Transport Area working group (tsvwg)                      K. De Schepper
Internet-Draft                                           Nokia Bell Labs
Intended status: Experimental                            B. Briscoe, Ed.
Expires: April 25, May 8, 2019                                           CableLabs
                                                           O. Bondarenko
                                                     Simula Research Lab
                                                                I. Tsang
                                                        October 22,
                                                       November 04, 2018

  DualQ Coupled AQMs for Low Latency, Low Loss and Scalable Throughput


   Data Centre TCP (DCTCP) was designed

   The Low Latency Low Loss Scalable Throughput (L4S) architecture
   allows data flows over the public Internet to provide predictably low achieve
   ultra-low queuing latency, near-zero loss, generally zero congestion loss and scaling
   of per-flow throughput scalability using
   explicit without the problems of traditional TCP.  To
   achieve this, L4S data flows use a 'scalable' congestion notification (ECN) control
   similar to Data Centre TCP (DCTCP) and an extremely simple
   marking behaviour on switches. a form of Explicit Congestion
   Notification (ECN) with modified behaviour.  However, DCTCP does until now,
   scalable congestion controls did not co-exist with existing TCP traffic---DCTCP is Reno/
   Cubic traffic---scalable controls are so aggressive that existing 'Classic'
   TCP algorithms approach drive themselves to starvation.  So,  Therefore, until now, DCTCP
   L4S controls could only be deployed where a clean-slate environment
   could be arranged, such as in private data centres. centres (hence the name
   DCTCP).  This specification defines `DualQ Coupled Active Queue
   Management (AQM)' to allow (AQM)', which enables these scalable congestion controls
   like DCTCP
   to safely co-exist with classic Classic Internet traffic.

   The Coupled AQM ensures that a flow runs at about the same rate
   whether it uses DCTCP or TCP Reno/Cubic, but Reno/Cubic.  It achieves this
   indirectly, without inspecting having to inspect transport layer flow identifiers.
   identifiers, When tested in a residential broadband setting, DCTCP achieved
   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 eliminates network configuration.

Status of This Memo

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Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   3
     1.1.  Problem and Scope . . . . . . . . . . . . . . . . . . . .   3
     1.2.  Terminology . . . . . . . . . . . . . . . . . . . . . . .   5
     1.3.  Features  . . . . . . . . . . . . . . . . . . . . . . . .   6
   2.  DualQ Coupled AQM . . . . . . . . . . . . . . . . . . . . . .   7
     2.1.  Coupled AQM . . . . . . . . . . . . . . . . . . . . . . .   7   8
     2.2.  Dual Queue  . . . . . . . . . . . . . . . . . . . . . . .   8   9
     2.3.  Traffic Classification  . . . . . . . . . . . . . . . . .   8   9
     2.4.  Overall DualQ Coupled AQM Structure . . . . . . . . . . .   9  10
     2.5.  Normative Requirements for a DualQ Coupled AQM  . . . . .  11  12
       2.5.1.  Functional Requirements . . . . . . . . . . . . . . .  11  12  Requirements in Unexpected Cases  . . . . . . . .  13
       2.5.2.  Management Requirements . . . . . . . . . . . . . . .  14  15
   3.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  15  16
   4.  Security Considerations . . . . . . . . . . . . . . . . . . .  15  16
     4.1.  Overload Handling . . . . . . . . . . . . . . . . . . . .  15  16
       4.1.1.  Avoiding Classic Starvation: Sacrifice L4S Throughput
               or Delay? . . . . . . . . . . . . . . . . . . . . . .  15  17
       4.1.2.  Congestion Signal Saturation: Introduce L4S Drop or
               Delay?  . . . . . . . . . . . . . . . . . . . . . . .  16  18
       4.1.3.  Protecting against Unresponsive ECN-Capable Traffic .  17  19
   5.  Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .  18  19
   6.  References  . . . . . . . . . . . . . . . . . . . . . . . . .  18  20
     6.1.  Normative References  . . . . . . . . . . . . . . . . . .  18  20
     6.2.  Informative References  . . . . . . . . . . . . . . . . .  18  20
   Appendix A.  Example DualQ Coupled PI2 Algorithm  . . . . . . . .  21  23
     A.1.  Pass #1: Core Concepts  . . . . . . . . . . . . . . . . .  21  23
     A.2.  Pass #2: Overload Details . . . . . . . . . . . . . . . .  27  30
   Appendix B.  Example DualQ Coupled Curvy RED Algorithm  . . . . .  30  33
   Appendix C.  Guidance on Controlling Throughput Equivalence . . .  36  39
   Appendix D.  Open Issues  . . . . . . . . . . . . . . . . . . . .  37  40
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  38  41

1.  Introduction

1.1.  Problem and Scope

   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.

   The Diffserv architecture provides Expedited Forwarding [RFC3246], so
   that low latency traffic can jump the queue of other traffic.
   However, on access links dedicated to individual sites (homes, small
   enterprises or mobile devices), often all traffic at any one time
   will be latency-sensitive and, if all the traffic on a link is marked
   as EF, Diffserv cannot reduce the delay of any of it.  In contrast,
   the Low Latency Low Loss Scalable throughput (L4S) approach removes
   the causes of any unnecessary queuing delay.

   The bufferbloat project has shown that excessively-large buffering
   (`bufferbloat') has been introducing significantly more delay than
   the underlying propagation time.  These delays appear only
   intermittently--only when a capacity-seeking (e.g.  TCP) flow is long
   enough for the queue to fill the buffer, making every packet in other
   flows sharing the buffer sit through the queue.

   Active queue management (AQM) was originally developed to solve this
   problem (and others).  Unlike Diffserv, which gives low latency to
   some traffic at the expense of others, AQM controls latency for _all_
   traffic in a class.  In general, AQMs introduce an increasing level
   of discard from the buffer the longer the queue persists above a
   shallow threshold.  This gives sufficient signals to capacity-seeking
   (aka. greedy) flows to keep the buffer empty for its intended
   purpose: absorbing bursts.  However, RED [RFC2309] and other
   algorithms from the 1990s were sensitive to their configuration and
   hard to set correctly.  So, AQM was not widely deployed. deployed in the 1990s.

