Unresponsive ECN-Capable Traffic .  22
   5.  Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .  22
   6.  Contributors  . . . . . . . . . . . . . . . . . . . . . . . .  23
   7.  References  . . . . . . . . . . . . . . . . . . . . . . . . .  23
     7.1.  Normative References  . . . . . . . . . . . . . . . . . .  23
     7.2.  Informative References  . . . . . . . . . . . . . . . . .  24
   Appendix A.  Example DualQ Coupled PI2 Algorithm  . . . . . . . .  27
     A.1.  Pass #1: Core Concepts  . . . . . . . . . . . . . . . . .  28
     A.2.  Pass #2: Overload Details . . . . . . . . . . . . . . . .  36
   Appendix B.  Example DualQ Coupled Curvy RED Algorithm  . . . . .  40
     B.1.  Curvy RED in Pseudocode . . . . . . . . . . . . . . . . .  40
     B.2.  Efficient Implementation of Curvy RED . . . . . . . . . .  46
   Appendix C.  Guidance on Controlling Throughput Equivalence . . .  48
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  49

1.  Introduction

   This document specifies a framework for DualQ Coupled AQMs, which is
   the network part of the L4S architecture [I-D.ietf-tsvwg-l4s-arch].
   L4S enables both ultra-low queuing latency and high throughput at the
   same time, for ad hoc numbers of capacity-seeking applications all
   sharing the same capacity.

1.1.  Outline of the Problem

   Latency is becoming the critical performance factor for many (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.  In the developed world, further
   increases in access network bit-rate offer diminishing returns,
   whereas latency is still a multi-faceted problem.  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.

   Traditionally ultra-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 EF [RFC3246].  Up to
   now it has not been possible to allow any number of low latency, high



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   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:

   o  Recent state-of-the-art active queue management (AQM) in the
      network, e.g. fq_CoDel [RFC8290], PIE [RFC8033], Adaptive
      RED [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 either cause queuing
      delay to vary or cause the link to be under-utilized.  These AQMs
      are tuned to allow a typical capacity-seeking TCP-Friendly flow to
      induce an average queue that roughly doubles the base RTT, adding
      5-15 ms of queuing on average (cf. 500 microseconds with L4S for
      the same mix of long-running and web traffic).  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).

   o  Similarly, recent research into using e2e congestion control
      without needing an AQM in the network (e.g.BBRv1 [BBRv1]) seems to
      have hit a similar lower limit to queuing delay of about 20ms on
      average (and any additional BBRv1 flow adds another 20ms of
      queuing) but there are also regular 25ms delay spikes due to
      bandwidth probes and 60ms spikes due to flow-starts.

   L4S learns from the experience of Data Center TCP [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 TCP-Friendly
       congestion controls;

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

   Without the former, a 'Classic' flow's round trip time (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




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   be hundreds of times the actual smoothing delay needed for the RTT of
   typical traffic from localized CDNs.

   These changes are the two main features of the family of so-called
   'Scalable' congestion controls (which includes DCTCP).  Both 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 need an extremely shallow ECN packet-marking
       threshold in the queue.

   2.  And 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.
   But, with ECN, the resulting high marking levels are fine.

   However, until now, Scalable congestion controls (like DCTCP) did not
   co-exist with existing ECN-capable TCP Reno [RFC5681] or Cubic
   [RFC8312] traffic --- Scalable controls are so aggressive that these
   'Classic' TCP algorithms 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).

   This document specifies a `DualQ Coupled AQM' extension that solves
   the problem of coexistence between Scalable and Classic flows,
   without having to inspect flow identifiers.  It is not like flow-
   queuing approaches [RFC8290] that classify packets by flow identifier
   into separate queues in order to isolate sparse flows from the higher
   latency in the queues assigned to heavier flows.  If a flow needs
   both low delay and high throughput, having a queue to itself does not
   isolate it from the harm it causes to itself.  In contrast, L4S
   addresses the root cause of the latency problem --- it is an enabler
   for the smooth low latency scalable behaviour of Scalable congestion
   controls, so that every packet in every flow can enjoy very low
   latency, then there is no need to isolate each flow into a separate
   queue.

1.2.  Scope

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

   Network:  A DualQ Coupled AQM (defined in the present document);

   End-system:  A Scalable congestion control (defined in Section 2.1.




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   Packet identifier:  The network and end-system parts of L4S can be
      deployed incrementally, because they both identify L4S packets
      using the experimentally assigned explicit congestion notification
      (ECN) codepoints in the IP header: ECT(1) and CE [RFC8311]
      [I-D.ietf-tsvwg-ecn-l4s-id].

   Data Center TCP (DCTCP [RFC8257]) is an example of a Scalable
   congestion control that has been deployed for some time in Linux,
   Windows and FreeBSD operating systems and Relentless TCP [Mathis09]
   is another example.  During the progress of this document through the
   IETF a number of other Scalable congestion controls were implemented,
   e.g.  TCP Prague [PragueLinux], QUIC Prague and the L4S variant of
   SCREAM for real-time media [RFC8298].  (Note: after the v3.19 Linux
   kernel, bugs were introduced into DCTCP's scalable behaviour and not
   all the patches applied for L4S evaluation had been applied to the
   mainline Linux kernel, which was at v5.2 at the time of writing).

   The focus of this specification is to get the network part of the L4S
   service in place.  Then, without any management intervention,
   applications can exploit this new network capability as 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 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; 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.  Here, the term 'site' is used loosely to mean a home, an
   office, a campus or mobile user equipment.

   Latency is not the only concern of L4S:

   o  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.



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   o  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 therefore
   outside the scope of this AQM document, even though the AQM is an
   enabler.

   The overall L4S architecture [I-D.ietf-tsvwg-l4s-arch] 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 [PI2]
   and [DCttH15] give the full rationale for the AQM's design, both
   discursively and in more precise mathematical form.

1.3.  Terminology

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

   The DualQ Coupled AQM uses two queues for two services.  Each of the
   following terms identifies both the service and the queue that
   provides the service:

   Classic (denoted by subscript C):  The `Classic' service is intended
      for all the behaviours that currently co-exist with TCP Reno (TCP
      Cubic, Compound, SCTP, etc).

   Low-Latency, Low-Loss and Scalable (L4S, denoted by subscript L):
      The `L4S' service is intended for a set of congestion controls
      with scalable properties, such as TCP Prague and DCTCP.  For the
      public Internet an L4S transport has to comply with the
      requirements in Section 4 of [I-D.ietf-tsvwg-ecn-l4s-id] (aka.
      the 'Prague L4S requirements').

   Either service can cope with a proportion of unresponsive or less-
   responsive traffic as well, as long (e.g.  DNS, VoIP, game sync
   datagrams, etc), just as a single queue AQM can if this traffic makes
   minimal contribution to queuing.  The DualQ Coupled AQM behaviour
   below is defined to be similar to a single FIFO queue with respect to
   unresponsive and overload traffic.






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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 TCP Prague to give stunningly low and predictably low
   latency, without compromising the performance of competing 'Classic'
   Internet traffic.

   Thousands of tests have been conducted in a typical fixed residential
   broadband setting.  Experiments used a range of base round trip
   delays up to 100ms 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 1ms (or 2 packets where serialization delay
   exceeded 1ms on slower links), with 99th percentile no worse than
   2ms.  No losses at all were introduced by the L4S AQM.  Details of
   the extensive experiments are available [PI2] [DCttH15].

   Subjective testing was also conducted by multiple people all
   simultaneously using very demanding high bandwidth low latency
   applications over a single shared access link [L4Sdemo16].  In one
   application, each user could use finger gestures to pan or zoom their
   own high definition (HD) sub-window of a larger video scene generated
   on the fly in 'the cloud' from a football match.  Another user
   wearing VR goggles was remotely receiving a feed from a 360-degree
   camera in a racing car, again with the sub-window in their field of
   vision generated on the fly in 'the cloud' dependent on their head
   movements.  Even though other users were also downloading large
   amounts of L4S and Classic data, playing a gaming benchmark and
   watchings videos over the same 40Mb/s downstream broadband link,
   latency was so low that the football picture appeared to stick to the
   user's finger on the touchpad and the experience fed from the remote
   camera did not noticeably lag head movements.  All the L4S data (even
   including the downloads) achieved the same ultra-low latency.  With
   an alternative AQM, the video noticeably lagged behind the finger
   gestures and head movements.

   Unlike Diffserv Expedited Forwarding, 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 (TCP Prague 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, and the latency of




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   Classic traffic does not suffer when a proportion of the traffic is
   L4S.

   The two queues are only necessary because:

   o  the large variations (sawteeth) of Classic flows need roughly a
      base RTT of queuing delay to ensure full utilization

   o  while Scalable flows do not need a queue to keep utilization high,
      but they cannot keep latency predictably low if they are mixed
      with legacy TCP flows,

   The L4S queue has latency priority, but 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 approach:

   o  the Coupled AQM that addresses throughput equivalence between
      Classic (e.g.  Reno, Cubic) flows and L4S flows (that satisfy the
      Prague L4S requirements).

   o  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 TCP's congestion window, cwnd, and its drop probability, p.
   To a first order approximation, cwnd of TCP 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-compatibility mode,
   which is relevant for typical RTTs under 20ms as long as the
   throughput of a single flow is less than about 700Mb/s.  In such
   cases it can be assumed that Cubic traffic behaves similarly to Reno
   (but with a slightly different constant of proportionality).  The
   term 'Classic' will be used for the collection of Reno-friendly
   traffic including Cubic in Reno mode.

   The 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



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   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 also used for traffic driven by a Scalable congestion
   control that also complies with the additional 'Prague L4S'
   requirements [I-D.ietf-tsvwg-ecn-l4s-id].

   For safe co-existence, 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.  [RFC8311] updates the original ECN specification
   [RFC3168] to allow these probabilities to be distinct, because RFC
   3168 required them to be the same.

   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, and allows 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 Classic 'TCP
   formula'.

   Stating this as a formula, the relation between Classic drop
   probability, p_C, and the coupled L4S probability p_CL needs to take
   the 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 under-
   utilization.  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.

   Nonetheless, coupled marking ensures that giving priority to L4S
   traffic still leaves the right amount of spare scheduling time for



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   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 L and 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 [I-D.ietf-tsvwg-ecn-l4s-id] requires the sender to use
   the ECT(1) and CE codepoints of the ECN field as this identifier,
   having assessed various alternatives.  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, [I-D.ietf-tsvwg-ecn-l4s-id] says 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 (see [I-D.ietf-tsvwg-ecn-l4s-id]), specific
   Diffserv codepoints such as EF (Expedited Forwarding) and Voice-Admit
   service classes (see [I-D.briscoe-tsvwg-l4s-diffserv]) or certain
   protocols (e.g.  ARP, DNS).  Note that the mechanism only reads these
   identifiers.  [I-D.ietf-tsvwg-ecn-l4s-id] says it "MUST NOT alter
   these non-ECN identifiers".

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.

   The classifier on the left separates incoming traffic between the two
   queues (L and C).  Each queue has its own AQM that determines the



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   likelihood of marking or dropping (p_L and p_C).  It has been
   proved [PI2] that it is preferable to control load with a linear
   controller, then square the output before applying it as a drop
   probability to TCP (because TCP 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, where

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

   Substituting for p_C in Eqn (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)

   where k is the constant coupling factor (see Appendix C).

