Transport Area working group (tsvwg) K. De Schepper
Internet-Draft Nokia Bell Labs
Intended status: Experimental B. Briscoe, Ed.
Expires: November 11, 2017 O. Bondarenko
Simula Research Lab
I. Tsang
Nokia Bell Labs
May 10, 2017

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


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---throughput starves. 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

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Table of Contents

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 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 [I-D.ietf-aqm-pie], 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 [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:

the `sawtooth' varying rate of TCP itself;
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:[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).

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 

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.

This AQM extension can be combined with any single qeueu 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 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.

2. DualQ Coupled AQM Algorithm

There are two main aspects to the algorithm:

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.

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

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

where k is the constant of proportionality. Optionally, k can be expressed as a power of 2, so k=2^k', where k' is another constant. Then implementations can avoid costly division by shifting p_L by k' bits to the right.

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. 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 PI2 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. PI2 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.

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:[I-D.ietf-tsvwg-ecn-l4s-id]).

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 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

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.

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.
[CRED_Insights] Briscoe, B., "Insights from Curvy RED (Random Early Detection)", BT Technical Report TR-TUB8-2015-003, July 2015.
[DCttH15] De Schepper, K., Bondarenko, O., Briscoe, B. and I. Tsang, "`Data Centre to the Home': Ultra-Low Latency for All", 2015.

(Under submission)

[I-D.ietf-aqm-fq-codel] Hoeiland-Joergensen, T., McKenney, P.,, d., Gettys, J. and E. Dumazet, "The FlowQueue-CoDel Packet Scheduler and Active Queue Management Algorithm", Internet-Draft draft-ietf-aqm-fq-codel-06, March 2016.
[I-D.ietf-aqm-pie] Pan, R., Natarajan, P., Baker, F. and G. White, "PIE: A Lightweight Control Scheme To Address the Bufferbloat Problem", Internet-Draft draft-ietf-aqm-pie-10, September 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", Internet-Draft draft-ietf-tcpm-cubic-04, 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", Internet-Draft draft-ietf-tcpm-dctcp-06, May 2017.
[I-D.ietf-tsvwg-ecn-experimentation] Black, D., "Explicit Congestion Notification (ECN) Experimentation", Internet-Draft draft-ietf-tsvwg-ecn-experimentation-00, November 2016.
[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", Internet-Draft draft-ietf-tsvwg-ecn-l4s-id-00, 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", Internet-Draft draft-ietf-tsvwg-l4s-arch-00, 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", Internet-Draft draft-sridharan-tcpm-ctcp-02, November 2008.
[Mathis09] 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.
[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.

(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.

Appendix A. Example DualQ Coupled PI2 Algorithm

As a first concrete example, the pseudocode below gives the DualQ Coupled AQM algorithm based on the PI2 Classic AQM, we used and tested. For this example only the pseudo code is given. An open source implementation for Linux is available at:

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 q is full
5:    else {
6:      if ( ecn(pkt) modulo 2 == 0 )   % ECN bits = not-ect or ect(0)
7:        cq.enqueue(pkt)
8:      else                                 % ECN bits = ect(1) or ce
9:        lq.enqueue(pkt)
10:   }
11: }

Figure 1: Example Enqueue Pseudocode for DualQ Coupled PI2 AQM

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() ) {
4:        lq.dequeue(pkt)
5:        if ( (pkt.time() > T) or (p * k > rand()) )  % coupling here
6:          mark(pkt)
7:        return(pkt)                % return the packet and stop here
8:      } else {
9:        cq.dequeue(pkt)
10:       if ( p > max(rand(), rand()) ) % only square part of (p/k)^2
11:         if ( ecn(pkt) == 0 )                 % ECN field = not-ect
12:           drop(pkt)                      % squared drop, redo loop
13:         else {
14:           mark(pkt)                                 % squared mark
15:           return(pkt)            % return the packet and stop here
16:         }
17:       else
18:         return(pkt)              % return the packet and stop here
19:     }
20:   }
21:   return(NULL)                              % no packet to dequeue
22: }

