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Versions: (draft-briscoe-tsvwg-aqm-dualq-coupled) 00 01

Transport Area working group (tsvwg)                      K. De Schepper
Internet-Draft                                           Nokia Bell Labs
Intended status: Experimental                            B. Briscoe, Ed.
Expires: January 4, 2018                                   O. Bondarenko
                                                     Simula Research Lab
                                                                I. Tsang
                                                         Nokia Bell Labs
                                                            July 3, 2017


  DualQ Coupled AQM for Low Latency, Low Loss and Scalable Throughput
                 draft-ietf-tsvwg-aqm-dualq-coupled-01

Abstract

   Data Centre TCP (DCTCP) was designed to provide predictably low
   queuing latency, near-zero loss, and throughput scalability using
   explicit congestion notification (ECN) and an extremely simple
   marking behaviour on switches.  However, DCTCP does not co-exist with
   existing TCP traffic---DCTCP is so aggressive that existing TCP
   algorithms approach starvation.  So, until now, DCTCP could only be
   deployed where a clean-slate environment could be arranged, such as
   in private data centres.  This specification defines `DualQ Coupled
   Active Queue Management (AQM)' to allow scalable congestion controls
   like DCTCP to safely co-exist with 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 without inspecting transport
   layer flow identifiers.  When tested in a residential broadband
   setting, DCTCP achieved 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

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

   Internet-Drafts are working documents of the Internet Engineering
   Task Force (IETF).  Note that other groups may also distribute
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   Internet-Drafts are draft documents valid for a maximum of six months
   and may be updated, replaced, or obsoleted by other documents at any
   time.  It is inappropriate to use Internet-Drafts as reference
   material or to cite them other than as "work in progress."



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   This Internet-Draft will expire on January 4, 2018.

Copyright Notice

   Copyright (c) 2017 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

   This document is subject to BCP 78 and the IETF Trust's Legal
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   described in the Simplified BSD License.

Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
     1.1.  Problem and Scope . . . . . . . . . . . . . . . . . . . .   3
     1.2.  Terminology . . . . . . . . . . . . . . . . . . . . . . .   5
     1.3.  Features  . . . . . . . . . . . . . . . . . . . . . . . .   5
   2.  DualQ Coupled AQM Algorithm . . . . . . . . . . . . . . . . .   7
     2.1.  Coupled AQM . . . . . . . . . . . . . . . . . . . . . . .   7
     2.2.  Dual Queue  . . . . . . . . . . . . . . . . . . . . . . .   8
     2.3.  Traffic Classification  . . . . . . . . . . . . . . . . .   8
     2.4.  Normative Requirements  . . . . . . . . . . . . . . . . .   8
   3.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .   9
   4.  Security Considerations . . . . . . . . . . . . . . . . . . .  10
     4.1.  Overload Handling . . . . . . . . . . . . . . . . . . . .  10
   5.  Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .  11
   6.  References  . . . . . . . . . . . . . . . . . . . . . . . . .  11
     6.1.  Normative References  . . . . . . . . . . . . . . . . . .  11
     6.2.  Informative References  . . . . . . . . . . . . . . . . .  11
   Appendix A.  Example DualQ Coupled PI2 Algorithm  . . . . . . . .  14
     A.1.  Pass #1: Core Concepts  . . . . . . . . . . . . . . . . .  15
     A.2.  Pass #2: Overload Details . . . . . . . . . . . . . . . .  18
   Appendix B.  Example DualQ Coupled Curvy RED Algorithm  . . . . .  21
   Appendix C.  Guidance on Controlling Throughput Equivalence . . .  26
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  28

1.  Introduction








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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
   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.  Then Diffserv is of little use.  Instead,
   we need to remove the causes of any unnecessary 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.

   More recent state-of-the-art AQMs, e.g.
   fq_CoDel [I-D.ietf-aqm-fq-codel], 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



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   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 [I-D.ietf-tcpm-dctcp])
   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.

   Given regular broadband bit-rates over WAN distances are
   already [RFC3649] beyond the scaling range of `classic' TCP Reno,
   `less unscalable' Cubic [I-D.ietf-tcpm-cubic] 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 [I-D.ietf-aqm-fq-codel] 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.  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 latency.





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   This AQM extension can be combined with any 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.

   The overall L4S architecture is described in
   [I-D.ietf-tsvwg-l4s-arch].  The supporting papers [PI216] and
   [DCttH15] give the full rationale for the AQM's design, both
   discursively and in more precise mathematical form.

1.2.  Terminology

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
   document are to be interpreted as described in [RFC2119].  In this
   document, these words will appear with that interpretation only when
   in ALL CAPS.  Lower case uses of these words are not to be
   interpreted as carrying RFC-2119 significance.

   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.
      Relentless [Mathis09]).

   Either service can cope with a proportion of unresponsive or less-
   responsive traffic as well (e.g.  DNS, VoIP, etc), just as a single
   queue AQM can.  The DualQ Coupled AQM behaviour is 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



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   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 available [PI216]
   [DCttH15].

   Subjective testing was also conducted using a demanding panoramic
   interactive video application run over a stack with DCTCP enabled and
   deployed on the testbed.  Each user could pan or zoom their own high
   definition (HD) sub-window of a larger video scene from a football
   match.  Even though the user was also downloading large amounts of
   L4S and Classic data, latency was so low that the picture appeared to
   stick to their finger on the touchpad (all the L4S data achieved the
   same ultra-low latency).  With an alternative AQM, the video
   noticeably lagged behind the finger gestures.

   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
   Internet.






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2.  DualQ Coupled AQM Algorithm

   There are two main aspects to the algorithm:

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

   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.  TCP Cubic implements a Reno-
   compatibility mode, which is the only relevant mode for typical RTTs
   under 20ms, while the throughput of a single flow is less than about
   500Mb/s.  Therefore we can assume that Cubic traffic behaves similar
   to Reno (but with a slightly different constant of proportionality),
   and we shall use the term 'Classic' for the collection of Reno and
   Cubic in Reno mode.

   In our supporting paper [PI216], we derive 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 we use the term 'L4S' traffic for all similar
   behaviour.

   In order to make a DCTCP flow run at roughly the same rate as a Reno
   TCP flow (all other factors being equal), we make the drop or marking
   probability for Classic traffic, p_C distinct from the marking
   probability for L4S traffic, p_L (in contrast to RFC3168 which
   requires them to be the same).  We make the Classic drop probability
   p_C proportional to the square of the L4S marking probability p_L.
   This is because we need to make the Reno flow rate equal the DCTCP
   flow rate, so we have to square the square root of p_C in the Reno
   rate equation to make it the same as the straight p_L in the DCTCP
   rate equation.

   There is a really simple way to implement the square of a probability
   - by testing the queue against two random numbers not one.  This is
   the approach adopted in Appendix A and Appendix B.

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



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

   where k is the constant of proportionality.

2.2.  Dual Queue

   Classic traffic builds a large queue, so a separate queue is provided
   for L4S traffic, and it is scheduled with strict priority.
   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 L4S and C packets.  A separate draft
   [I-D.ietf-tsvwg-ecn-l4s-id] recommends using the ECT(1) codepoint of
   the ECN field as this identifier, having assessed various
   alternatives.

   Given L4S work is currently on the experimental track, but the
   definition of the ECN field is on the standards track [RFC3168],
   another standards track document has proved necessary to make the
   ECT(1) codepoint available for experimentation
   [I-D.ietf-tsvwg-ecn-experimentation].

2.4.  Normative Requirements

   In the Dual Queue, L4S packets MUST be given priority over Classic,
   although strict priority MAY not be appropriate.

   All L4S traffic MUST be ECN-capable, although some Classic traffic
   MAY also be ECN-capable.

   Whatever identifier is used for L4S traffic, it will still be
   necessary to agree on the meaning of an ECN marking on L4S traffic,
   relative to a drop of Classic traffic.  In order to prevent
   starvation of Classic traffic by scalable L4S traffic (e.g.  DCTCP)
   the drop probability of Classic traffic MUST be proportional to the
   square of the marking probability of L4S traffic, In other words, the
   power to which p_L is raised in Eqn. (1) MUST be 2.

   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). k does not have to
   be standardized because differences do not prevent interoperability.



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   However, k has to take some value, and each operator can make that
   choice.

   A value of k=2 is currently RECOMMENDED as the default for Internet
   access networks.  Assuming scalable congestion controls for the
   Internet will be as aggressive as DCTCP, this will ensure their
   congestion window will be roughly the same as that of a standards
   track TCP congestion control (Reno) [RFC5681] and other so-called
   TCP-friendly controls such as TCP Cubic in its TCP-friendly mode.

   The 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.

   Whatever value is recommended, 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.

   Typically, access network operators isolate customers from each other
   with some form of layer-2 multiplexing (TDM in DOCSIS, CDMA in 3G) or
   L3 scheduling (WRR in broadband), 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 small flows.

   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.  Curvy RED
   requires less operations per packet than RED and can be used if the
   range of RTTs is limited.  DualPI2 is a simplification of PIE with
   stable Proportional-Integral control for both Classic and L4S
   congestion controls.  Nonetheless, it would be possible to control
   the queues with other alternative AQMs, as long as the above
   normative requirements (those expressed in capitals) are observed,
   which are intended to be independent of the specific AQM.

   {ToDo: Add management and monitoring requirements}

3.  IANA Considerations

   This specification contains no IANA considerations.






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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 performance.  This
   is a policy issue that needs to be separable from a basic AQM, but an
   AQM does need to handle overload.  A trade-off needs to be made
   between complexity and the risk of either class harming the other.
   It is an operator policy to define what must happen if the service
   time of the classic queue becomes too great.  In the following
   subsections three optional non-exclusive overload protections are
   defined.  Their objective is for the overload behaviour of the DualQ
   AQM to be similar to a single queue AQM.  The example implementation
   in Appendix A implements the 'delay on overload' policy.  Other
   overload protections can be envisaged:

   Minimum throughput service:   By replacing the priority scheduler
      with a weighted round robin scheduler, a minimum throughput
      service can be guaranteed for Classic traffic.  Typically the
      scheduling weight of the Classic queue will be small (e.g. 5%) to
      avoid interference with the coupling but big enough to avoid
      complete starvation of Classic traffic.

   Delay on overload:  To control milder overload of responsive traffic,
      particularly when close to the maximum congestion signal, delay
      can be used as an alternative congestion control mechanism.  The
      Dual Queue Coupled AQM can be made to behave like a single First-
      In First-Out (FIFO) queue with different service times by
      replacing the priority scheduler with a very simple scheduler that
      could be called a "time-shifted FIFO", which is the same as the
      Modifier Earliest Deadline First (MEDF) scheduler of [MEDF].  The
      scheduler adds T_m 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 defines the maximum extra queuing delay
      (T_m) of Classic packets relative to L4S.

   Drop on overload:  On severe overload, e.g. due to non responsive
      traffic, queues will typically overflow and packet drop will be
      unavoidable.  It is important to avoid unresponsive ECN traffic
      (either Classic or L4S) driving the AQM to 100% drop and mark
      probability.  Congestion controls that have a minimum congestion
      window will become unresponsive to ECN marking when the marking
      probability is high.  This situation can be avoided by applying



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      the drop probability to all packets of all traffic types when it
      exceeds a certain threshold or by limiting the drop and marking
      probabilities to a lower maximum value (up to where fairnes
      between the different traffic types is still guaranteed) and rely
      on delay to control temporary high congestion and eventually queue
      overflow.  If the classic drop probability is applied to all types
      of traffic when it is higher than a threshold probability the
      queueing delay can be controlled up to any overload situation, and
      no further measures are required.  If a maximum classic and
      coupled L4S probability of less than 100% is used, both queues
      need scheduling opportunities and should eventually experience
      drop.  This can be achieved with a scheduler that guarantees a
      minimum throughput for each queue, such as a weighted round robin
      or time-shifted FIFO scheduler.  In that case a common queue limit
      can be configured that will drop packets of both types of traffic.