   It can be seen that these two transformations of p' implement the
   required coupling given in equation (1) earlier.

   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 strict priority over the C
   queue, whenever the L queue grows, the AQM should apply marking
   probability p'_L, but p_L should not fall below p_CL.  This suggests:

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

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














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                           _________
                                  | |    ,------.
                        L4S 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 |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, giving priority to L4S traffic.
   Priority has to be conditional in some way (see Section 4.1).  Simple
   strict priority is inappropriate otherwise it could lead the L4S
   queue to starve the Classic queue.  For example, consider the case
   where a continually busy L4S queue blocks a DNS request in the
   Classic queue, arbitrarily delaying the start of a new Classic flow.

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

   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.





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   Curvy RED is derived from RED [RFC2309], but its configuration
   parameters are insensitive to link rate and it requires less
   operations per packet.  However, DualPI2 is more responsive and
   stable over a wider range of RTTs than Curvy RED.  As a consequence,
   DualPI2 has attracted more development and evaluation attention than
   Curvy RED, leaving the Curvy RED design incomplete and not so fully
   evaluated.

   Both AQMs regulate their queue 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.

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 used for each queue.

2.5.1.  Functional Requirements

   A Dual Queue Coupled AQM implementation MUST utilize two queues, each
   with an AQM algorithm.  The two queues can be part of a larger
   queuing hierarchy [I-D.briscoe-tsvwg-l4s-diffserv].

   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.

   [I-D.ietf-tsvwg-ecn-l4s-id] 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 an 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.





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   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 Eqn.  (1).

   The constant of proportionality, k, in Eqn (1) determines the
   relative flow rates of Classic and L4S flows when the AQM concerned
   is the bottleneck (all other factors being equal).
   [I-D.ietf-tsvwg-ecn-l4s-id] says, "The constant of proportionality
   (k) does not have to be standardised for interoperability, but a
   value of 2 is RECOMMENDED."

   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 congestion control
   (Reno) [RFC5681] and other so-called TCP-friendly controls, such as
   TCP Cubic in its TCP-friendly mode.

   The choice of k is a matter of operator policy, and operators MAY
   choose a different value using Table 1 and the guidelines in
   Appendix C.

   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 DOCSIS3.1, CDMA in 3G, SC-FDMA in
   LTE) or L3 scheduling (WRR in DSL), rather than relying on TCP 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.

2.5.1.1.  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 recommended that the AQM in each queue inspects the ECN field
   to determine what sort of congestion notification to signal, then
   decides whether to apply congestion notification to this particular
   packet, as follows:

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



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      *  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 or latency
         policing):

         +  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)

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

   o  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 "SHOULDs", 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 marked with one codepoint actually has a
   congestion response associated with another codepoint.

   If the DualQ Coupled AQM has detected overload, it MUST signal
   congestion solely using drop, irrespective of the ECN field.
   Switching to drop if ECN marking is persistently high is required by
   Section 7 of [RFC3168] and Section 4.2.1 of [RFC7567].

2.5.2.  Management Requirements

2.5.2.1.  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:



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

   o  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 TCP flows from under-utilizing capacity.  For
      example:

      *  for the PI2 algorithm (Appendix A) the queuing delay target is
         set to 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 under-utilization by a single TCP flow would be unlikely.

   o  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.

      Stability parameter(s) that are manually calculated assuming a
      maximum RTT might be directly configurable instead.

   o  Coupling factor, k;

   o  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 to a C packet is w times that of an L
         packet.

      *  for a time-shifted FIFO (TS-FIFO) scheduler (see Section 4.1.1)
         a time-shift of tshift means that the maximum delay to a C



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         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.

   o  The maximum Classic ECN marking probability, p_Cmax, before
      switching over to drop.

2.5.2.2.  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:

   o  Bits forwarded, from which utilization can be calculated;

   o  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;

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

   o  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.

2.5.2.3.  Anomaly Detection

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

   o  Start-time and duration of overload state.



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      A hysteresis mechanism SHOULD be used to prevent flapping in and
      out of overload causing an event storm.  For instance, exit 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.

2.5.2.4.  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 TCP-
   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 [I-D.ietf-tsvwg-l4s-arch].

   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 specification contains no IANA considerations.

4.  Security Considerations

4.1.  Overload Handling

   Where the interests of users or flows might conflict, it could be
   necessary to police traffic to isolate any harm to the performance of
   individual flows.  However it is hard to avoid unintended side-
   effects with policing, and in a trusted environment policing is not
   necessary.  Therefore per-flow policing needs to be separable from a
   basic AQM, as an option under policy control.

   However, a basic DualQ AQM does at least need to handle overload.  A
   useful objective would be for the overload behaviour of the DualQ AQM
   to be at least no worse than a single queue AQM.  However, a trade-
   off needs to be made between complexity and the risk of either
   traffic class harming the other.  In each of the following three
   subsections, an overload issue specific to the DualQ is described,
   followed by proposed solution(s).

   Under overload the higher priority L4S service will have to sacrifice
   some aspect of its performance.  Alternative solutions are provided



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   below that each relax a different factor: e.g. throughput, delay,
   drop.  These choices need to be made either by the developer or by
   operator policy, rather than by the IETF.

4.1.1.  Avoiding Classic Starvation: Sacrifice L4S Throughput or Delay?

   Priority of L4S is required to be conditional to avoid total
   starvation of Classic by heavy L4S traffic.  This raises the question
   of whether to sacrifice L4S throughput or L4S delay (or some other
   policy) to mitigate starvation of Classic:

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

      The scheduling weight of the Classic queue should be small (e.g.
      1/16).  Then, in most traffic scenarios the scheduler will not
      interfere and it will not need to - the coupling mechanism and the
      end-systems will share out the capacity across both queues as if
      it were a single pool.  However, because the congestion coupling
      only applies in one direction (from C to L), 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 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:  To control milder overload of responsive
      traffic, particularly when close to the maximum congestion signal,
      the operator could choose to control overload of the Classic queue



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      by allowing some delay to 'leak' across to the L4S queue.  The
      scheduler can be made to behave like a single First-In First-Out
      (FIFO) queue with different service times by implementing a very
      simple conditional priority scheduler that could be called a
      "time-shifted FIFO" (see the Modifier Earliest Deadline First
      (MEDF) scheduler of [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,
      this time-shifted 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.

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

4.1.2.  Congestion Signal Saturation: Introduce L4S Drop or Delay?

   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 one AQM first saturates to a
   probability of 100% leaving no room to push back the load any harder.
   If k>1, L4S will saturate first, even though saturation could be
   caused by unresponsive traffic in either queue.

   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 TCP-like flow
   that is normally responsive, but above a certain congestion level it
   will not be able to reduce its congestion window below the minimum of
   2 segments [RFC5681], effectively becoming unresponsive.  (Note that
   L4S traffic ought to remain responsive below a window of 2 segments
   (see [I-D.ietf-tsvwg-ecn-l4s-id]).

   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 tail drop too):

   Drop on Saturation:  Saturation can be avoided by setting a maximum
      threshold for 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 queueing delay can be kept at the target in any
      overload situation, including with unresponsive traffic, and no
      further measures are required [DualQ-Test].



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   Delay on Saturation:  When L4S marking saturates, instead of
      switching to drop, the drop and marking probabilities 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
      time-shifted 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.

4.1.3.  Protecting against Unresponsive ECN-Capable Traffic

   Unresponsive traffic has a greater advantage if it is also ECN-
   capable.  The advantage is undetectable at normal low levels of drop/
   marking, but it becomes significant with the higher levels of drop/
   marking typical during overload.  This is an issue whether the ECN-
   capable traffic is L4S or Classic.

   This raises the question of whether and when to switch off ECN
   marking and use solely drop instead, as required by both Section 7 of
   [RFC3168] and Section 4.2.1 of [RFC7567].

   Experiments with the DualPI2 AQM (Appendix A) have shown that
   introducing 'drop on saturation' at 100% L4S marking addresses this
   problem with unresponsive ECN as well as addressing the saturation
   problem.  It leaves only a small range of congestion levels where
   unresponsive traffic gains any advantage from using the ECN
   capability, and the advantage is hardly detectable [DualQ-Test].

5.  Acknowledgements

   Thanks to Anil Agarwal, Sowmini Varadhan's, Gabi Bracha, Nicolas
   Kuhn, Tom Henderson and David Pullen for detailed review comments
   particularly of the appendices and suggestions on how to make the
   explanations clearer.  Thanks also to Tom Henderson for insights on
   the choice of schedulers and queue delay measurement techniques.

   The early contributions of Koen De Schepper, Bob Briscoe, Olga
   Bondarenko and Inton Tsang were part-funded by the European Community
   under its Seventh Framework Programme through the Reducing Internet
   Transport Latency (RITE) project (ICT-317700).  Bob Briscoe's
   contribution was also part-funded by the Research Council of Norway
   through the TimeIn project.  The views expressed here are solely
   those of the authors.





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6.  Contributors

   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 drafts) 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.

      Tom Henderson <tomh@tomh.org> of CableLabs, US implemented various
      Coupled DualQ AQMs for ns3, including DualPI2 and DualPIE over
      point to point and DOCSIS 3.1 link models and conducted extensive
      evaluations.

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

7.  References

7.1.  Normative References

   [I-D.ietf-tsvwg-ecn-l4s-id]
              Schepper, K. and B. Briscoe, "Identifying Modified
              Explicit Congestion Notification (ECN) Semantics for
              Ultra-Low Queuing Delay (L4S)", draft-ietf-tsvwg-ecn-l4s-
              id-06 (work in progress), March 2019.

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119,
              DOI 10.17487/RFC2119, March 1997,
              <https://www.rfc-editor.org/info/rfc2119>.

   [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,
              <https://www.rfc-editor.org/info/rfc3168>.

   [RFC8311]  Black, D., "Relaxing Restrictions on Explicit Congestion
              Notification (ECN) Experimentation", RFC 8311,
              DOI 10.17487/RFC8311, January 2018,
              <https://www.rfc-editor.org/info/rfc8311>.



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7.2.  Informative References

   [Alizadeh-stability]
              Alizadeh, M., Javanmard, A., and B. Prabhakar, "Analysis
              of DCTCP: Stability, Convergence, and Fairness", ACM
              SIGMETRICS 2011 , June 2011,
              <https://dl.acm.org/citation.cfm?id=1993753>.

   [AQMmetrics]
              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) 4866:35--46 DOI:
              10.1117/12.473021, 2002,
              <https://www.cs.purdue.edu/homes/fahmy/papers/ldc.pdf>.

   [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 , August 2001,
              <http://www.icir.org/floyd/red.html>.

   [BBRv1]    Cardwell, N., Cheng, Y., Hassas Yeganeh, S., and V.
              Jacobson, "BBR Congestion Control", Internet Draft draft-
              cardwell-iccrg-bbr-congestion-control-00, July 2017,
              <https://tools.ietf.org/html/
              draft-cardwell-iccrg-bbr-congestion-control-00>.

   [CoDel]    Nichols, K. and V. Jacobson, "Controlling Queue Delay",
              ACM Queue 10(5), May 2012,
              <http://queue.acm.org/issuedetail.cfm?issue=2208917>.