   More recent state-of-the-art AQMs, e.g. fq_CoDel [RFC8290],
   PIE [RFC8033], Adaptive RED [ARED01], are easier to configure,
   because they define the queuing threshold in time not bytes, so it is
   invariant for different link rates.  However, no matter how good the
   AQM, the sawtoothing rate of TCP will either cause queuing delay to
   vary or cause the link to be under-utilized.  Even with a perfectly
   tuned AQM, the additional queuing delay will be of the same order as
   the underlying speed-of-light delay across the network.  Flow-queuing
   can isolate one flow from another, but it cannot isolate a TCP flow
   from the delay variations it inflicts on itself, and it has other
   problems - it overrides the flow rate decisions of variable rate
   video applications, it does not recognise the flows within IPSec VPN
   tunnels and it is relatively expensive to implement.

   It seems that further changes to the network alone will now yield
   diminishing returns.  Data Centre TCP (DCTCP [RFC8257]) teaches us
   that a small but radical change to TCP is needed to cut two major
   outstanding causes of queuing delay variability:

   1.  the `sawtooth' varying rate of TCP itself;

   2.  the smoothing delay deliberately introduced into AQMs to permit
       bursts without triggering losses.

   The former causes a flow's round trip time (RTT) to vary from about 1
   to 2 times the base RTT between the machines in question.  The latter
   delays the system's response to change by a worst-case
   (transcontinental) RTT, which could be hundreds of times the actual
   RTT of typical traffic from localized CDNs.

   Latency is not our only concern:

   3.  It was known when TCP was first developed that it would not scale
       to high bandwidth-delay products. products [TCP-CA].

   Given regular broadband bit-rates over WAN distances are
   already [RFC3649] beyond the scaling range of `classic' TCP Reno,
   `less unscalable' Cubic [RFC8312] and
   Compound [I-D.sridharan-tcpm-ctcp] variants of TCP have been
   successfully deployed.  However, these are now approaching their
   scaling limits.  Unfortunately, fully scalable TCPs such as DCTCP
   cause `classic' TCP to starve itself, which is why they have been
   confined to private data centres or research testbeds (until now).

   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.  The AQM is not like
   flow-queuing approaches [RFC8290] that classify packets by flow
   identifier into numerous separate queues in order to isolate sparse
   flows from the higher latency in the queues assigned to heavier flow.
   flows.  In contrast, the AQM exploits the behaviour of scalable
   congestion controls like DCTCP so that every packet in every flow
   sharing the queue for DCTCP-like traffic can be served with very low

   This AQM extension can be combined with any AQM designed for a single
   queue AQM that generates a statistical or deterministic mark/drop
   probability driven by the queue dynamics.  In many cases it
   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.

   The overall L4S architecture is described [I-D.ietf-tsvwg-l4s-arch] gives more
   detail, including on wider deployment aspects such as coexistence 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

1.2.  Terminology

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   document are to be interpreted as described in [RFC2119].  In this
   document, these words will appear with that interpretation [RFC2119] when, and
   only when when, they appear in ALL CAPS.  Lower case uses of these words are not to be
   interpreted all capitals, as carrying RFC-2119 significance. 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 DCTCP (e.g.  DCTCP [RFC8257], Relentless [Mathis09]).

   Either service can cope with a
      TCP [Mathis09], the L4S variant of SCREAM for real-time
      media {ToDo: ref}).  For the public Internet a scalable control
      has to comply with the requirements in [I-D.ietf-tsvwg-ecn-l4s-id]
      (aka. the 'TCP Prague requirements').

   Either service can cope with a proportion of unresponsive or less-
   responsive traffic as well well, as long (e.g.  DNS, VoIP, game sync
   datagrams, etc), just as a single queue AQM can. 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.

1.3.  Features

   The AQM couples marking and/or dropping across the two queues such
   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 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.  Typical
   experiments used base round trip delays up to 100ms between the data
   centre and home network, and large amounts of background traffic in
   both queues.  For every L4S packet, the AQM kept the average queuing
   delay below 1ms (or 2 packets if serialization delay is bigger for
   slow links), and no losses at all were introduced by the AQM.
   Details of the extensive experiments will be made are available [PI2] [DCttH15].

   Subjective testing was also conducted by multiple people all
   simultaneously using a very demanding panoramic
   interactive video application run high bandwidth low latency
   applications over a stack with DCTCP enabled and
   deployed on the testbed.  Each 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.  Even though the  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 their the
   user's finger on the touchpad (all 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). latency.  With
   an alternative AQM, the video noticeably lagged behind the finger gestures.
   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 like DCTCP 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
   Classic traffic does not suffer when a proportion of the traffic is
   L4S.  The two queues are only necessary because DCTCP-like flows
   cannot keep latency predictably low and keep utilization high if they
   are mixed with legacy TCP flows,

   The experiments used the Linux implementation of DCTCP that is
   deployed in private data centres, without any modification despite
   its known deficiencies.  Nonetheless, certain modifications will be
   necessary before DCTCP is safe to use on the Internet, which are
   recorded in Appendix A of [I-D.ietf-tsvwg-ecn-l4s-id].  However, the
   focus of this specification is to get the network service in place.
   Then, without any management intervention, applications can exploit
   it by migrating to scalable controls like DCTCP, which can then
   evolve _while_ their benefits are being enjoyed by everyone on the

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 (e.g.  DCTCP) flows (that satisfy the
      TCP Prague 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.