   To keep the throughput of both L4S and Classic flows equal over the
   full load range, a different control strategy needs to be defined
   above the point where one congestion control first saturates to a
   probability of 100% (if k>1, L4S will saturate first).  Possible
   strategies include: also dropping L4S; increasing the queueing delay
   for both; or ensuring that L4S traffic still responds to marking
   below a window of 2 segments (see [I-D.ietf-tsvwg-ecn-l4s-id]).

5.  Acknowledgements

   Thanks to Anil Agarwal for detailed review comments and suggestions
   on how to make our explanation clearer.

   The authors' contributions are part-funded by the European Community
   under its Seventh Framework Programme through the Reducing Internet
   Transport Latency (RITE) project (ICT-317700).  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,
              <http://www.rfc-editor.org/info/rfc2119>.

6.2.  Informative References







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   [ARED01]   Floyd, S., Gummadi, R., and S. Shenker, "Adaptive RED: An
              Algorithm for Increasing the Robustness of RED's Active
              Queue Management", ACIRI Technical Report , August 2001,
              <http://www.icir.org/floyd/red.html>.

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

   [CRED_Insights]
              Briscoe, B., "Insights from Curvy RED (Random Early
              Detection)", BT Technical Report TR-TUB8-2015-003, July
              2015,
              <http://www.bobbriscoe.net/projects/latency/credi_tr.pdf>.

   [DCttH15]  De Schepper, K., Bondarenko, O., Briscoe, B., and I.
              Tsang, "`Data Centre to the Home': Ultra-Low Latency for
              All", 2015, <http://www.bobbriscoe.net/projects/latency/
              dctth_preprint.pdf>.

              (Under submission)

   [I-D.ietf-aqm-fq-codel]
              Hoeiland-Joergensen, T., McKenney, P.,
              dave.taht@gmail.com, d., Gettys, J., and E. Dumazet, "The
              FlowQueue-CoDel Packet Scheduler and Active Queue
              Management Algorithm", draft-ietf-aqm-fq-codel-06 (work in
              progress), March 2016.

   [I-D.ietf-tcpm-cubic]
              Rhee, I., Xu, L., Ha, S., Zimmermann, A., Eggert, L., and
              R. Scheffenegger, "CUBIC for Fast Long-Distance Networks",
              draft-ietf-tcpm-cubic-04 (work in progress), February
              2017.

   [I-D.ietf-tcpm-dctcp]
              Bensley, S., Thaler, D., Balasubramanian, P., Eggert, L.,
              and G. Judd, "Datacenter TCP (DCTCP): TCP Congestion
              Control for Datacenters", draft-ietf-tcpm-dctcp-08 (work
              in progress), June 2017.

   [I-D.ietf-tsvwg-ecn-experimentation]
              Black, D., "Explicit Congestion Notification (ECN)
              Experimentation", draft-ietf-tsvwg-ecn-experimentation-00
              (work in progress), November 2016.






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   [I-D.ietf-tsvwg-ecn-l4s-id]
              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-00 (work in progress), November 2016.

   [I-D.ietf-tsvwg-l4s-arch]
              Briscoe, B., Schepper, K., and M. Bagnulo, "Low Latency,
              Low Loss, Scalable Throughput (L4S) Internet Service:
              Architecture", draft-ietf-tsvwg-l4s-arch-00 (work in
              progress), November 2016.

   [I-D.sridharan-tcpm-ctcp]
              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.

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

   [MEDF]     Menth, M., Schmid, M., Heiss, H., and T. Reim, "MEDF - a
              simple scheduling algorithm for two real-time transport
              service classes with application in the UTRAN", Proc. IEEE
              Conference on Computer Communications (INFOCOM'03) Vol.2
              pp.1116-1122, March 2003.

   [PI216]    De Schepper, K., Bondarenko, O., Briscoe, B., and I.
              Tsang, "PI2: A Linearized AQM for both Classic and
              Scalable TCP", ACM CoNEXT'16 , December 2016,
              <https://riteproject.files.wordpress.com/2015/10/
              pi2_conext.pdf>.

              (To appear)

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

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



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

   [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,
              <http://www.rfc-editor.org/info/rfc3246>.

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

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

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

   [RFC8033]  Pan, R., Natarajan, P., Baker, F., and G. White,
              "Proportional Integral Controller Enhanced (PIE): A
              Lightweight Control Scheme to Address the Bufferbloat
              Problem", RFC 8033, DOI 10.17487/RFC8033, February 2017,
              <http://www.rfc-editor.org/info/rfc8033>.

Appendix A.  Example DualQ Coupled PI2 Algorithm

   As a first concrete example, the pseudocode below gives the DualPI2
   algorithm, which is a DualQ Coupled AQM algorithm based on the PI2
   algorithm [PI216] 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.  The first pass also uses regular arithmetic, whereas
   some integer arithmetic more suitable for kernel operations appears
   in 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:
   https://github.com/olgabo/dualpi2.




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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 functions:

   o  initialization code (Figure 1) that sets parameter defaults (the
      API for setting non-default values is omitted for brevity)

   o  enqueue code (Figure 2)

   o  dequeue code (Figure 3)

   o  code to regularly update the base probability (p) used in the
      dequeue code (Figure 4).

   The base probability (p) is an internal variable from which the
   marking and dropping probabilities for L4S and Classic traffic (p_L
   and p_C) are derived.  Specifically, p_L = p * k and p_C = p^2, from
   Equation (1) (see lines 4a and 4b in Figure 4).

   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 1.

   1:  dualpi2_params_init(...) {               % Set parameter defaults
   2:    target = 15 ms              % PI AQM Classic queue delay target
   3:    tshift = 2 * target                       % Scheduler time bias
   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:    alpha_U = alpha *Tupdate % PI integral gain per update interval
   8:    beta_U = beta * Tupdate  % PI prop'nal gain per update interval
   9:    T_time = 1 ms                   % L4S marking threshold in time
   10:   T_len = 2 * MTU            % Min L4S marking threshold in bytes
   11:   k = 2                                         % Coupling factor
   12:   limit = MAX_LINK_RATE * 250 ms               % Dual buffer size
   13:   p_Cmax = 1/4                       % Max Classic drop/mark prob
   14:   p_Lmax = min(k*sqrt(p_Cmax), 1)          % Max L4S marking prob
   15: }

       Figure 1: Example Header Pseudocode for DualQ Coupled PI2 AQM








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   1:  dualpi2_enqueue(lq, cq, pkt) { % Test limit and classify lq or cq
   2:    stamp(pkt)                      % attach arrival time to packet
   3:    if ( lq.len() + cq.len() > limit )
   4:      drop(pkt)                     % drop packet if buffer is full
   5:    else {                                      % Packet classifier
   6:      if ( ecn(pkt) modulo 2 == 1 )       % ECN bits = ECT(1) or CE
   7:        lq.enqueue(pkt)
   8:      else                           % ECN bits = not-ECT or ECT(0)
   9:        cq.enqueue(pkt)
   10:   }
   11: }

      Figure 2: 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 ( lq.time() + tshift >= cq.time() ) {  % time-shifted FIFO
   4:        lq.dequeue(pkt)
   5:        if ( ((pkt.time() > T_time)              % step marking ...
   6:              AND (lq.len > T_len))
   7:            OR (p_L > rand()) )              % ...or linear marking
   8:          mark(pkt)
   9:      } else {
   10:       cq.dequeue(pkt)
   11:       if ( p_C > rand() ) {                     % probability 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 3: Example Dequeue Pseudocode for DualQ Coupled PI2 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)
   4a:   p_L = p * k            % L4S prob = base prob * coupling factor
   4b:   p_C = p^2                        % Classic prob = (base prob)^2
   5:    prevq = curq
   6:  }

     Figure 4: Example PI-Update Pseudocode for DualQ Coupled PI2 AQM



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   When packets arrive, first a common queue limit is checked as shown
   in line 3 of the enqueuing pseudocode in Figure 2.  Note that the
   limit is deliberately tested before enqueue to avoid any bias against
   larger packets (so the actual buffer has to be one packet larger than
   limit).  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 6).  Packets
   with a codepoint having an LSB of 0 (Not-ECT and ECT(0)) will be
   enqueued in the Classic queue.  Otherwise, ECT(1) and CE packets will
   be enqueued in the L4S queue.  Optional packet classification
   flexibility is omitted for brevity.

   The dequeue pseudocode schedules one packet for dequeuing (or zero if
   the queue is empty).  It also makes all the AQM decisions on dropping
   and marking.  It 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 implements time-
   shifted FIFO scheduling.  It takes the packet that waited the
   longest, biased against the Classic traffic by a time-shift of
   tshift.

   o  If an L4S packet is scheduled, lines 5 to 8 mark the packet if
      either the L4S threshold is exceeded, or if a random marking
      decision is drawn according to k times the probability p
      (maintained by the dualpi2_update() function discussed below).
      The L4S threshold is usually in units of time (default T_time = 1
      ms).  However, on slow links the packet serialization time can
      approach the threshold T_time, so line 6 sets a floor of 2 MTU to
      the threshold.

   o  If a Classic packet is scheduled, lines 10 to 17 drop or mark the
      packet based on the squared probability p_C = p^2 (hence the name
      PI2 for Classic traffic).

   The probability p is kept up to date by the core PI algorithm in
   Figure 4 which is executed every Tupdate ([RFC8033] now recommends
   16ms).  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) as defined in [RFC8033] and b) the change in
   queuing delay since the last sample.  The name 'PI' represents the
   fact that the second factor is proportional to load while the first
   is the integral of the load (so it removes any standing queue).  In
   corner cases, p can overflow the range [0,1] so the resulting value
   of p has to be bounded (omitted from the pseudocode).

   Alpha_U and beta_U are gain factors chosen based on stability
   analysis to convert changes in queueing delay into changes in



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   probability.  They are therefore in units of 'per second of delay' or
   Hz.  The suffix '_U' represents 'per update time' (Tupdate).  If a
   briefer update time is configured, alpha_U and beta_U also have to be
   reduced to ensure that the same response is given over time, so that
   a smaller Tupdate will only result in a response with finer steps,
   not a more aggressive response.  Therefore, alpha_U and beta_U are
   derived from alpha and beta, which each represent a 'gain factor per
   second of update time', so they can be configured independently of
   the update time (see lines 7 and 8 of Figure 1).

   Unlike in PIE, alpha_U and beta_U do not need to be tuned every
   Tupdate dependent on p.  Instead, in PI2 alpha_U and beta_U can be
   constants because the squaring applied to Classic traffic tunes them
   inherently, as explained in [PI216].

   Note that p solely depends on the queuing time in the Classic queue.
   In line 2, the current queuing delay is evaluated by inspecting the
   timestamp of the next packet to schedule in the Classic queue.  The
   function cq.time() subtracts the time stamped at enqueue from the
   current time and implicitly takes the current queuing delay as 0 if
   the queue is empty.

   Because the L4S marking probability (p_L) 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.

A.2.  Pass #2: Overload Details

   Figure 5 repeats the dequeue function of Figure 3, but with overload
   details added.  Similarly Figure 6 repeats the core PI algorithm of
   Figure 4 with overload details added.  The initialization and enqueue
   functions are unchanged.

   In line 13 of the initialization function (Figure 1), 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 14 translates this into a maximum L4S marking probability
   (p_Lmax) by rearranging Equation (1).  With the default coupling
   factor of k=2, this translates to a maximum L4S marking probability
   of 1 or 100%. This is intended to ensure that the L4S queue starts to



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   introduce dropping once marking saturates and can rise no further.
   The 'TCP Prague' requirements [I-D.ietf-tsvwg-ecn-l4s-id] require
   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 5).
   Lines 8c to 8g drop L4S packets with probability p^2 by comparing p
   against two random numbers.  Lines 8h to 8i mark the remaining
   packets with probability p_L.

   Lines 2c to 2d in the core PI algorithm (Figure 6) deal with overload
   of the L4S queue when there is no Classic traffic.  This is
   necessary, because the core PI algorithm maintains the right
   probability of drop to regulate overload, but it depends on the
   length of the Classic queue.  If there is no Classic queue the naive
   algorithm in Figure 4 drops nothing, even if the L4S queue is
   overloaded - so tail drop takes over (lines 3 and 4 of Figure 2).

   If the test at line 2a finds that the Classic queue is empty, line 2d
   measures the current queue delay using the L4S queue not the Classic
   queue, 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 5).  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.




















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   1:  dualpi2_dequeue(lq, cq) { % Couples L4S & Classic queues, lq & cq
   2:    while ( lq.len() + cq.len() > 0 )
   3:      if ( lq.time() + tshift >= cq.time() ) {  % time-shifted FIFO
   4a:       lq.dequeue(pkt)
   4b:       if ( p_L < p_Lmax ) {       % Check for overload saturation
   5:          if ( ((pkt.time() > T_time)            % step marking ...
   6:                AND (lq.len > T_len))
   7:              OR (p_L > rand()) )            % ...or linear marking
   8a:            mark(pkt)
   8b:       } else {                              % overload saturation
   8c:         if ( p > max(rand(), rand()) ) {        % probability 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_L > rand() )             % probability p_L = k * p
   8i:           mark(pkt)         % linear marking of remaining packets
   8j:       }
   9:      } else {
   10:       cq.dequeue(pkt)
   11:       if ( p > max(rand(), rand()) ) {          % probability p^2
   12a:        if ( (ecn(pkt) == 0)                % ECN field = not-ECT
   12b:             OR (p_L >= p_Lmax) ) {       % 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 5: 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_L = p * k            % L4S prob = base prob * coupling factor
   5:    prevq = curq
   6:  }

     Figure 6: Example PI-Update Pseudocode for DualQ Coupled PI2 AQM
                         (Including Overload Code)



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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 7: Example Dequeue Pseudocode for DualQ Coupled Curvy RED AQM

   Packet classification code is not shown, as it is no different from
   Figure 2.  Classic ECN handling is not shown.  Potential
   classification schemes are discussed in Section 2.  The Curvy RED
   algorithm has not been maintained to the same degree as the DualPI2
   algorithm.  Some ideas used in DualPI2 could be translated into Curvy
   RED, such as i) the time-shifted FIFO scheduler ii) the time-based
   L4S threshold; iii) overload protection.  {ToDo}.



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   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 8).




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   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
      pseudocode.

   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.





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

   Classic:

      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 2.4 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.



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

   Notes:

   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.



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   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 8) 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










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                     +---------------+------+-------+
                     | 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.





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

Authors' Addresses

   Koen De Schepper
   Nokia Bell Labs
   Antwerp
   Belgium

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


   Bob Briscoe (editor)
   Simula Research Lab

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


   Olga Bondarenko
   Simula Research Lab
   Lysaker
   Norway

   Email: olgabnd@gmail.com
   URI:   https://www.simula.no/people/olgabo


   Ing-jyh Tsang
   Nokia Bell Labs
   Antwerp
   Belgium

   Email: ing-jyh.tsang@nokia.com














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