   [CRED_Insights]
              Briscoe, B., "Insights from Curvy RED (Random Early
              Detection)", BT Technical Report TR-TUB8-2015-003
              arXiv:1904.07339 [cs.NI], July 2015,
              <https://arxiv.org/abs/1904.07339>.

   [DCttH15]  De Schepper, K., Bondarenko, O., Briscoe, B., and I.
              Tsang, "`Data Centre to the Home': Ultra-Low Latency for
              All", RITE project Technical Report , 2015,
              <http://riteproject.eu/publications/>.

   [DOCSIS3.1]
              CableLabs, "MAC and Upper Layer Protocols Interface
              (MULPI) Specification, CM-SP-MULPIv3.1", Data-Over-Cable
              Service Interface Specifications DOCSIS(R) 3.1 Version i17
              or later, January 2019, <https://specification-
              search.cablelabs.com/CM-SP-MULPIv3.1>.




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   [DualPI2Linux]
              Albisser, O., De Schepper, K., Briscoe, B., Tilmans, O.,
              and H. Steen, "DUALPI2 - Low Latency, Low Loss and
              Scalable (L4S) AQM", Proc. Linux Netdev 0x13 , March 2019,
              <https://www.netdevconf.org/0x13/
              session.html?talk-DUALPI2-AQM>.

   [DualQ-Test]
              Steen, H., "Destruction Testing: Ultra-Low Delay using
              Dual Queue Coupled Active Queue Management", Masters
              Thesis, Dept of Informatics, Uni Oslo , May 2017.

   [I-D.briscoe-tsvwg-l4s-diffserv]
              Briscoe, B., "Interactions between Low Latency, Low Loss,
              Scalable Throughput (L4S) and Differentiated Services",
              draft-briscoe-tsvwg-l4s-diffserv-02 (work in progress),
              November 2018.

   [I-D.ietf-tsvwg-l4s-arch]
              Briscoe, B., Schepper, K., and M. Bagnulo, "Low Latency,
              Low Loss, Scalable Throughput (L4S) Internet Service:
              Architecture", draft-ietf-tsvwg-l4s-arch-03 (work in
              progress), October 2018.

   [L4Sdemo16]
              Bondarenko, O., De Schepper, K., Tsang, I., and B.
              Briscoe, "Ultra-Low Delay for All: Live Experience, Live
              Analysis", Proc. MMSYS'16 pp33:1--33:4, May 2016,
              <http://dl.acm.org/citation.cfm?doid=2910017.2910633
              (videos of demos: https://riteproject.eu/
              dctth/#1511dispatchwg )>.

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

   [Mathis09]
              Mathis, M., "Relentless Congestion Control", PFLDNeT'09 ,
              May 2009, <http://www.hpcc.jp/pfldnet2009/
              Program_files/1569198525.pdf>.

   [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, March 2003.




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   [PI2]      De Schepper, K., Bondarenko, O., Briscoe, B., and I.
              Tsang, "PI2: A Linearized AQM for both Classic and
              Scalable TCP", ACM CoNEXT'16 , December 2016,
              <https://riteproject.files.wordpress.com/2015/10/
              pi2_conext.pdf>.

   [PragueLinux]
              Briscoe, B., De Schepper, K., Albisser, O., Misund, J.,
              Tilmans, O., Kuehlewind, M., and A. Ahmed, "Implementing
              the `TCP Prague' Requirements for Low Latency Low Loss
              Scalable Throughput (L4S)", Proc. Linux Netdev 0x13 ,
              March 2019, <https://www.netdevconf.org/0x13/
              session.html?talk-tcp-prague-l4s>.

   [RFC0970]  Nagle, J., "On Packet Switches With Infinite Storage",
              RFC 970, DOI 10.17487/RFC0970, December 1985,
              <https://www.rfc-editor.org/info/rfc970>.

   [RFC2309]  Braden, B., Clark, D., Crowcroft, J., Davie, B., Deering,
              S., Estrin, D., Floyd, S., Jacobson, V., Minshall, G.,
              Partridge, C., Peterson, L., Ramakrishnan, K., Shenker,
              S., Wroclawski, J., and L. Zhang, "Recommendations on
              Queue Management and Congestion Avoidance in the
              Internet", RFC 2309, DOI 10.17487/RFC2309, April 1998,
              <https://www.rfc-editor.org/info/rfc2309>.

   [RFC3246]  Davie, B., Charny, A., Bennet, J., Benson, K., Le Boudec,
              J., Courtney, W., Davari, S., Firoiu, V., and D.
              Stiliadis, "An Expedited Forwarding PHB (Per-Hop
              Behavior)", RFC 3246, DOI 10.17487/RFC3246, March 2002,
              <https://www.rfc-editor.org/info/rfc3246>.

   [RFC3649]  Floyd, S., "HighSpeed TCP for Large Congestion Windows",
              RFC 3649, DOI 10.17487/RFC3649, December 2003,
              <https://www.rfc-editor.org/info/rfc3649>.

   [RFC5681]  Allman, M., Paxson, V., and E. Blanton, "TCP Congestion
              Control", RFC 5681, DOI 10.17487/RFC5681, September 2009,
              <https://www.rfc-editor.org/info/rfc5681>.

   [RFC5706]  Harrington, D., "Guidelines for Considering Operations and
              Management of New Protocols and Protocol Extensions",
              RFC 5706, DOI 10.17487/RFC5706, November 2009,
              <https://www.rfc-editor.org/info/rfc5706>.







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   [RFC7567]  Baker, F., Ed. and G. Fairhurst, Ed., "IETF
              Recommendations Regarding Active Queue Management",
              BCP 197, RFC 7567, DOI 10.17487/RFC7567, July 2015,
              <https://www.rfc-editor.org/info/rfc7567>.

   [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,
              <https://www.rfc-editor.org/info/rfc8033>.

   [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>.

   [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,
              <https://www.rfc-editor.org/info/rfc8290>.

   [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,
              <https://www.rfc-editor.org/info/rfc8312>.

   [SigQ-Dyn]
              Briscoe, B., "Rapid Signalling of Queue Dynamics",
              Technical Report TR-BB-2017-001 arXiv:1904.07044 [cs.NI],
              September 2017, <https://arxiv.org/abs/1904.07044>.

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



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   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 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,
   M, G, u, m, %, ... are assumed to be converted to their appropriate
   multiple or fraction.  A real implementation that wants to use
   integer values needs to handle appropriate scaling factors and allow
   accordingly 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 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:

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

   o  the enqueue function dualpi2_enqueue(lq, cq, pkt) (Figure 3)

   o  the dequeue function dualpi2_dequeue(lq, cq, pkt) (Figure 4)

   o  recur(likelihood) for de-randomized ECN marking (shown at the end
      of Figure 4).

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

   o  the base AQM function that implements the PI algorithm
      dualpi2_update(lq, cq) (Figure 6) used to regularly update the




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      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:

   o  scheduler(), which selects between the head packets of the two
      queues; the choice of scheduler technology is discussed later;

   o  cq.len() or lq.len() returns the current length (aka. backlog) of
      the relevant queue in bytes;

   o  cq.time() or lq.time() returns the current queuing delay (aka.
      sojourn time or service time) of the relevant queue in units of
      time (see Note a);

   o  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 Base 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.

























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   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
   6:
   7:    % PI2 AQM parameters
   8:    RTT_max = 100 ms                      % Worst case RTT expected
   9:    RTT_typ = 15 ms                                   % Typical RTT
   11:   % PI2 constants derived from above PI2 parameters
   10:   p_Cmax = min(1/k^2, 1)             % Max Classic drop/mark prob
   12:   target = RTT_typ            % PI AQM Classic queue delay target
   13:   Tupdate = min(RTT_typ, RTT_max/3)        % PI sampling interval
   14:   alpha = 0.1 * Tupdate / RTT_max^2      % PI integral gain in Hz
   15:   beta = 0.3 / RTT_max               % PI proportional gain in Hz
   16:
   17:   % L4S ramp AQM parameters
   18:   minTh = 475 us        % L4S min marking threshold in time units
   19:   range = 525 us                % Range of L4S ramp in time units
   20:   Th_len = 2 * MTU           % Min L4S marking threshold in bytes
   21:   % L4S constants incl. those derived from other parameters
   22:   p_Lmax = 1                               % Max L4S marking prob
   23:   floor = Th_len / MIN_LINK_RATE
   24:   if (minTh < floor) {
   25:     % Shift ramp so minTh >= serialization time of 2 MTU
   26:     minTh = floor
   27:   }
   28:   maxTh = minTh+range   % L4S max marking threshold in time units
   29: }

       Figure 2: Example Header Pseudocode for DualQ Coupled PI2 AQM

   The overall goal of the code is to maintain the base probability (p',
   p-prime as in Section 2.4), which is an internal variable from which
   the marking and dropping probabilities for L4S and Classic traffic
   (p_L and p_C) are derived, with p_L in turn being derived from p_CL.
   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.









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   1:  dualpi2_enqueue(lq, cq, pkt) { % Test limit and classify lq or cq
   2:    if ( lq.len() + cq.len() + MTU > limit)
   3:      drop(pkt)                     % drop packet if buffer is full
   4:    timestamp(pkt)                  % attach arrival time to packet
   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.len() + cq.len() > 0 )
   3:      if ( scheduler() == lq ) {
   4:        lq.dequeue(pkt)                      % Scheduler chooses lq
   5:        p'_L = laqm(lq.time())                     % Native L4S AQM
   6:        p_L = max(p'_L, p_CL)                  % Combining function
   7:        if ( recur(p_L) )                          % Linear marking
   8:          mark(pkt)
   9:      } else {
   10:       cq.dequeue(pkt)                      % Scheduler chooses cq
   11:       if ( p_C > rand() ) {              % 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(likelihood) {      % Returns TRUE with a certain likelihood
   24:   count += likelihood
   25:   if (count > 1) {
   26:     count -= 1
   27:     return TRUE
   28:   }
   29:   return FALSE
   30: }

      Figure 4: Example Dequeue Pseudocode for DualQ Coupled PI2 AQM





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   When packets arrive, first a common queue limit is checked 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.  This
   assumes that queue delay is measured using the sojourn time technique
   (see Note a for alternatives).

   At lines 5-9, the packet is classified and enqueued to the Classic or
   L4S queue dependent on the least significant bit 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 [I-D.ietf-tsvwg-ecn-l4s-id]).

   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).

   o  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 saw-teeth 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:



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      *  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 13 of
         Figure 2.  It defaults to 16 ms in the reference Linux
         implementation because it has to be rounded to a multiple of 4
         ms).

   o  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:

   o  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.

   o  It uses instantaneous queueing 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).

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

   o  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 18 & 19 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 under-utilization of the
   link (because the amplitude of DCTCP's sawteeth is so small).  Based
   on extensive experiments, for the public Internet a default minimum
   ECN marking threshold of about RTT_typ/30 is recommended.

   A minimum marking threshold parameter (Th_len) in transmission units
   (default 2 MTU) is also necessary to ensure that the ramp does not
   trigger excessive marking on slow links.  The code in lines 24-27 of
   the initialization function (Figure 2) converts 2 MTU into time units



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   and shifts the ramp so that the min threshold is no shallower than
   this floor.

   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

   The coupled marking probability, p_CL depends on the base probability
   (p'), which is kept up to date by the core PI algorithm in Figure 6
   executed 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) and implicitly takes the current queuing
   delay as 0 if the queue is empty.

   The algorithm centres on line 3, which is a classical Proportional-
   Integral (PI) controller that alters p' dependent on: a) the error
   between the current queuing delay (curq) and the target queuing delay
   ('target' - see [RFC8033]); 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 _P_roportional to load
   while the first is the _I_ntegral of the load (so it removes any
   standing queue in excess of the target).

   The two 'gain factors' in line 3, alpha and beta, respectively weight
   how strongly each of these elements ((a) and (b)) alters p'.  They
   are in units of 'per second of delay' or Hz, because they transform




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   differences in queueing 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 smaller Tupdate, p' should change by
   the same amount per second, but in finer more frequent steps.  So
   alpha depends on Tupdate (see line 14 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 13, the update interval should be at least as frequent
   as once per the RTT of a typical flow (RTT_typ) as long as it does
   not exceed roughly RTT_max/3.  For link rates from 4 - 200 Mb/s, a
   target RTT of 15ms and a maximum RTT of 100ms, it has been verified
   through extensive testing that Tupdate=16ms (as recommended in
   [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 over-compensating 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
   (RTT_max).

   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 14 & 15 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 a range of 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



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   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.

   Notes:

   a.  The drain rate of the queue can vary if it is scheduled relative
       to other queues, or to cater for fluctuations in a wireless
       medium.  To auto-adjust to changes in drain rate, the queue must
       be measured in time, not bytes or packets [AQMmetrics] [CoDel].
       Queuing delay could be measured directly by storing a per-packet
       time-stamp as each packet is enqueued, and subtracting this from
       the system time when the packet is dequeued.  If time-stamping 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 [RFC8034]).

   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 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
       algorithms.

       A ramp is more general that 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 4 of Figure 5 because, if minTh is equal to
       maxTh, the condition for this ramp calculation cannot arise.

A.2.  Pass #2: Overload Details

   Figure 7 repeats the dequeue function of Figure 4, but with overload
   details added.  Similarly Figure 8 repeats the core PI algorithm of




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   Figure 6 with overload details added.  The initialization, enqueue,
   L4S AQM and recur functions are unchanged.

   In line 10 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. p_Cmax is the point at which it is
   deemed that the Classic queue has become persistently overloaded, so
   it switches to using drop, even for ECN-capable packets.  ECT packets
   that are not dropped can still be ECN-marked.

   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 coupled to the L4S queue, p_CL will
   always be 100% for any k (by equation (1) in Section 2).  So, for
   readability, the constant p_Lmax is defined as 1 in line 22 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
   [I-D.ietf-tsvwg-ecn-l4s-id] state that, when an L4S congestion
   control detects a drop, it falls back to a response that coexists
   with 'Classic' TCP.  So it is correct that, when the L4S queue drops
   packets, it drops them proportional to p'^2, as if they are Classic
   packets.

   Both these switch-overs are triggered by the tests for overload
   introduced 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.

   Lines 2c to 2d in the core PI algorithm (Figure 8) deal with overload
   of the L4S queue when there is 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 no Classic queue the naive PI
   update function in 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, the test at line 2a of the full PI update function in
   Figure 8 keeps delay on target using drop.  If the test at line 2a of
   finds that the Classic queue is empty, line 2d measures the current



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   queue delay using the L4S queue instead.  While the L4S queue is not
   overloaded, its delay will always be tiny compared to the target
   Classic queue delay.  So p_CL will be driven to zero, and the L4S
   queue will naturally be governed solely by p'_L from the native L4S
   AQM (lines 5 and 6 of the dequeue algorithm in Figure 7).  But, if
   unresponsive L4S source(s) cause overload, the DualQ transitions
   smoothly to L4S marking based on the PI algorithm.  If overload
   increases further, it naturally transitions from marking to dropping
   by the switch-over mechanism already described.

   1:  dualpi2_dequeue(lq, cq, pkt) {     % Couples L4S & Classic queues
   2:    while ( lq.len() + cq.len() > 0 ) {
   3:      if ( scheduler() == lq ) {
   4a:       lq.dequeue(pkt)                             % L4S scheduled
   4b:       if ( p_CL < p_Lmax ) {      % Check for overload saturation
   5:          p'_L = laqm(lq.time())                   % Native L4S AQM
   6:          p_L = max(p'_L, p_CL)                % Combining function
   7:          if ( recur(p_L) )                        % Linear marking
   8a:           mark(pkt)
   8b:       } else {                              % overload saturation
   8c:         if ( p_C > rand() ) {            % 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 ( p_CL > rand() )          % probability p_CL = k * p'
   8i:           mark(pkt)         % linear marking of remaining packets
   8j:       }
   9:      } else {
   10:       cq.dequeue(pkt)                         % Classic scheduled
   11:       if ( p_C > rand() ) {              % 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 Overload Code)






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   1:  dualpi2_update(lq, cq) {                % Update p' every Tupdate
   2a:   if ( cq.len() > 0 )
   2b:     curq = cq.time() %use queuing time of first-in Classic packet
   2c:   else                                      % Classic queue empty
   2d:     curq = lq.time()    % use queuing time of first-in L4S packet
   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 4.1).

   o  A well-understood weighted scheduler such as weighted round robin
      (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.  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.

   o  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 time-shifted 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 50ms.  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;

      *  TS-FIFO is only appropriate if time-stamping of packets is
         feasible;

      *  Even if time-stamping is supported, the sojourn time of the
         head packet is always stale.  For instance, if a burst arrives
         at an empty queue, the sojourn time will only measure the delay



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         of the burst once the burst is over, even though the queue knew
         about it from the start.  At the cost of more operations and
         more storage, a 'scaled sojourn time' metric of queue delay can
         be used, which is the sojourn time of a packet scaled by the
         ratio of the queue sizes when the packet departed and arrived
         [SigQ-Dyn].

   o  A strict priority scheduler would be inappropriate, because it
      would starve Classic if L4S was overloaded.