   We focus on Reno as the worst case, because if we do not harm Reno,
   we will not harm Cubic.  Nonetheless, TCP Cubic implements a Reno-compatibility Reno-
   compatibility mode, which is the only relevant mode for typical RTTs
   under 20ms as long as the throughput of a single flow is less than
   about 500Mb/s.  Therefore it can be assumed that Cubic traffic
   behaves similarly to Reno (but with a slightly different constant of proportionality), and the
   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
   like this, so the term 'L4S' traffic will be used for all similar

   In order to make

   For safe co-existence, under stationary conditions, a DCTCP flow has
   to run at roughly the same rate as a Reno TCP flow (all other factors
   being equal), 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 (in contrast p_L.  [RFC8311] updates the original ECN specification
   [RFC3168] to RFC3168
   which requires allow these probabilities to be distinct, because RFC
   3168 required them to be the same).  To same.

   Also, to remain stable, Classic
   traffic needs p_C sources need the network to change smooth
   p_C so it changes relatively slowly, whereas slowly.  In contrast, L4S traffic
   needs avoids
   smoothing in the network, because it delays all signals for a worst-
   case RTT.  So instead, L4S sources smooth the ECN marking probability
   themselves, so they expect the network to be controlled rapidly by generate ECN marks with a
   probability p_L that track tracks the instantaneous unsmoothed queue.  It is necessary to make the Classic

   The Coupled AQM achieves safe coexistence by making the Classic drop
   probability p_C proportional to the square of a variable we shall
   call p_CL, which 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 it squares the squaring of
   p_CL counterbalances the square root of p_C in the Reno rate equation to make it proportional
   to the smoothed value of p_L used in the DCTCP rate equation. Classic 'TCP

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

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

   where k is the constant of proportionality. proportionality, which we shall call the
   coupling factor.

2.2.  Dual Queue

   Classic traffic typically builds a large queue to prevent under-
   utilization.  Therefore a separate queue is provided for L4S traffic,
   and it is scheduled with priority over Classic.  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
   Classic flows to each get equivalent throughput to DCTCP flows (all
   other factors such as RTT being equal).  The algorithm achieves this
   without having to inspect flow identifiers.

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 draft
   specification [I-D.ietf-tsvwg-ecn-l4s-id] recommends using requires the sender to use
   the ECT(1) codepoint 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, the classifier device MUST NOT alter the ECN field,
   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, other identifiers could be used to classify certain
   additional packet types into the L queue, that are deemed not to risk
   harming 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 DualQ Coupled AQM mechanism only reads these classifiers, it MUST NOT re-mark re-
   mark or alter these identifiers (except for marking the ECN field
   with the CE codepoint - with increasing frequency to indicate
   increasing congestion).

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
   likelihood of marking or dropping (p_L and p_C).  It has been
   proved [PI2] that it is preferable to control TCP load with a linear PI
   controller, then square the output before applying it as a drop
   probability to TCP. 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 we get our the slow-moving input to ECN marking in the L queue as: (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.  Substituting for p'
   from equation (3) into (2):

      p_C = ( p_CL / k )^2.

   The actual probability p_L that we apply to the L queue needs to
   track the immediate L queue delay, as well as track p_CL under
   stationary conditions.  So we use a native AQM in the L queue that
   calculates a marking probability p'L p'_L as a function of the instantaneous L
   queue.  And, given the L queue has conditional strict priority over
   the C queue, whenever the L queue grows, we should apply marking
   probability p'_L, but p_L should not fall below p_CL.  This suggests:

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

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

   This allows p_L to be coupled to p_C by marking L4S traffic
   proportionately to the intermediate output from the first stage.
   Specifically, the output of the base AQM is coupled across to the L
   queue in proportion to the output of the base AQM

                                  | |    ,------.
                        L4S queue | |===>| ECN  |
                       ,'| _______|_|    |marker|\
                     <'  |         |     `------'\\
                      //`'         v        ^ p_L \\
                     //       ,-------.     |      \\
                    //        |Native |p'L |p'_L |       \\,.
                   //         |  L4S  |-->(MAX)  |--->(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
   we call it just PI2 [PI2].  PI2 is a principled simplification of PIE
   that is both more responsive and more stable in the face of
   dynamically varying load.

   Curvy RED is derived from RED [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 attention than Curvy RED,
   leaving the Curvy RED design incomplete and not so fully evaluated.

   Both AQMs regulate their queue in units of time not 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

   In the

   A Dual Queue, L4S packets Queue Coupled AQM implementation MUST utilize two queues, each
   with an AQM algorithm.  The two queues can be given part of a larger
   queuing hierarchy [I-D.briscoe-tsvwg-l4s-diffserv].

   The AQM algorithm for the low latency (L) queue MUST apply ECN

   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.

   Whatever identifier is used for L4S experiments,

   [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
   prevent starvation of Classic traffic by 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)."  In
   other words, in any DualQ Coupled AQM, the power to which p_L is
   raised in Eqn. (1) MUST be 2.
   The term 'likelihood' is used to allow for marking and dropping to be
   either probabilistic or deterministic.

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

   {ToDo: The requirements for scalable congestion controls on the
   Internet (termed the TCP Prague requirements)
   [I-D.ietf-tsvwg-ecn-l4s-id] are not necessarily final.  If the
   aggressiveness of DCTCP is not defined as the benchmark for scalable
   controls on the Internet, the recommended value of k will also be
   subject to change.}

   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 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 users.
   However, on the public Internet, access network operators typically
   isolate customers from each other with some form of layer-2
   multiplexing (TDM (OFDM(A) in DOCSIS, DOCSIS3.1, CDMA in 3G) 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 L4S, and it
   will not affect the relative throughput of small flows.  Requirements in Unexpected Cases

   The flexibility to allow operator-specific classifiers (Section 2.3)
   leads to the need to specify what the AQM in each queue ought to do
   with packets that do not carry the ECN field expected for that queue.
   It is 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:

      *  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

         +  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').

   If the DualQ Coupled AQM has detected overload, it will signal
   congestion solely using drop, irrespective of the ECN field.

   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.

2.5.2.  Management Requirements

   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:

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

   o  Expected typical RTT (a parameter for typical or target queuing
      delay in each queue might be configurable instead); instead; if so it MUST
      be expressed in units of time);

   o  Expected maximum RTT (a stability parameter that depends on
      maximum RTT might be configurable instead);

   o  Coupling factor, k;

   o  The limit to the conditional priority of L4S (scheduler-dependent,
      e.g. the scheduler weight for WRR, or the time-shift for time-
      shifted FIFO);

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

   An experimental DualQ Coupled AQM SHOULD allow the operator to
   monitor each of the following operational statistics:

   o  Bits forwarded (total and statistics on demand, per
   queue and per configurable sample interval), interval, for performance
   monitoring and perhaps also for accounting in some cases:

   o  Bits forwarded, from which utilization can be calculated

   o  Q delay (per queue over sample interval) {ToDo: max per interval,
      histogram with configurable edges (from which percentile(s) can be
      derived), not incl. medium access delay} calculated;

   o  Total packets arriving, enqueued and dequeued (per queue per
      sample interval) to distinguish tail
      discard from proactive AQM discard;

   o  ECN packets marked, non-ECN packets dropped, ECN packets dropped
      (per queue per sample interval), dropped,
      from which marking and dropping probabilities can be calculated calculated;

   o  Time and duration  Queue delay (not including serialization delay of each overload event.

   The 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 for variables like Q delay (mean, percentiles, etc.) will depend on
      implementation constraints.

3.  IANA Considerations

   This specification contains no IANA considerations.

4.  Security Considerations

4.1.  Overload Handling

   Where the interests  To facilitate comparative evaluation
      of users or flows might conflict, it could be
   necessary different implementations and approaches, an implementation
      SHOULD allow mean and 99th percentile queue delay to police traffic be derived
      (per queue per sample interval).  A relatively simple way to isolate 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.

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

   o  Start-time and duration of overload state.

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

   [RFC5706] suggests that deployment, coexistence and scaling should
   also be covered as management requirements.  The raison d'etre of the
   DualQ Couple 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, these motivating issues are explained in the Introduction
   and detailed in the L4S architecture [I-D.ietf-tsvwg-l4s-arch].
   Also, 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
   below that each relax a different factor: e.g. throughput, delay,
   drop.  Some of these  These choices might need to be determined made either by operator
   policy the developer or by the developer,
   operator policy, rather than by the IETF. {ToDo: Reach
   consensus on which it is to be in each case.}

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

   Priority of L4S is required to be conditional to avoid total
   throughput 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 to guarantee a minimum throughput
      service for Classic traffic.  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 a large part of the capacity set aside for L4S, using
      WRR could significantly reduce the capacity left for any
      responsive L4S flows.

   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
      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 implementation in Appendix A can implement 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, but even though saturation can 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, 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. required [DualQ-Test].

   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 only 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 and Gabi Bracha for
   detailed review comments particularly of the appendices and
   suggestions on how to make our explanation clearer.  Thanks also to
   Greg White for improving the normative requirements and both Greg and
   Tom Henderson for insights on the choice of schedulers
   and schedulers, queue delay
   measurement techniques.

   The authors' contributions were originally 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.

6.  References

6.1.  Normative References

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

6.2.  Informative References

   [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,

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

              Briscoe, B., "Insights from Curvy RED (Random Early
              Detection)", BT Technical Report TR-TUB8-2015-003, July

   [DCttH15]  De Schepper, K., Bondarenko, O., Briscoe, B., and I.
              Tsang, "`Data Centre to the Home': Ultra-Low Latency for
              All", 2015, <

              (Under submission)

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

              Briscoe, B., "Interactions between Low Latency, Low Loss,
              Scalable Throughput (L4S) and Differentiated Services",
              draft-briscoe-tsvwg-l4s-diffserv-00 (work in progress),
              March 2018.

              Schepper, K., Briscoe, B., and I. Tsang, "Identifying
              Modified Explicit Congestion Notification (ECN) Semantics
              for Ultra-Low Queuing Delay", draft-ietf-tsvwg-ecn-l4s-
              id-02 (work in progress), March 2018.

              Briscoe, B., Schepper, K., and M. Bagnulo, "Low Latency,
              Low Loss, Scalable Throughput (L4S) Internet Service:
              Architecture", draft-ietf-tsvwg-l4s-arch-02 (work in
              progress), March 2018.

              Sridharan, M., Tan, K., Bansal, D., and D. Thaler,
              "Compound TCP: A New TCP Congestion Control for High-Speed
              and Long Distance Networks", draft-sridharan-tcpm-ctcp-02
              (work in progress), November 2008.

              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,
              (videos of demos:
              dctth/#1511dispatchwg )>.

              Mathis, M., "Relentless Congestion Control", PFLDNeT'09 ,
              May 2009, <

   [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.

   [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,

              (To appear)

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

   [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,

   [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,

   [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,

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

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

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

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

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

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

   [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, <>.

   [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,

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

   [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,

   [TCP-CA]   Jacobson, V. and M. Karels, "Congestion Avoidance and
              Control", Laurence Berkeley Labs Technical Report ,
              November 1988, <>.

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 step threshold (in units of queuing
   time) is used for the Native L4S AQM, but a ramp is also described as
   an alternative.  And the PI2 algorithm [PI2] is used for the Classic
   AQM.  PI2 is an improved variant of the PIE AQM [RFC8033].

   We will introduce the pseudocode 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.

   A full open source implementation for Linux is available at:

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 four five functions:

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

   o  enqueue code (Figure 3)

   o  dequeue code (Figure 4)

   o  a ramp function (Figure 5) used to calculate the ECN-marking
      probability for the L4S queue

   o  code to regularly update the base probability (p) used in the
      dequeue code (Figure 5). 6).

   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

   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]).

   In our 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.  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

   1:  dualpi2_params_init(...) {         % Set input parameter defaults
   2:    % PI2 AQM parameters
   3:    target = 15 ms              % PI AQM Classic queue delay target
   4:    Tupdate = 16 ms            % PI Classic queue sampling interval
   5:    alpha = 10 Hz^2                              % PI integral gain
   6:    beta = 100 Hz^2                          % PI proportional gain
   7:    p_Cmax = 1/4                       % Max Classic drop/mark prob
   8:    % Constants derived from PI2 AQM parameters
   9:    alpha_U = alpha *Tupdate % PI integral gain per update interval
   10:   beta_U = beta * Tupdate  % PI prop'nal gain per update interval
   12:   % DualQ Coupled framework parameters
   13:   k = 2                                         % Coupling factor
   14:   % scheduler weight or equival't parameter (scheduler-dependent)
   15:   limit = MAX_LINK_RATE * 250 ms               % Dual buffer size
   17:   % L4S ramp AQM parameters
   18:   T_time   minTh = 1 ms 475 us        % L4S min marking threshold in time units
   19:   T_len   range = 525 us                % Range of L4S ramp in time units
   20:   Th_len = 2 * MTU           % Min L4S marking threshold in bytes
   21:   % Constants derived from L4S AQM parameters
   22:   p_Lmax = min(k*sqrt(p_Cmax), 1)          % Max L4S marking prob
   23:   floor = Th_len * 8 / MIN_LINK_RATE   % MIN_LINK_RATE is in Mb/s
   24:   if (minTh < floor) {
   25:     % Adjust ramp to exceed serialization time of 2 MTU
   26:     range = max(range - (floor-minTh), 1)   % 1us avoids /0 error
   27:     minTh = floor
   28:   }
   29:   maxTh = minTh+range   % L4S min marking threshold in time units
   30: }

       Figure 2: Example Header Pseudocode for DualQ Coupled PI2 AQM

   For brevity the pseudocode shows some parameters in units of
   microseconds (us), but a real implementation would probably use

   The overall goal of the code is to maintain the base probability (p),
   which is an internal variable from which the marking and dropping
   probabilities for L4S and Classic traffic (p_L and p_C) are derived.
   The variable named p in the pseudocode and in this walk-through is
   the same as p' (p-prime) in Section 2.4.  The probabilities p_L and
   p_C are derived in lines 3, 4 and 5 of the dualpi2_update() function
   (Figure 5) 6) then used in the dualpi2_dequeue() function (Figure 4).
   The code walk-through below builds up to explaining that part of the
   code eventually, but it starts from packet arrival.

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

   {ToDo: Generalize 5-7 for any L AQM (see email to Tom 9-Aug-18)}
   5:        if ( ((lq.time() > T_time)        p'_L = laqm(lq.time())                     % step marking ... Native L4S AQM
   6:              AND (lq.len() > T_len))        p_L = max(p'_L, p_CL)                  % Combining function
   7:            OR (p_CL        if ( p_L > rand()) rand() )                        % ...or linear 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: }

      Figure 4: Example Dequeue Pseudocode for DualQ Coupled PI2 AQM

   When packets arrive, first a common queue limit is checked as shown
   in line 2 of the enqueuing pseudocode in Figure 3.  Note that the
   limit is deliberately tested before enqueue to avoid any bias against
   larger packets (so depending whether the implementation stores a
   packet while testing whether to drop it from the tail, it might be
   necessary for the actual buffer memory to be one MTU larger than

   Line 2 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).

   Returning to the shared buffer case, if limit is not exceeded, the
   packet will be classified and enqueued to the Classic or L4S queue
   dependent on the least significant bit of the ECN field in the IP
   header (line 5).  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 very sloppy.

   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, lines 5 to 7 and 8 mark ECN-mark the packet
      either the L4S threshold (T_time) is exceeded, or if a random marking decision is drawn according to p_L.  Line 6
      calculates p_L as the maximum of the coupled L4S probability p_CL (maintained by
      and the
      dualpi2_update() function discussed below). probability from the native L4S AQM p'_L.  This logical 'OR' on
      a per-packet basis implements
      the max() function shown in Figure 1 to couple the outputs of the
      two AQMs together.  The L4S threshold  Of the two probabilities input to p_L in line

      *  p'_L is usually calculated per packet in units of time (default T_time = 1 ms).  However, on
      slow links line 5 by the packet serialization time can approach the
      threshold T_time, so line 6 sets a floor of T_len (=2 MTU) to the
      threshold, otherwise marking laqm() function
         (see Figure 5),

      *  whereas p_CL is always too frequent on slow links. maintained by the dualpi2_update() function
         which runs every Tupdate (default 16ms) (see Figure 2).

   o  If a Classic packet is scheduled, lines 10 to 17 drop or mark the
      packet based on the squared probability p_C.

   There is some concern that using a step function for the

   The Native L4S AQM requires end-systems to smooth the signal for a lot longer -
   until its fidelity algorithm (Figure 5) is sufficient.  The latency benefits of a ramp are
   being investigated as a simple alternative to the step.  This ramp
   would be function, similar
   to the RED algorithm, with but simpler due to the following differences:

   o  The min and max of the ramp are 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 without to remove smoothing (smoothing delay
      (L4S senders smooth incoming ECN feedback when necessary).

   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 done no need
      to keep ECN marking probability low.

   o  Marking does not have to be randomized.  Determinism is being
      experimented with instead of randomness; to reduce the delay
      necessary to smooth out the noise of randomness from the signal.
      In this case, for each packet, the algorithm would accumulate p_L
      in a counter and mark the packet that took the counter over 1,
      then subtract 1 from the counter and continue.

   This 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 the parameter initialization code in
   Figure 2.  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 23-28 of Figure 2 converts 2 MTU into time units and adjusts
   the ramp thresholds to be no shallower than this floor.

   An operator can effectively turn the ramp into a step function, as
   used by DCTCP, by setting the range to its minimum value (e.g. 1 ns).
   Then the condition for the end-systems).

   o  Determinism ramp calculation will hardly ever arise.
   There is being experimented with instead some concern that using the step function of randomness; to
      reduce DCTCP for the delay necessary
   Native L4S AQM requires end-systems to smooth out the noise signal for an
   unnecessarily large number of randomness
      from the signal.  For each packet, the algorithm would accumulate
      p'_L in a counter and mark the packet that took the counter over
      1, then subtract 1 from the counter and continue.

   o  The ramp rises linearly directly from 0 round trips to 1, not ensure sufficient
   fidelity.  A ramp seems to be no worse than a an
      intermediate value of p'_L as RED would, because there step in initial
   experiments with existing DCTCP.  Therefore, it is no need
      to keep ECN marking probability low.

   This recommended that a
   ramp algorithm would require two configuration parameters (min
   and max threshold is configured in units place of queuing time), in contrast a step, which will allow congestion
   control algorithms to the
   single parameter of investigate faster smoothing algorithms.

   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 would use a step. bit-shift
   6:    else
   7:      return 0
   8:  }

            Figure 5: Example Pseudocode for the Native L4S AQM

   1:  dualpi2_update(lq, cq, target) {         % Update p every Tupdate
   2:    curq = cq.time()  % use queuing time of first-in Classic packet
   3:    p = p + alpha_U * (curq - target) + beta_U * (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 5: 6: Example PI-Update Pseudocode for DualQ Coupled PI2 AQM


   p_CL depends on the base probability (p) (p), which is kept up to date by
   the core PI algorithm in Figure 5, which is 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 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_U and beta_U, 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 differences in queueing delay into changes in probability.

   alpha_U and beta_U are derived from the input parameters alpha and
   beta (see lines 5 and 6 of Figure 2).  These recommended values of
   alpha and beta come from the stability analysis in [PI2] so that the
   AQM can change p as fast as possible in response to changes in load
   without over-compensating and therefore causing oscillations in the

   alpha and beta determine how much p ought to change if it was updated
   every second.  It is best to update p as frequently as possible, but
   the update interval (Tupdate) will probably be constrained by
   hardware performance.  For link rates from 4 - 200 Mb/s, we found
   Tupdate=16ms (as recommended in [RFC8033]) is sufficient.  However
   small the chosen value of Tupdate, p should change by the same amount
   per second, but in finer more frequent steps.  So the gain factors
   used for updating p in Figure 5 6 need to be scaled by (Tupdate/1s),
   which is done in lines 9 and 10 of Figure 2).  The suffix '_U'
   represents 'per update time' (Tupdate).

   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 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, which is necessary to ensure that
   Classic TCP and DCTCP controls have the same stability.  So, if alpha
   is 10 Hz^2, the effective gain factor for the L4S queue is k*alpha,
   which is 20 Hz^2 with the default coupling factor of k=2.

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

   {ToDo: Scaling beta with Tupdate and scaling both alpha & beta with

A.2.  Pass #2: Overload Details

   Figure 6 7 repeats the dequeue function of Figure 4, but with overload
   details added.  Similarly Figure 7 8 repeats the core PI algorithm of
   Figure 5 6 with overload details added.  The initialization and initialization, enqueue
   and L4S AQM functions are unchanged.

   In line 7 of the initialization function (Figure 2), the default
   maximum Classic drop probability p_Cmax = 1/4 or 25%. This is the
   point at which it is deemed that the Classic queue has become
   persistently overloaded, so it switches to using solely drop, even
   for ECN-capable packets.  This protects the queue against any
   unresponsive traffic that falsely claims that it is responsive to ECN
   marking, as required by [RFC3168] and [RFC7567].

   Line 21 22 of the initialization function translates this into a maximum
   L4S marking probability (p_Lmax) by rearranging Equation (1).  With a
   coupling factor of k=2 (the default) or greater, this translates to a
   maximum L4S marking probability of 1 (or 100%).  This is intended to
   ensure that the L4S queue starts to introduce dropping once marking
   saturates and can rise no further.  The 'TCP Prague' 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 the L4S queue drops
   packets 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 6). 7).
   Lines 8c to 8g drop L4S packets with probability p^2.  Lines 8h to 8i
   mark the remaining packets with probability p_CL.  If p_Lmax = 1,
   which is the suggested default configuration, 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 7) 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
   algorithm in Figure 5 6 drops nothing, even if the L4S queue is
   overloaded - so tail drop would have to take over (lines 3 and 4 of
   Figure 3).

   If the test at line 2a finds that the Classic queue is empty, line 2d
   measures the current 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_L will be driven to
   zero, and the L4S queue will naturally be governed solely by
   threshold marking (lines 5 and 6 of the dequeue algorithm in
   Figure 6). 7).  But, if unresponsive L4S source(s) cause overload, the
   DualQ transitions smoothly to L4S marking based on the PI algorithm.
   And as overload increases, it naturally transitions from marking to
   dropping by the switch-over mechanism already described.

   1:  dualpi2_dequeue(lq, cq) { % Couples L4S & Classic queues, lq & cq
   2:    while ( lq.len() + cq.len() > 0 )
   3:      if ( scheduler() == lq ) {
   4a:       lq.dequeue(pkt)
   4b:       if ( p_CL < p_Lmax ) {      % Check for overload saturation
   5:          if ( ((lq.time() > T_time)          p'_L = laqm(lq.time())                   % step marking ... Native L4S AQM
   6:                AND (lq.len > T_len))          p_L = max(p'_L, p_CL)                % Combining function
   7:              OR (p_CL          if ( p_L > rand()) rand() )                      % ...or linear 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)
   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 6: 7: Example Dequeue Pseudocode for DualQ Coupled PI2 AQM
             (Including Integer Arithmetic and Overload Code)

   1:  dualpi2_update(lq, cq, target) {         % 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_U * (curq - target) + beta_U * (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 7: 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.  The scheduler weight for Classic should be
      low, e.g. 1/16.

   o  Alternatively, a time-shifted FIFO could be used.  This is a very
      simple scheduler, but it does not fully isolate latency in the L4S
      queue from uncontrolled bursts in the Classic queue.  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 "if (scheduler() == lq )" test in
      line 3 of the dequeue code would simply be replaced by "if (
      lq.time() + tshift >= cq.time() )".  For the public Internet a
      good value for tshift is 50ms.  For private networks with smaller
      diameter, about 4*target would be reasonable.

   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 we used and tested.
   Although we designed the AQM to be efficient in integer arithmetic,
   to aid understanding it is first given using real-number arithmetic.
   Then, one possible optimization for integer arithmetic is given, also
   in pseudocode.  To aid comparison, the line numbers are kept in step
   between the two by using letter suffixes where the longer code needs
   extra lines.

   1:  dualq_dequeue(lq, cq) {  % Couples L4S & Classic queues, lq & cq
   2:    if ( lq.dequeue(pkt) ) {
   3a:     p_L = cq.sec() / 2^S_L
   3b:     if ( lq.byt() > T )
   3c:       mark(pkt)
   3d:     elif ( p_L > maxrand(U) )
   4:        mark(pkt)
   5:      return(pkt)                % return the packet and stop here
   6:    }
   7:    while ( cq.dequeue(pkt) ) {
   8a:     alpha = 2^(-f_C)
   8b:     Q_C = alpha * pkt.sec() + (1-alpha)* Q_C    % Classic Q EWMA
   9a:     sqrt_p_C = Q_C / 2^S_C
   9b:     if ( sqrt_p_C > maxrand(2*U) )
   10:       drop(pkt)                        % Squared drop, redo loop
   11:     else
   12:       return(pkt)              % return the packet and stop here
   13:   }
   14:   return(NULL)                           % no packet to dequeue
   15: }

   16: maxrand(u) {                % return the max of u random numbers
   17:     maxr=0
   18:     while (u-- > 0)
   19:         maxr = max(maxr, rand())               % 0 <= rand() < 1
   20:     return(maxr)
   21: }

   Figure 8: 9: Example Dequeue Pseudocode for DualQ Coupled Curvy RED AQM

   Packet classification code is not shown, as it is no different from
   Figure 3.  Potential classification schemes are discussed in
   Section 2.3.  The Curvy RED algorithm has not been maintained to the
   same degree as the DualPI2 algorithm.  Some ideas used in DualPI2
   would need to be translated into Curvy RED, such as i) the
   conditional priority scheduler instead of strict priority ii) the
   time-based L4S threshold; iii) turning off ECN as overload
   protection; iv) Classic ECN support.  These are not shown in the
   Curvy RED pseudocode, but would need to be implemented for
   production. {ToDo}

   At the outer level, the structure of dualq_dequeue() implements
   strict priority scheduling.  The code is written assuming the AQM is
   applied on dequeue (Note 1) . Every time dualq_dequeue() is called,
   the if-block in lines 2-6 determines whether there is an L4S packet
   to dequeue by calling lq.dequeue(pkt), and otherwise the while-block
   in lines 7-13 determines whether there is a Classic packet to
   dequeue, by calling cq.dequeue(pkt).  (Note 2)
   In the lower priority Classic queue, a while loop is used so that, if
   the AQM determines that a classic packet should be dropped, it
   continues to test for classic packets deciding whether to drop each
   until it actually forwards one.  Thus, every call to dualq_dequeue()
   returns one packet if at least one is present in either queue,
   otherwise it returns NULL at line 14.  (Note 3)

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

   L4S:  If the test at line 2 determines there is an L4S packet to
      dequeue, the tests at lines 3a and 3c determine whether to mark
      it.  The first is a simple test of whether the L4S queue (lq.byt()
      in bytes) is greater than a step threshold T in bytes (Note 4).
      The second test is similar to the random ECN marking in RED, but
      with the following differences: i) the marking function does not
      start with a plateau of zero marking until a minimum threshold,
      rather the marking probability starts to increase as soon as the
      queue is positive; ii) marking depends on queuing time, not bytes,
      in order to scale for any link rate without being reconfigured;
      iii) marking of the L4S queue does not depend on itself, it
      depends on the queuing time of the _other_ (Classic) queue, where
      cq.sec() is the queuing time of the packet at the head of the
      Classic queue (zero if empty); iv) marking depends on the
      instantaneous queuing time (of the other Classic queue), not a
      smoothed average; v) 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 3a the marking probability p_L is set to the
      Classic queueing time qc.sec() in seconds divided by the L4S
      scaling parameter 2^S_L, which represents the queuing time (in
      seconds) at which marking probability would hit 100%. Then in line
      3d (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.  The
      scaling parameter is expressed as a power of 2 so that division
      can be implemented as a right bit-shift (>>) in line 3 of the
      integer variant of the pseudocode (Figure 9). 10).

   Classic:  If the test at line 7 determines that there is at least one
      Classic packet to dequeue, the test at line 9b determines whether
      to drop it.  But before that, line 8b updates Q_C, which is an
      exponentially weighted moving average (Note 5) of the queuing time
      in the Classic queue, where pkt.sec() is the instantaneous
      queueing time of the current Classic packet and alpha is the EWMA
      constant for the classic queue.  In line 8a, alpha is represented
      as an integer power of 2, so that in line 8 of the integer code
      the division needed to weight the moving average can be
      implemented by a right bit-shift (>> f_C).

      Lines 9a and 9b implement the drop function.  In line 9a the
      averaged queuing time Q_C is divided by the Classic scaling
      parameter 2^S_C, in the same way that queuing time was scaled for
      L4S marking.  This scaled queuing time is given the variable name
      sqrt_p_C because it will be squared to compute Classic drop
      probability, so before it is squared it is effectively the square
      root of the drop probability.  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 (Note 6).  Again, the scaling
      parameter is expressed as a power of 2 so that division can be
      implemented as a right bit-shift in line 9 of the integer

   The marking/dropping functions in each queue (lines 3 & 9) are two
   cases of a new generalization of RED called Curvy RED, motivated as
   follows.  When we compared the performance of our AQM with fq_CoDel
   and PIE, we came to the conclusion that their goal of holding queuing
   delay to a fixed target is 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 one parameter, the scaling, not three.  The diadvantage
   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 support is limited
   otherwise an adaptation mechanism is required.