Figure 2: Example Dequeue Pseudocode for DualQ Coupled PI2 AQM

1:  dualpi2_update(lq, cq) {                  % Update p every Tupdate
2:    curq = cq.time()   % use queuing time of first-in Classic packet
3:    alpha_U = alpha * Tupdate    % done once when parameters are set
4:    beta_U = beta * Tupdate      % done once when parameters are set
5:    p = p + alpha_U * (curq - target) + beta_U * (curq - prevq)
6:    prevq = curq
7:  }

Figure 3: Example PI-Update Pseudocode for DualQ Coupled PI2 AQM

When packets arrive, first a common queue limit is checked as shown in line 3 of the enqueuing pseudocode in Figure 1. 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.

The pseudocode in Figure 2 summarises the per packet dequeue implementation of the DualPI2 code. Line 3 implements the time-shifted FIFO scheduling. It takes the packet that waited the longest, biased by a time-shift of tshift for the Classic traffic. If an L4S packet is scheduled, lines 5 and 6 mark the packet if either the L4S threshold T 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 coupling factor is applied here for determining the L4S marking probability so that Classic TCP control is independent from the L4S coupling factor. If a Classic packet is scheduled, lines 10 to 16 drop or mark the packet based on 2 random decisions resulting in the squared probability p^2 (hence the name PI2 for Classic traffic). Note that p is not reduced here by the factor k, as p has already been multiplied by the factor k when it was used to mark the L4S traffic. The coupling factor gives Classic TCP and DCTCP traffic equal throughput; Because L4S marking is factored up by k, the dynamic gain parameters alpha and beta also have to be factored up by k for the L4S queue, which is necessary to ensure that Classic TCP and DCTCP controls have the same stability.

The probability p is kept up to date by the core PI algorithm in Figure 3 which is executed every Tupdate ([I-D.ietf-aqm-pie] now recommends 16ms, but in our testing so far we have used the earlier recommendation of 32ms). 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. Line 3 and 4 only need to be executed when the configuration parameters are changed. Alpha and beta in Hz are gain factors per 1 second. If a briefer update time is configured, alpha_U and beta_U (_U = per Tupdate) also have to be reduced, to ensure that the same response is given over time. As such, a smaller Tupdate will only result in a response with smaller and finer steps, not a more aggressive response. The new probability is calculated in line 5, where target is the target queuing delay, as defined in [I-D.ietf-aqm-pie]. In corner cases, p can overflow the range [0,1] so the resulting value of p has to be bounded (omitted from the pseudocode). Unlike PIE, alpha_U and beta_U are not tuned dependent on p, every Tupdate. 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].

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, PI2 achieves good results with the following parameters:

  • tshift = 40ms
  • T = max(1ms, serialization time of 2 MTU)
  • target = 20ms
  • Tupdate = 32ms
  • k = 2
  • alpha = 10Hz (alpha*k = 20Hz for L4S)
  • beta = 100Hz (beta*k = 200Hz for L4S)

Appendix B. Example DualQ Coupled Curvy RED Algorithm

As another example, the pseudocode below gives the Curvy RED based DualQ Coupled AQM 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 4: Example Dequeue Pseudocode for DualQ Coupled Curvy RED AQM

Packet classification code is not shown, as it is no different from Figure 1. Potential classification schemes are discussed in Section 2. Overload protection code will be included in a future draft {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):

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 5).
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.

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 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 (Section 2.1). So S_L and k count as only one parameter;
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.

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 5: 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 5) 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

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

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 the recommended value of k=0 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 would achieve throughput equivalence, and our experiments verified the formula very closely.

Authors' Addresses

Koen De Schepper Nokia Bell Labs Antwerp, Belgium EMail: URI:
Bob Briscoe (editor) Simula Research Lab EMail: URI:
Olga Bondarenko Simula Research Lab Lysaker, Norway EMail: URI:
Ing-jyh Tsang Nokia Bell Labs Antwerp, Belgium EMail: