RFC 9332

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

📅 published January 2023, from ietf

Part 1 of 15 🎀

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

Okay bestie, let's do the paperwork first 📋 This is RFC 9332, and it's Experimental, which means it's not a Standards Track thing. It's for trying stuff out and testing it 🧪 It was published in January 2023 by K. De Schepper (Nokia Bell Labs), B. Briscoe, Ed. (Independent), and G. White (CableLabs). The ISSN is 2070-1721. The title block has no Obsoletes or Updates line, so this RFC isn't replacing or updating any other RFC 🙅‍♀️

Abstract 🌸

This spec is a framework for coupling the Active Queue Management (AQM) algorithms in two queues. Each queue is for flows that react to congestion in different ways 💖 The big goal is helping the Internet move from the scaling problems of standard TCP-Reno-friendly ('Classic') congestion controls to the family of 'Scalable' congestion controls 🚀 Scalable controls are built for consistently very low queuing latency, very low congestion loss, and scaling per-flow throughput, and they use Explicit Congestion Notification (ECN) in a modified way ✨

Here's the catch: until the Coupled Dual Queue (DualQ) came along, these Scalable L4S congestion controls could only be deployed where a clean-slate environment could be set up, like private data centres 🏢 So this is kind of a big deal, ngl 😭

The spec first explains how a Coupled DualQ works 🧠 Then it lists the normative requirements needed for it to work well 💅 All of this is independent of which two AQMs you use, but pseudocode examples of specific AQMs are in the appendices 🦋

Status of This Memo 🎀

This document is not an Internet Standards Track specification. It's published for examination, experimental implementation, and evaluation 🧪

This document defines an Experimental Protocol for the Internet community. It's a product of the Internet Engineering Task Force (IETF) and represents the consensus of the IETF community 🫶 It got public review and was approved for publication by the Internet Engineering Steering Group (IESG). Not every IESG-approved document is a candidate for any level of Internet Standard, so see Section 2 of RFC 7841 👀

Info about the current status of this document, any errata, and how to give feedback is at https://www.rfc-editor.org/info/rfc9332 🔗

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

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

Table of Contents 🧚

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

1. Introduction ✨

This document specifies a framework for DualQ Coupled AQMs, which can serve as the network part of the L4S architecture [RFC9330] 🦋 A DualQ Coupled AQM has two queues: L4S and Classic 👯‍♀️ The L4S queue is for Scalable congestion controls that can keep queuing latency super low (sub-millisecond on average) and still get high throughput at the same time 🔥 The Coupled DualQ acts like a semi-permeable membrane 🫧 The L4S queue keeps the sub-millisecond average queuing delay of L4S separate from Classic latency, while the coupling between the queues pools the capacity of both queues. That way, ad hoc numbers of capacity-seeking applications sharing the same capacity can get roughly equivalent throughput per flow, whichever queue they use 💜 The DualQ does this indirectly, without inspecting transport-layer flow identifiers, and without hurting Classic traffic performance compared to a single queue 🙌 Honestly the DualQ design is low complexity and needs no configuration for the public Internet 🍓

1.1. Outline of the Problem

okay bestie, latency is literally becoming THE critical performance factor for most apps on the public Internet ✨ Think interactive web, web services, voice, conversational video, interactive video, interactive remote presence, instant messaging, online gaming, remote desktop, cloud-based apps, and video-assisted remote control of machinery and industrial processes 🤖 Once access network bitrates reach the levels that are common in the developed world, more speed gives diminishing returns unless latency gets addressed too [Dukkipati06] 📉 In the last decade or so, people have done a lot to cut propagation time by placing caches or servers closer to users 🌍 But queuing is still a major intermittent component of latency 😤

Previously, very low latency was only available for a few selected low-rate apps that keep their sending rate inside a specially carved-off portion of capacity. That portion gets prioritized over other traffic, e.g., Diffserv Expedited Forwarding (EF) [RFC3246] 🎀 Up to now, it hasn't been possible for any number of low-latency, high-throughput apps to seek to fully utilize available capacity, because the capacity-seeking process itself causes too much queuing delay 💀

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

  • Recent state-of-the-art AQM in the network, e.g., Flow Queue CoDel [RFC8290], Proportional Integral controller Enhanced (PIE) [RFC8033], and Adaptive Random Early Detection (ARED) [ARED01]), has reduced queuing delay for all traffic, not just a select few apps 🙌 However, no matter how good the AQM, the capacity-seeking (sawtoothing) rate of TCP-like congestion controls represents a lower limit that will cause either the queuing delay to vary or the link to be underutilized 😩 These AQMs are tuned to allow a typical capacity-seeking TCP-Reno-friendly flow to induce an average queue that roughly doubles the base round-trip time (RTT), adding 5-15 ms of queuing on average for a mix of long-running flows and web traffic (cf. 500 microseconds with L4S for the same traffic mix [L4Seval22]). However, for many apps, low delay isn't useful unless it's consistently low 🥺 With these AQMs, 99th percentile queuing delay is 20-30 ms (cf. 2 ms with the same traffic over L4S) ⭐
  • Similarly, recent research into using end-to-end congestion control without needing an AQM in the network (e.g., Bottleneck Bandwidth and Round-trip propagation time (BBR) [BBR-CC]) seems to have hit a similar queuing delay floor of about 20 ms on average. But there are also regular 25 ms delay spikes due to bandwidth probes and 60 ms spikes due to flow-starts 📈💀

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

  1. Far smaller rate variations (sawteeth) than Reno-friendly congestion controls.
  2. A shift of smoothing and hence smoothing delay from network to sender.

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

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

  1. The smaller sawteeth allow an extremely shallow ECN packet-marking threshold in the queue.
  2. No smoothing in the network means that every fluctuation of the queue is signalled immediately.

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

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

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

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

1.2. Context, Scope, and Applicability

L4S involves complementary changes in the network and on end systems, and it's giving teamwork 🤝

  • Network: A DualQ Coupled AQM (defined in the present document) or a modification to flow queue AQMs (described in paragraph "b" in Section 4.2 of the L4S architecture [RFC9330]).
  • End system: A Scalable congestion control (defined in Section 4 of the L4S ECN protocol spec [RFC9331]).
  • Packet identifier: The network and end-system parts of L4S can be deployed incrementally, because they both identify L4S packets using the experimentally assigned ECN codepoints in the IP header: ECT(1) and CE [RFC8311] [RFC9331] 🏷️

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

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

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

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

Latency is not the only concern of L4S 👀

  • The 'Low Loss' part of the name denotes that L4S generally achieves zero congestion loss (which would otherwise cause retransmission delays), due to its use of ECN 🫧
  • The 'Scalable throughput' part of the name denotes that the per-flow throughput of Scalable congestion controls should scale indefinitely, avoiding the imminent scaling problems with 'TCP-Friendly' congestion control algorithms [RFC3649] 📊

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

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

1.3. Terminology 💅

okay so before we get into the good stuff, we need to agree on the vocab 🎀 The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in BCP 14 [RFC2119] [RFC8174] when, and only when, they appear in all capitals, as shown here. 🫶

The DualQ Coupled AQM runs two queues for two services, and the names are very intentional ✨

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

Low Latency, Low Loss, and Scalable throughput (L4S) Service/Queue: The 'L4S' service is for traffic from Scalable congestion control algorithms, such as the Prague congestion control [PRAGUE-CC], which was derived from Data Center TCP [RFC8257]. It's giving main character energy, but it's not just Prague 👑 The L4S service is for more general traffic too. It allows the set of congestion controls with similar scaling properties to Prague to evolve, such as the examples listed below (Relentless, SCReAM, etc.). The term 'L4S queue' means a queue providing the L4S service. 🦋

Classic Congestion Control: This is a congestion control behaviour that can coexist with standard Reno [RFC5681] without causing significantly negative impact on its flow rate [RFC5033]. Okay, the tea ☕ With Classic congestion controls, such as Reno or CUBIC, flow rate has scaled since TCP congestion control was first designed in 1988. So now it takes hundreds of round trips (and growing) to recover after a congestion signal (whether a loss or an ECN mark), as shown in the examples in Section 5.1 of the L4S architecture [RFC9330] and in [RFC3649]. 😭 Therefore, control of queuing and utilization becomes very slack, and the slightest disturbances (e.g., from new flows starting) prevent a high rate from being attained. It's so not it 💀

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

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

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

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

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

Reno-friendly: This is the subset of Classic traffic that is friendly to the standard Reno congestion control defined for TCP in [RFC5681]. The TFRC spec [RFC5348] indirectly implies that 'friendly' is defined as "generally within a factor of two of the sending rate of a TCP flow under the same conditions". 'Reno-friendly' is used here in place of 'TCP-friendly', because the latter has gotten imprecise. The TCP protocol is now used with so many different congestion control behaviours, and Reno is used in non-TCP transports, such as QUIC [RFC9000]. Honestly, it's giving confusing if we don't fix it 🎀

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

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

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

1.4. Features 🌸

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

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

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

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

The two queues are only necessary because:

  • The large variations (sawteeth) of Classic flows need roughly a base RTT of queuing delay to ensure full utilization.
  • Scalable flows do not need a queue to keep utilization high, but they cannot keep latency consistently low if they are mixed with Classic traffic.

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

2. DualQ Coupled AQM 👑

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

  1. The Coupled AQM that addresses throughput equivalence between Classic (e.g., Reno or CUBIC) flows and L4S flows (that satisfy the Prague L4S requirements). ✨
  2. The Dual-Queue structure that provides latency separation for L4S flows, isolating them from the typically large Classic queue. 💖

2.1. Coupled AQM

okay so back in the 1990s, people worked out the 'TCP formula' 🧮✨ which links the steady-state congestion window, cwnd, to the drop probability, p, of standard Reno congestion control [RFC5681]. To a first-order approximation, Reno's steady-state cwnd is inversely proportional to the square root of p. the square root part is literally the whole plot 🌸

The design focuses on Reno as the worst case, bestie, because if something does no harm to Reno, it won't harm CUBIC or any traffic designed to be friendly to Reno 💅 TCP CUBIC has a Reno-friendly mode, and that's relevant for typical RTTs under 20 ms as long as a single flow's throughput is less than about 350 Mb/s. in those cases, you can assume CUBIC traffic acts a lot like Reno 🦋 The term 'Classic' is used for the whole collection of Reno-friendly traffic, which includes CUBIC and maybe other experimental congestion controls that are meant not to significantly impact the flow rate of Reno 💜

A supporting paper [PI2] works out the equivalent rate equation for DCTCP, and here cwnd is inversely proportional to p (not the square root) 😭 In this case, p is the ECN-marking probability. DCTCP isn't the only congestion control that acts like this, so the term 'Scalable' covers all similar congestion control behaviours (see examples in Section 1.2) 🌈 The term 'L4S' is used for traffic driven by a Scalable congestion control that also complies with the additional 'Prague L4S requirements' [RFC9331] 👑

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

Also, to stay stable, Classic sources need the network to smooth p_C so it changes relatively slowly ✨ It's hard for a network node to know the RTTs of all the flows, so a Classic AQM adds a worst-case RTT of smoothing delay (about 100-200 ms) 🥲 In contrast, L4S shifts responsibility for smoothing ECN feedback over to the sender. That only delays its response by its own RTT, and it allows a more immediate response if necessary 🔥

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

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

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

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

2.2. Dual Queue

okay this one is so simple but so important 🎀 Classic traffic needs to build a large queue to prevent underutilization. So a separate queue is provided for L4S traffic, and it's scheduled with priority over the Classic queue. That priority is conditional, though, to prevent starvation of Classic traffic in certain conditions (see Section 2.4) 🙈

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

2.3. Traffic Classification

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

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

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

2.4. Overall DualQ Coupled AQM Structure ✨

Okay bestie, so Figure 1 shows the overall layout that basically any DualQ Coupled AQM is gonna have 🎀 It's meant to help you understand how the current designs work, but it's not trying to stop anyone from getting creative with other ways of meeting the normative requirements in Section 2.5, which are the bare-minimum stuff that defines a DualQ Coupled AQM 💅 Also, the diagram only shows what happens under normal conditions. Overload and operator-specific classifiers get their own spotlight in Section 2.5.1.1 🌸

The classifier on the left splits incoming traffic between the two queues, L and C 🦋 Each queue has its own AQM that decides how likely it is to mark or drop packets (p_L and p_C). In [PI2], it was proved that it's better to control load with a linear controller and then square the output before using it as a drop probability for Reno-friendly traffic. That's because Reno congestion control cuts its load in proportion to the square root of the increase in drop 🧠 So the AQM for Classic traffic has two stages: i) a base stage that outputs an internal probability p' (pronounced 'p-prime'), and ii) a squaring stage that outputs p_C, where:

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

If you substitute for p_C in equation (1), you get:

p' = p_CL / k.

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

p_CL = k*p'.                          (3)

Now the actual ECN-marking probability p_L that gets applied to the L queue has to track the immediate L queue delay when there's only L-only congestion, and also track p_CL when the congestion is coupled 🌈 So the L queue uses a 'Native AQM' that works out a probability p'_L as a function of the instantaneous L queue delay. And since the L queue has conditional priority over the C queue, whenever the L queue grows, the AQM ought to apply marking probability p'_L, but p_L ought to not fall below p_CL. That gives us:

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

and it's been found to work really well in practice 🔥

The two transformations of p' in equations (2) and (3) are how the required coupling in equation (1) gets implemented, earlier on in the doc 💖

The constant of proportionality, or coupling factor k, in equation (1) sets the ratio between the congestion probabilities (loss or marking) that L4S and Classic traffic experience 💜 So k indirectly sets the ratio between L4S and Classic flow rates, because flows (assuming they're responsive) adjust their rate based on congestion probability. Appendix C.2 gives guidance on picking k and how it affects relative flow rates 🍓

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

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

                 Figure 1: DualQ Coupled AQM Schematic

After the AQMs do their dropping or marking, the scheduler sends their packets out to the link 🚀 Even though the scheduler gives priority to the L queue, that priority isn't as strong as the coupling from the C queue. Here's why: as the C queue grows, the 'Base AQM' sends more congestion signals to L traffic (as well as to C). When L flows slow down in response, they use less than their scheduling share for L traffic. Because the scheduler is work preserving, it fits any C traffic into the gaps 🫶

Giving the L queue priority means very low L queue delay, since the L queue stays empty whenever the coupling is controlling L traffic 🧚 Also, the coupling only has to go in one direction, from Classic to L4S. The priority has to be conditional in some way so the C queue doesn't get starved in the short term (see Section 4.2.2), which gives C traffic a way to push in. Here's the tea: with normal responsive L traffic, the coupled ECN marking lets C traffic push back even against strict priority, by congestion marking the L traffic so it yields some space 😭 But if there's only a small finite set of C packets (like a DNS request or an initial window of data), some Classic AQMs won't induce enough ECN marking in the L queue, no matter how long that small set of C packets waits. Then, if the L queue stays busy, the C traffic would never get a scheduling opportunity from a strict priority scheduler 💀 Ideally, the Classic AQM would be designed to increase the coupled marking the longer the C packets have been waiting, but that's not always practical, which is why L priority has to be conditional. Giving C traffic a small weight or a limited waiting time improves response times for short Classic messages, such as DNS requests, and improves Classic flow startup because immediate capacity is available ✨

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

  • DualPI2 uses a Proportional Integral (PI) controller as the Base AQM. Honestly, this Base AQM with just the squared output and no L4S queue can be used as a drop-in replacement for PIE [RFC8033], in which case it's just called PI2 [PI2]. PI2 is a principled simplification of PIE that is both more responsive and more stable when load changes dynamically 👑
  • Curvy RED is derived from RED [RED], except its configuration parameters are delay-based so they're insensitive to link rate, and it requires fewer operations per packet than RED. However, DualPI2 is more responsive and stable over a wider range of RTTs than Curvy RED. As a result, at the time of writing, DualPI2 has gotten way more development and evaluation attention than Curvy RED, so the Curvy RED design isn't as fully evaluated 🙈

Both AQMs regulate their queue against targets configured in units of time rather than bytes. As already explained, this means the configuration stays invariant for different drain rates 🌸 With AQMs in a DualQ structure, this matters a lot, because the drain rate of each queue can change rapidly as flows for the two queues arrive and depart, even when the combined link rate is constant 😤

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

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

2.5. Normative Requirements for a DualQ Coupled AQM 💅

The following requirements are meant to capture only the essential aspects of a DualQ Coupled AQM 🫶 They're designed to be independent of the particular AQMs implemented for each queue, but still define the DualQ framework built around those AQMs 💖

2.5.1. Functional Requirements 👑

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

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

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

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

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

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

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

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

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

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

2.5.1.1. Requirements in Unexpected Cases 🙈

Okay so operator-specific classifiers (Section 2.3) are super flexible, which means we have to spell out what the AQM in each queue should do with packets that don't carry the ECN field that queue expects. 💅 Each AQM is gonna look at the ECN field to figure out what kind of congestion notification to send, and then decide whether to actually apply it to this packet. Here's how it goes:

  • If a packet that does not carry an ECT(1) or a CE codepoint gets classified into the L queue, then:
    • if the packet is ECT(0), the L AQM SHOULD apply CE marking using a probability that suits Classic congestion control and the target delay in the L queue ✨
    • if the packet is Not-ECT, it depends on whether something else is protecting the L queue from misbehaving flows (like per-flow queue protection [DOCSIS-Q-PROT] or latency policing) 🛡️:
      • if separate queue protection is provided, the L AQM SHOULD ignore the packet and forward it unchanged. That means it shouldn't calculate whether to apply congestion notification, and it should neither drop nor CE mark the packet (for instance, the operator might classify EF traffic that is unresponsive to drop into the L queue, alongside responsive L4S-ECN traffic) 💖
      • if separate queue protection is not provided, the L AQM SHOULD apply drop using a drop probability that suits Classic congestion control and the target delay in the L queue 😤
  • If a packet that carries an ECT(1) codepoint gets classified into the C queue:
    • the C AQM SHOULD apply CE marking using the Coupled AQM probability p_CL (= k*p') 🦋

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

If the DualQ Coupled AQM has detected overload, it MUST introduce Classic drop to both types of ECN-capable traffic until the overload episode has subsided. This is non-negotiable bestie 😭

Introducing drop if ECN marking is persistently high is recommended in Section 7 of the ECN spec [RFC3168] and in Section 4.2.1 of the AQM Recommendations [RFC7567]. 🌸

2.5.2. Management Requirements 🧚

2.5.2.1. Configuration

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

  • Optional packet classifier(s) to use in addition to the ECN field (see Section 2.3).
  • Expected typical RTT, which can be used to determine the queuing delay of the Classic AQM at its operating point, so that typical lone flows don't underutilize capacity. For example:
    • for the PI2 algorithm (Appendix A), the queuing delay target is dependent on the typical RTT.
    • for the Curvy RED algorithm (Appendix B), the queuing delay at the desired operating point of the curvy ramp is configured to encompass a typical RTT.
    • if another Classic AQM was used, it would be likely to need an operating point for the queue based on the typical RTT, and if so, it SHOULD be expressed in units of time.

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

  • Expected maximum RTT, which can be used to set the stability parameter(s) of the Classic AQM. For example:
    • for the PI2 algorithm (Appendix A), the gain parameters of the PI algorithm depend on the maximum RTT.
    • for the Curvy RED algorithm (Appendix B), the smoothing parameter is chosen to filter out transients in the queue within a maximum RTT.

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

  • Coupling factor, k (see Appendix C.2).
  • A limit to the conditional priority of L4S. This is scheduler-dependent, but it SHOULD be expressed as a relation between the max delay of a C packet and an L packet. For example:
    • for a WRR scheduler, a weight ratio between L and C of w:1 means that the maximum delay of a C packet is w times that of an L packet.
    • for a time-shifted FIFO (TS-FIFO) scheduler (see Section 4.2.2), a time-shift of tshift means that the maximum delay to a C packet is tshift greater than that of an L packet. tshift could be expressed as a multiple of the typical RTT rather than as an absolute delay. ⭐
  • The maximum Classic ECN-marking probability, p_Cmax, before introducing drop.

2.5.2.2. Monitoring

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

  • bits forwarded, from which utilization can be calculated;
  • total packets in the three categories: arrived, presented to the AQM, and forwarded. The difference between the first two will measure any non-AQM tail discard. The difference between the last two will measure proactive AQM discard;
  • ECN packets marked, non-ECN packets dropped, and ECN packets dropped, which can be combined with the three total packet counts above to calculate marking and dropping probabilities; and
  • queue delay (not including serialization delay of the head packet or medium acquisition delay) -- see further notes below.

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

2.5.2.3. Anomaly Detection

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

  • Start time and duration of overload state.

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

2.5.2.4. Deployment, Coexistence, and Scaling

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

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

3. IANA Considerations 🎀

This document has no IANA actions. ✨

4. Security Considerations 😱

4.1. Low Delay without Requiring Per-flow Processing

Okay this section is lowkey the most important one, so pay attention bestie 🫶 The L4S architecture [RFC9330] compares the DualQ and FQ approaches to L4S. Its privacy considerations section motivates the DualQ on the grounds that users who want to encrypt application flow identifiers, e.g., in IPsec or other encrypted VPN tunnels, don't have to sacrifice low delay ([RFC8404] encourages avoidance of such privacy compromises). 🔐

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

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

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

4.2. Handling Unresponsive Flows and Overload ✨

Okay bestie, this section is all about the chaos 💀. What happens when flows refuse to behave, and when the link is basically drowning? 🌊 Without any per-flow control 🙈, it's important that the basic DualQ Coupled AQM doesn't give unresponsive flows any more throughput advantage than a single-queue AQM would, and that it at least handles overload situations 🔥. Overload means incoming load significantly or persistently exceeds output capacity. It's not meant to be a precise term, since "significant" and "persistent" are matters of degree 🌈.

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

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

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

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

This case is not covered by the regular Coupled DualQ mechanism (Section 2.1), but the last paragraph in Section 2.5.1.1 sets out a requirement to handle the case where ECN-capable traffic could starve non-ECN-capable traffic. Section 4.2.3 below discusses the general options and gives specific examples.

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

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

4.2.1. Unresponsive Traffic without Overload 🦋

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

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

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

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

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

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

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

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

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

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

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

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

4.2.3. L4S ECN Saturation: Introduce Drop or Delay? 💥

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

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

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

Drop on Saturation: Persistent saturation can be defined by a maximum threshold for coupled L4S ECN marking (assuming k>1) before saturation starts to make the flow rates of the different traffic types diverge. Above that, the drop probability of Classic traffic is applied to all packets of all traffic types. Then experiments have shown that queuing delay can be kept at the target in any overload situation, including with unresponsive traffic, and no further measures are required (Section 4.2.3.1).

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

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

4.2.3.1. Protecting against Overload by Unresponsive ECN-Capable Traffic ✨

okay so 🫶 without a specific overload mechanism, unresponsive traffic gets an extra edge if it's ECN-capable too 👀. At normal low marking levels you literally can't tell 🙈. But during overload, when marking is way higher, that edge gets huge and the flow can dodge a big chunk of drops 😭. And this is a problem whether the ECN-capable traffic is L4S or Classic 💅.

So the big question is whether and when to start dropping ECN-capable traffic 📜, which is something both Section 7 of the ECN spec [RFC3168] and Section 4.2.1 of the AQM recommendations [RFC7567] bring up.

Here's the tea ☕. Experiments with the DualPI2 AQM (Appendix A) showed that introducing 'drop on saturation' at 100% coupled L4S marking fixes this unresponsive ECN problem 🎉, and it also fixes the saturation problem. At saturation, DualPI2 switches into overload mode 🚨, where the Base AQM is driven by the max delay of both queues, and it introduces probabilistic drop to both queues equally.

The leftover window is tiny 🦋. It's only a small range of congestion levels just below saturation where unresponsive traffic gets any advantage from using the ECN capability (compared to being unresponsive without ECN), and even then the advantage is hardly detectable (see [DualQ-Test] and section IV-G of [L4Seval22]). Also, overload with an unresponsive ECT(1) flow gets no more bandwidth advantage than with ECT(0) 💖.

5. References 📚

5.1. Normative References

5.2. Informative References

Appendix A. Example DualQ Coupled PI2 Algorithm 🎀

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

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

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

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

A.1. Pass #1: Core Concepts

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

  • The initialization function dualpi2_params_init(...) (Figure 2) that sets parameter defaults (the API for setting non-default values is omitted for brevity).
  • The enqueue function dualpi2_enqueue(lq, cq, pkt) (Figure 3).
  • The dequeue function dualpi2_dequeue(lq, cq, pkt) (Figure 4).
  • The recurrence function recur(q, likelihood) for de-randomized ECN marking (shown at the end of Figure 4).
  • The L4S AQM function laqm(qdelay) (Figure 5) used to calculate the ECN-marking probability for the L4S queue.
  • The Base AQM function that implements the PI algorithm dualpi2_update(lq, cq) (Figure 6) used to regularly update the base probability (p'), which is squared for the Classic AQM as well as being coupled across to the L4S queue.

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

  • scheduler(), which selects between the head packets of the two queues. The choice of scheduler technology is discussed later.
  • cq.byt() or lq.byt() returns the current length (a.k.a. backlog) of the relevant queue in bytes.
  • cq.len() or lq.len() returns the current length of the relevant queue in packets.
  • cq.time() or lq.time() returns the current queuing delay of the relevant queue in units of time (see Note a below).
  • mark(pkt) and drop(pkt) for ECN marking and dropping a packet.

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

1:  dualpi2_params_init(...) {         % Set input parameter defaults
2:    % DualQ Coupled framework parameters
5:    limit = MAX_LINK_RATE * 250 ms               % Dual buffer size
3:    k = 2                                         % Coupling factor
4:    % NOT SHOWN % scheduler-dependent weight or equival't parameter
6:
7:    % PI2 Classic AQM parameters
8:    target = 15 ms                             % Queue delay target
9:    RTT_max = 100 ms                      % Worst case RTT expected
10:   % PI2 constants derived from above PI2 parameters
11:   p_Cmax = min(1/k^2, 1)             % Max Classic drop/mark prob
12:   Tupdate = min(target, RTT_max/3)        % PI sampling interval
13:   alpha = 0.1 * Tupdate / RTT_max^2      % PI integral gain in Hz
14:   beta = 0.3 / RTT_max               % PI proportional gain in Hz
15:
16:   % L4S ramp AQM parameters
17:   minTh = 800 us        % L4S min marking threshold in time units
18:   range = 400 us                % Range of L4S ramp in time units
19:   Th_len = 1 pkt           % Min L4S marking threshold in packets
20:   % L4S constants
21:   p_Lmax = 1                               % Max L4S marking prob
22: }

Figure 2: Example Header Pseudocode for DualQ Coupled PI2 AQM

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

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

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

Figure 3: Example Enqueue Pseudocode for DualQ Coupled PI2 AQM

Okay so, this is where the dequeue magic happens ✨ Here's the whole dance in one go 💃

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

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

Figure 4: Example Dequeue Pseudocode for DualQ Coupled PI2 AQM

When packets arrive, the shared queue limit gets checked first, like line 2 of the enqueuing pseudocode in Figure 3 🎀 This assumes one shared buffer for both queues (Note b talks about whether separate buffers are the better move 👀). To avoid any bias against bigger packets, 1 MTU of space is always allowed, and the limit is tested before the enqueue happens. Iconic, honestly 💅

If the limit isn't exceeded, the packet gets timestamped on line 4. This only happens if the sojourn time technique is being used to measure queue delay (see Note a below for the other options) ⏱️

Lines 5-9 are the sorting hat 🧚 The packet gets classified and sent to either the Classic or the L4S queue, based on the least significant bit (LSB) of the ECN field in the IP header (line 6). Packets with an LSB of 0 (Not-ECT and ECT(0)) go into the Classic queue. Otherwise, ECT(1) and CE packets land in the L4S queue. There's extra optional classification flexibility too, but it's left out for brevity. If you want the full tea, check the L4S ECN protocol [RFC9331] 🍵

The dequeue pseudocode in Figure 4 gets called over and over, whenever the lower layer is ready to forward a packet. It picks one packet to schedule (or zero, if the queue is empty), then hands control back to the caller so nothing blocks while that packet is being forwarded 🚀 While it's making that call, it also makes the AQM decisions about dropping or marking. Doing the AQMs at enqueue instead would move some work away from the critical moment when each packet is dequeued. But it would also add a whole queue's worth of delay to the control signals, making the control loop sloppier. For a typical RTT, that would double the Classic queue's feedback delay 😬

All the dequeue code sits inside one big while loop. So if it decides to drop a packet, it just keeps going until it finds a packet to schedule 🔁 Line 3 is where the scheduler picks between the L4S queue (lq) and the Classic queue (cq). The detailed scheduler implementation isn't shown here (more on that later).

  • If an L4S packet gets scheduled, lines 7 and 8 ECN-mark it with likelihood p_L. The recur() function at the end of Figure 4 does the job. It's preferred over random marking because it avoids the delay that randomization adds when interpreting congestion signals, and it still desynchronizes the sawteeth of the flows 🦋 Line 6 works out p_L as the maximum of the coupled L4S probability p_CL and the probability from the Native L4S AQM p'_L. This is how the max() function from Figure 1 couples the outputs of the two AQMs together. The two inputs to p_L on line 6 come from different places:
    • p'_L is calculated per packet on line 5 by the laqm() function (see Figure 5).
    • p_CL is maintained by the dualpi2_update() function, which runs every Tupdate (Tupdate is set on line 12 of Figure 2).
  • If a Classic packet gets scheduled, lines 10 to 17 drop or mark it with probability p_C 🎯

The Native L4S AQM (Figure 5) is a ramp function, kind of like RED, but simplified in a few ways:

  • The extent of the ramp is defined in units of queuing delay, not bytes. That way the configuration stays invariant as the queue departure rate varies 📏
  • It uses instantaneous queuing delay. That skips the complexity of smoothing, and also avoids baking a worst-case RTT of smoothing delay into the network (see Section 2.1) 🙅‍♀️
  • The ramp rises linearly straight from 0 to 1, not up to an intermediate value of p'_L the way RED does. There's no need to keep the ECN-marking probability low 📈
  • Marking doesn't have to be randomized. Determinism is used instead of randomness, to cut down on the delay needed to smooth out the noise from the signal 🧘‍♀️

The ramp function needs two config parameters: the minimum threshold (minTh) and the width of the ramp (range). Both are in units of queuing time, as shown on lines 17 and 18 of the initialization function in Figure 2. The ramp can also be configured as a step (see Note c) 🪜

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

Figure 5: Example Pseudocode for the Native L4S AQM

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

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

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

Now the coupled marking probability p_CL depends on the base probability p'. That base probability stays up to date by running the core PI algorithm in Figure 6 every Tupdate 🔄

Here's the key tea: p' depends only on the queuing time in the Classic queue. On line 2, the current queuing delay (curq) is worked out from how long the head packet has been sitting in the Classic queue (cq). The cq.time() function (not shown) subtracts the enqueue timestamp from the current time (see Note a below). If the queue is empty, it just treats the current queuing delay as 0 ☕

The real star is line 3, which is a classical PI controller. It changes p' based on two things: a) the error between the current queuing delay (curq) and the target queuing delay (target), and b) the change in queuing delay since the last sample. The "PI" is short for the fact that the second factor (how fast the queue is growing) is Proportional to load, while the first is the Integral of the load. So it's what removes any standing queue above the target 🧠

The target can be set from local knowledge, but the goal is for the default to be a good compromise anywhere in the intended deployment environment, which is the public Internet 🌍 According to [PI2param], the target queuing delay on line 8 of Figure 2 relates to the typical base RTT worldwide, RTT_typ, through two factors: target = RTT_typ * g * f. Below, we summarize the reasoning behind those factors and add one more adjustment. Together, the two factors make sure that in a large proportion of cases (say 90%), the sawtooth variations in RTT of a single flow fit within the buffer without underutilizing the link 🫶 Frankly, these factors are educated guesses. But the emphasis is way closer to "educated" than to "guess" 🤓 (see [PI2param] for the full background):

  • RTT_typ is taken as 25 ms. This comes from an average CDN latency measured in each country, weighted by the number of Internet users in that country, to produce an overall weighted average for the Internet [PI2param]. Countries were ranked by number of Internet users. Once 90% of Internet users were covered, smaller countries were excluded, to avoid small sample sizes that would be less representative. Also, importantly, the data for the average CDN latency in China (the country with the largest number of Internet users) was removed. The CDN latency was a significant outlier there, and on reflection, the experimental technique seemed inappropriate to the CDN market in China 🙈
  • g is taken as 0.38. The factor g is a geometry factor that characterizes the shape of the sawteeth of prevalent Classic congestion controllers. It's the fraction of the amplitude of the sawtooth variability in queue delay that lies below the AQM's target. For instance, at low bitrates the geometry factor of standard Reno is 0.5, but at higher rates it tends towards just under 1. According to the census of congestion controllers that Mishra et al. ran in Jul-Oct 2019 [CCcensus19], most Classic TCP traffic uses CUBIC. And according to the analysis in [PI2param], if it runs over a PI2 AQM, a large proportion of this CUBIC traffic would be in its Reno-friendly mode, which has a geometry factor of ~0.39 (for all known implementations). The rest of the CUBIC traffic would be in true CUBIC mode, which has a geometry factor of ~0.36. Without modelling the sawtooth profiles of all the other, less prevalent congestion controllers, we estimate a 7:3 weighted average of these two. That gives an average geometry factor of 0.38 🧮
  • f is taken as 2. The factor f is a safety factor that increases the target queue to allow for the distribution of RTT_typ around its mean. Otherwise, the target queue would only avoid underutilization for users below the mean. It also gives a safety margin for the proportion of paths in use that span beyond the distance between a user and their local CDN. Right now, no data is available on the variance of queue delay around the mean in each region, so there's plenty of room for this guess to become more educated 📚
  • [PI2param] recommends target = RTT_typ * g * f = 25 ms * 0.38 * 2 = 19 ms. However, a further adjustment is warranted, because target keeps moving year-on-year 📉 The paper is based on data collected in 2019, and it mentions evidence from the Speedtest Global Index suggesting that RTT_typ dropped by 17% (fixed) or 12% (mobile) between 2020 and 2021. So we recommend a default of target = 15 ms at the time of writing (2021) 💜

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

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

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

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

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

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

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

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

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

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

  • Classic and coupled marking or dropping (i.e., based on p_C and p_CL from the PI controller) is not applied to a packet if the aggregate queue length in bytes is < 2 MTU (prior to enqueuing the packet or dequeuing it, depending on whether the AQM is configured to be applied at enqueue or dequeue); and
  • in the WRR scheduler, the 'credit' indicating which queue should transmit is only changed if there are packets in both queues (i.e., if there is actual resource contention). This means that a properly paced L flow might never be delayed by the WRR. The WRR credit is reset in favour of the L queue when the link is idle 🚦

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

Notes:

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

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

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

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

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

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

A.2. Pass #2: Edge-Case Details ✨

Okay bestie, pass #2 is where we level up the pseudocode and add two spicy edge cases: super slow links 🐢 and overload 💀. Figure 7 is the dequeue function from Figure 4 with both edge cases baked in, and Figure 8 is the core PI algorithm from Figure 6 with the overload details added. The initialization, enqueue, L4S AQM, and recur functions are unchanged, so no new drama there 💅

The link rate can be so low that one single packet takes longer to serialize than the threshold delay where ECN marking starts in the L queue 🙈 So we need a minimum marking threshold measured in packets instead of time (Th_len, default 1 packet, line 19 of Figure 2). This keeps the ramp from going wild and marking way too much on slow links. If an implementation knows the link rate, it can set this minimum when it's configured. For example, it would divide 1 MTU by the link rate to get a serialization time. If the lower threshold of the Native L AQM ramp is lower than that serialization time, it could increase the thresholds to shift the bottom of the ramp to 2 MTU. This is the approach used in DOCSIS [DOCSIS3.1], because the configured link rate is dedicated to the DualQ 🎀

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

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

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

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

When the Classic ECN-marking probability reaches the p_Cmax threshold (1/k^2), the marking probability coupled to the L4S queue, p_CL, will always be 100% for any k (by equation (1) in Section 2.1). So, for readability, the constant p_Lmax is defined as 1 in line 21 of the initialization function (Figure 2). This is intended to make sure the L4S queue starts to introduce dropping once ECN marking saturates at 100% and can't rise any further 🦋 The 'Prague L4S requirements' [RFC9331] state that when an L4S congestion control detects a drop, it falls back to a response that coexists with 'Classic' Reno congestion control. So it's correct that when the L4S queue drops packets, it drops them proportional to p'^2, as if they are Classic packets.

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

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

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

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

       Figure 7: Example Dequeue Pseudocode for DualQ Coupled PI2 AQM
                     (Including Code for Edge-Cases)
1:  dualpi2_update(lq, cq) {                % Update p' every Tupdate
2a:   curq = max(cq.time(), lq.time())    % use greatest queuing time
3:    p' = p' + alpha * (curq - target) + beta * (curq - prevq)
4:    p_CL = p' * k  % Coupled L4S prob = base prob * coupling factor
5:    p_C = p'^2                       % Classic prob = (base prob)^2
6:    prevq = curq
7:  }

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

The choice of scheduler technology is critical to overload protection (see Section 4.2.2). Here's the lineup 👑

  • A well-understood weighted scheduler such as WRR is recommended. As long as the scheduler weight for Classic is small (e.g., 1/16), its exact value is unimportant, because it doesn't normally determine capacity shares. The weight is only important to prevent unresponsive L4S traffic from starving Classic traffic in the short term (see Section 4.2.2). This is because capacity sharing between the queues is normally determined by the coupled congestion signal, which overrides the scheduler by making L4S sources leave roughly equal per-flow capacity available for Classic flows.
  • Alternatively, a time-shifted FIFO (TS-FIFO) could be used. It works by selecting the head packet that has waited the longest, biased against the Classic traffic by a time-shift of tshift. To implement TS-FIFO, the scheduler() function in line 3 of the dequeue code would simply be implemented as the scheduler() function at the bottom of Figure 10 in Appendix B. For the public Internet, a good value for tshift is 50 ms. For private networks with smaller diameter, about 4*target would be reasonable. TS-FIFO is a very simple scheduler, but complexity might need to be added to address some deficiencies (which is why it is not recommended over WRR):
    • TS-FIFO does not fully isolate latency in the L4S queue from uncontrolled bursts in the Classic queue;
    • using sojourn time for TS-FIFO is only appropriate if timestamping of packets is feasible; and
    • even if timestamping is supported, the sojourn time of the head packet is always stale, so a more instantaneous measure of queue delay could be used (see Note a in Appendix A.1).
  • A strict priority scheduler would be inappropriate, as discussed in Section 4.2.2.

Appendix B. Example DualQ Coupled Curvy RED Algorithm 🌈

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

B.1. Curvy RED in Pseudocode

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

  • the initialization function cred_params_init(...) (Figure 2) that sets parameter defaults (the API for setting non-default values is omitted for brevity);
  • the dequeue function cred_dequeue(lq, cq, pkt) (Figure 4); and
  • the scheduling function scheduler(), which selects between the head packets of the two queues.

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

  • the enqueue function, which is identical to that used for DualPI2, dualpi2_enqueue(lq, cq, pkt) in Figure 3;
  • mark(pkt) and drop(pkt) for ECN marking and dropping a packet;
  • cq.byt() or lq.byt() returns the current length (a.k.a. backlog) of the relevant queue in bytes; and
  • cq.time() or lq.time() returns the current queuing delay of the relevant queue in units of time (see Note a in Appendix A.1).

Okay bestie, so Curvy RED got tested before DualPI2 💅 which means some of the glow-ups DualPI2 got never got tested on Curvy RED 🥺 In the pseudocode below, the easy upgrades have been added because they'll probably help too, but nobody has proved that with experiments yet 🙈 The three upgrades are: i) a conditional priority scheduler instead of strict priority; ii) a time-based threshold for the Native L4S AQM; and iii) ECN support for the Classic AQM. A recent evaluation proved that a minimum ECN-marking threshold (minTh) makes performance way better, so that's in there too ✨

Overload protection isn't in the Curvy RED pseudocode, so the main features stay front and center 🎀 It would be added in exactly the same way as in Appendix A.2 for the DualPI2 pseudocode. The Native L4S AQM uses a step threshold, but a ramp like the one described for DualPI2 could be used instead 🌈 The scheduler uses the simple TS-FIFO algorithm, but it could be swapped out for WRR 💜

The Curvy RED algorithm hasn't been maintained or evaluated as much as DualPI2, so it's a bit more of a side character 🦋 In early experiments on broadband access links, from 4 Mb/s up to 200 Mb/s with base RTTs from 5 ms to 100 ms, Curvy RED did really well with the default parameters in Figure 9 💖

The parameters are sorted by whether they belong to the Classic AQM, the L4S AQM, or the framework that couples them together 🧚 Constants and variables derived from those parameters are listed at the end of each group. These are the raw input parameters for the algorithm. A configuration front-end could accept more meaningful parameters (e.g., RTT_max and RTT_typ) and convert them into these raw parameters, the same way it was done for DualPI2 in Appendix A 🍓 Where needed, the parameters get explained more in the pseudocode walk-through below.