   There follows a summary listing of the two parameters used for each
   of the two queues:


      S_C :   The scaling factor of the dropping function scales Classic
         queuing times in the range [0, 2^(S_C)] seconds into a dropping
         probability in the range [0,1].  To make division efficient, it
         is constrained to be an integer power of two;

      f_C :  To smooth the queuing time of the Classic queue and make
         multiplication efficient, we use a negative integer power of
         two for the dimensionless EWMA constant, which we define as
         alpha = 2^(-f_C).

   L4S :

      S_L (and k'):   As for the Classic queue, the scaling factor of
         the L4S marking function scales Classic queueing times in the
         range [0, 2^(S_L)] seconds into a probability in the range
         [0,1].  Note that S_L = S_C + k', where k' is the coupling
         between the queues.  So S_L and k' count as only one parameter;
         k' is related to k in Equation (1) (Section 2.1) by k=2^k',
         where both k and k' are constants.  Then implementations can
         avoid costly division by shifting p_L by k' bits to the right.

      T :  The queue size in bytes at which step threshold marking
         starts in the L4S queue.

   {ToDo: These are the raw parameters used within the algorithm.  A
   configuration front-end could accept more meaningful parameters and
   convert them into these raw parameters.}

   From our experiments so far, recommended values for these parameters
   are: S_C = -1; f_C = 5; T = 5 * MTU 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) {ToDo
   incorporate a summary of that report into this draft}. The setting of
   k depends on policy (see Section 2.5 and Appendix C respectively for
   its recommended setting and guidance on alternatives).

   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.  We
   have solely used U=1 in our experiments so far, but results might be
   even better with U=2 or higher.

   Note that the dropping function at line 9 calls maxrand(2*U), which
   gives twice as much curviness as the call to maxrand(U) in the
   marking function at line 3.  This is the trick that implements the
   square rule in equation (1) (Section 2.1).  This is based on the fact
   that, given a number X from 1 to 6, the probability that two dice
   throws will both be less than X is the square of the probability that
   one throw will be less than X.  So, when U=1, the L4S marking
   function is linear and the Classic dropping function is squared.  If
   U=2, L4S would be a square function and Classic would be quartic.
   And so on.

   The maxrand(u) function in lines 16-21 simply generates u random
   numbers and returns the maximum (Note 7).  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:  dualq_dequeue(lq, cq) {  % Couples L4S & Classic queues, lq & cq
   2:     if ( lq.dequeue(pkt) ) {
   3:        if ((lq.byt() > T) || ((cq.ns() >> (S_L-2)) > maxrand(U)))
   4:           mark(pkt)
   5:        return(pkt)              % return the packet and stop here
   6:     }
   7:     while ( cq.dequeue(pkt) ) {
   8:         Q_C += (pkt.ns() - Q_C) >> f_C           % Classic Q EWMA
   9:        if ( (Q_C >> (S_C-2) ) > maxrand(2*U) )
   10:          drop(pkt)                     % Squared drop, redo loop
   11:       else
   12:          return(pkt)           % return the packet and stop here
   13:    }
   14:    return(NULL)                           % no packet to dequeue
   15: }

   Figure 9: 10: Optimised Example Dequeue Pseudocode for Coupled DualQ AQM
                         using Integer Arithmetic


   1.  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 [CoDel].  In our Linux
       implementation, it was easiest to measure queuing time at
       dequeue.  Queuing time can be estimated when a packet is enqueued
       by measuring the queue length in bytes and dividing by the recent
       drain rate.

   2.  An implementation has to use priority queueing, but it need not
       implement strict priority.

   3.  If packets can be enqueued while processing dequeue code, an
       implementer might prefer to place the while loop around both
       queues so that it goes back to test again whether any L4S packets
       arrived while it was dropping a Classic packet.

   4.  In order not to change too many factors at once, for now, we keep
       the marking function for DCTCP-only traffic as similar as
       possible to DCTCP.  However, unlike DCTCP, all processing is at
       dequeue, so we determine whether to mark a packet at the head of
       the queue by the byte-length of the queue _behind_ it.  We plan
       to test whether using queuing time will work in all
       circumstances, and if we find that the step can cause
       oscillations, we will investigate replacing it with a steep
       random marking curve.

   5.  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.

   6.  In practice at line 10 the Classic queue would probably test for
       ECN capability on the packet to determine whether to drop or mark
       the packet.  However, for brevity such detail is omitted.  All
       packets classified into the L4S queue have to be ECN-capable, so
       no dropping logic is necessary at line 3.  Nonetheless, L4S
       packets could be dropped by overload code (see Section 4.1).

   7.  In the integer variant of the pseudocode (Figure 9) 10) real numbers
       are all represented as integers scaled up by 2^32.  In lines 3 &
       9 the function maxrand() is arranged to return an integer in the
       range 0 <= maxrand() < 2^32.  Queuing times are also scaled up by
       2^32, but in two stages: i) In lines 3 and 8 queuing times
       cq.ns() and pkt.ns() are returned in 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.

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.

   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, we used
   the measured RTTs to calculate that a value of k'=3 (equivalant to
   k=8) would achieve throughput equivalence, and our 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.

Appendix D.  Open Issues

   Most of the following open issues are also tagged '{ToDo}' at the
   appropriate point in the document:

      Operational guidance to monitor L4S experiment

      PI2 appendix: scaling of alpha & beta, esp. dependence of beta_U
      on Tupdate

      Curvy RED appendix: complete the unfinished parts

Authors' Addresses

   Koen De Schepper
   Nokia Bell Labs


   Bob Briscoe (editor)


   Olga Bondarenko
   Simula Research Lab


   Ing-jyh Tsang