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) and
   consists of the following five functions:

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

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

   o  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:

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

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

   o  cq.len() or lq.len() returns the current length (aka. backlog) of
      the relevant queue in bytes;





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   o  cq.time() or lq.time() returns the current queuing delay (aka.
      sojourn time or service time) 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; 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
   pseudocode.

   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 categorised 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.














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   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)
   6:
   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
   14:
   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



























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   1:  cred_dequeue(lq, cq, pkt) {       % Couples L4S & Classic queues
   2:    while ( lq.len() + cq.len() > 0 ) {
   3:      if ( scheduler() == lq ) {
   4:        lq.dequeue(pkt)                            % L4S scheduled
   5a:       p_CL = (cq.time() - 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 * qc.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



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   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 time-shifted FIFO scheduler is shown
   at lines 28-33, which would be suitable if simplicity is paramount
   (see Note 2).

   Within each queue, the decision whether to forward, drop or mark is
   taken as follows (to simplify the explanation, it is assumed that
   U=1):

   L4S:  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: ii) marking depends on queuing time,
      not bytes, in order to scale for any link rate without being
      reconfigured; ii) marking of the L4S queue does not depend on
      itself, it depends on the queuing time of the _other_ (Classic)
      queue, where cq.time() is the queuing time of the packet at the
      head of the Classic queue (zero if empty); iii) marking depends on
      the instantaneous queuing time (of the other Classic queue), not a
      smoothed average; 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 excess of the Classic queueing delay qc.time() above
      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 marking probability will linearly increase with queueing
      time.

   Classic:  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



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      queuing time in the Classic queue, where qc.time() is the current
      instantaneous queueing time of the Classic queue and gamma is the
      EWMA constant (default 1/32, see line 12 of the initialization
      function).

      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 & 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 TCP 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 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 required.

   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 1ms at 60Mb/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 respectively for
   its recommended setting and guidance on alternatives).




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   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.

   Notes:

   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
       rapidly.

   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 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



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   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 16-21 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.len() + cq.len() > 0 ) {
   3:      if ( scheduler() == lq ) {
   4:        lq.dequeue(pkt)                            % L4S scheduled
   5:        if ((lq.time() > T) OR (cq.ns() >> (S_L-2) > maxrand(U)))
   6:          mark(pkt)
   7:      } else {
   8:        cq.dequeue(pkt)                        % Classic scheduled
   9:        Q_C += (cq.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 Coupled DualQ 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
   lines 5 and 10 queuing times cq.ns() and pkt.ns() are returned in



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   integer nanoseconds, making the values about 2^30 times larger than
   when the units were seconds, ii) then in lines 3 and 9 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 the division needed to weight the moving average can be
   implemented by a right bit-shift (>> g_C).

Appendix C.  Guidance on Controlling Throughput Equivalence

                     +---------------+------+-------+
                     | RTT_C / RTT_L | Reno | Cubic |
                     +---------------+------+-------+
                     |             1 | k'=1 | k'=0  |
                     |             2 | k'=2 | k'=1  |
                     |             3 | k'=2 | k'=2  |
                     |             4 | k'=3 | k'=2  |
                     |             5 | k'=3 | k'=3  |
                     +---------------+------+-------+

    Table 1: Value of k' for which DCTCP throughput is roughly the same
               as Reno or Cubic, for some example RTT ratios

   k' is related to k in Equation (1) (Section 2.1) by k=2^k'.

   To determine the appropriate policy, the operator first has to judge
   whether it wants DCTCP flows to have roughly equal throughput with
   Reno or with Cubic (because, even in its Reno-compatibility mode,
   Cubic is about 1.4 times more aggressive than Reno).  Then the
   operator needs to decide at what ratio of RTTs it wants DCTCP and
   Classic flows to have roughly equal throughput.  For example choosing
   k'=0 (equivalent to k=1) will make DCTCP throughput roughly the same
   as Cubic, _if their RTTs are the same_.

   However, even if the base RTTs are the same, the actual RTTs are
   unlikely to be the same, because Classic (Cubic or Reno) traffic
   needs a large queue to avoid under-utilization and excess drop,
   whereas L4S (DCTCP) does not.  The operator might still choose this
   policy if it judges that DCTCP throughput should be rewarded for
   keeping its own queue short.

   On the other hand, the operator will choose one of the higher values
   for k', if it wants to slow DCTCP down to roughly the same throughput
   as Classic flows, to compensate for Classic flows slowing themselves
   down by causing themselves extra queuing delay.




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   The values for k' in the table are derived from the formulae, which
   was developed in [DCttH15]:

       2^k' = 1.64 (RTT_reno / RTT_dc)                  (2)
       2^k' = 1.19 (RTT_cubic / RTT_dc )                (3)

   For localized traffic from a particular ISP's data centre, using the
   measured RTTs, it was calculated that a value of k'=3 (equivalant to
   k=8) would achieve throughput equivalence, and experiments verified
   the formula very closely.

   For a typical mix of RTTs from local data centres and across the
   general Internet, a value of k'=1 (equivalent to k=2) is recommended
   as a good workable compromise.

Authors' Addresses

   Koen De Schepper
   Nokia Bell Labs
   Antwerp
   Belgium

   Email: koen.de_schepper@nokia.com
   URI:   https://www.bell-labs.com/usr/koen.de_schepper


   Bob Briscoe (editor)
   CableLabs
   UK

   Email: ietf@bobbriscoe.net
   URI:   http://bobbriscoe.net/


   Greg White
   CableLabs
   Louisville, CO
   US

   Email: G.White@CableLabs.com











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