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

1:  cred_params_init(...) {            % Set input parameter defaults
2:    % DualQ Coupled framework parameters
3:    limit = MAX_LINK_RATE * 250 ms               % Dual buffer size
4:    k' = 1                        % Coupling factor as a power of 2
5:    tshift = 50 ms                % Time-shift of TS-FIFO scheduler
6:    % Constants derived from Classic AQM parameters
7:    k = 2^k'                    % Coupling factor from equation (1)
6:
7:    % Classic AQM parameters
8:    g_C = 5            % EWMA smoothing parameter as a power of 1/2
9:    S_C = -1          % Classic ramp scaling factor as a power of 2
10:   minTh = 500 ms    % No Classic drop/mark below this queue delay
11:   % Constants derived from Classic AQM parameters
12:   gamma = 2^(-g_C)                     % EWMA smoothing parameter
13:   range_C = 2^S_C                         % Range of Classic ramp
14:
15:   % L4S AQM parameters
16:   T = 1 ms             % Queue delay threshold for Native L4S AQM
17:   % Constants derived from above parameters
18:   S_L = S_C - k'        % L4S ramp scaling factor as a power of 2
19:   range_L = 2^S_L                             % Range of L4S ramp
20: }

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

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

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

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

The dequeue pseudocode in Figure 10 gets called over and over whenever the lower layer is ready to forward a packet 💅 Each call schedules one packet for dequeuing (or zero if the queue is empty), then hands control back to the caller so it doesn't block while that packet is being forwarded ✨ While it's picking, it also makes the dropping or marking decisions. Applying the AQMs at enqueue instead would move some processing away from the critical moment when each packet leaves the queue. But it would also tack a whole queue of delay onto the control signals, making the control loop very sloppy 😭

The code assumes the AQMs are applied on dequeue (Note 1). All the dequeue code sits inside one big while loop, so if it decides to drop a packet, it just keeps going until it picks a packet to schedule 🔁 If both queues are empty, the routine returns NULL at line 20. Line 3 is where the conditional priority scheduler chooses between the L4S queue (lq) and the Classic queue (cq) 🎀 The TS-FIFO scheduler is at lines 28-33, which is the one to use if simplicity is the top priority (see Note 2).

Inside each queue, the call on whether to forward, drop, or mark goes like this (to keep things simple, we assume U = 1):

L4S: If the test at line 3 finds an L4S packet to dequeue, the tests at lines 5b and 5c decide whether to mark it 🌸 The first is a plain check on whether the L4S queue delay (lq.time()) is bigger than a step threshold T (Note 3). The second is similar to random ECN marking in RED, but with some key differences: i) marking depends on queuing time, not bytes, so it scales to any link rate without being reconfigured; ii) marking of the L4S queue depends on a logical OR of two tests, one against its own queuing time and one against the queuing time of the _other_ (Classic) queue; iii) the tests use the instantaneous queuing time of the L4S queue, but a smoothed average of the other (Classic) queue; and iv) the queue is compared with the maximum of U random numbers (but when U = 1, that's the same as the single random number RED uses) 🧠

Specifically, line 5a sets the coupled marking probability p_CL to however far the averaged Classic queuing delay Q_C goes past the minimum queuing delay threshold (minTh), all divided by the L4S scaling parameter range_L. range_L is the queuing delay (in seconds) added to minTh at which the marking probability hits 100% 💯 Then, at line 5c (if U = 1), the result gets compared with a uniformly distributed random number between 0 and 1. That means that over range_L, the marking probability rises in a straight line with queuing time 📈

Classic: If the scheduler at line 3 picks a Classic packet and jumps to line 7, the test at line 10b decides whether to drop or mark it 👑 But first, line 9a updates Q_C, an exponentially weighted moving average (Note 4) of the queuing time of the Classic queue. cq.time() is the current instantaneous queuing time of the packet at the head of the Classic queue (zero if it's empty), and gamma is the exponentially weighted moving average (EWMA) constant (default 1/32; see line 12 of the initialization function) 🦋

Lines 10a and 10b implement the Classic AQM. At line 10a, the averaged queuing time Q_C gets divided by the Classic scaling parameter range_C, the same way queuing time was scaled for L4S marking. This scaled value gets squared to compute the Classic drop probability. So before it's squared, it's effectively the square root of the drop probability, which is why it's named sqrt_p_C 🤓 The squaring happens by comparing it with the maximum of two random numbers (assuming U = 1). Comparing against the maximum of two is the same as a logical 'AND' of two tests, and that's what makes drop probability rise with the square of queuing time 💅

The AQM functions in each queue (lines 5c and 10b) are two cases of a new generalization of RED called 'Curvy RED', and here's the motivation 🌈 When this AQM was compared with FQ-CoDel and PIE, their goal of holding queuing delay to a fixed target seemed misguided [CRED_Insights]. As the number of flows goes up, if the AQM doesn't let host congestion controllers raise queuing delay, it has to introduce abnormally high levels of loss. Then loss, rather than queuing, becomes the main cause of delay for short flows, because of timeouts and tail losses 😭

Curvy RED keeps delay in check with a softened target that lets delay creep up as load increases ✨ It does this by increasing drop probability along 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 goes up, it puts up a growing barrier against higher delay 🚧 But unlike RED, it needs only two parameters, not three. The downside of Curvy RED (compared to a PI controller, for example) is that it isn't adapted to a wide range of RTTs. Curvy RED can be used as is when the RTT range you need to support is limited; otherwise, an adaptation mechanism is needed 🙈

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

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

Notes:

  1. The alternative of applying the AQMs at enqueue would shift some processing away from the critical time when each packet is dequeued. However, it would also add a whole queue of delay to the control signals, making the control loop sloppier (for a typical RTT, it would double the Classic queue's feedback delay). On a platform where packet timestamping is feasible, e.g., Linux, it's also easiest to apply the AQMs at dequeue, because that's where queuing time is also measured 🧚
  2. okay so WRR isolates the L4S queue from big delay bursts in the Classic queue better than TS-FIFO does 💅, but it's slightly less simple ✨ If WRR got used, you'd need a low default Classic weight (e.g., 1/16) configured instead of the time-shift in line 5 of the initialization function (Figure 9) 🎀
  3. A step function is shown for simplicity 💖 A ramp function (see Figure 5 and the discussion around it in Appendix A.1) is recommended, because it's more general than a step and has the potential to enable L4S congestion controls to converge more rapidly 🦋
  4. An EWMA is only one possible way to filter bursts 🌸 Other, more adaptive smoothing methods could be valid, and it might be appropriate to decrease the EWMA faster than it increases, e.g., by using the minimum of the smoothed and instantaneous queue delays, min(Q_C, qc.time()) ✨

B.2. Efficient Implementation of Curvy RED 💜

Okay, so the code optimisation depends on the platform 🙈 but the notes below explain where Curvy RED's design was especially motivated by efficient implementation. It's giving engineering brain, no cap 🧠

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

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

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

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

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

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

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

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

Appendix C. Choice of Coupling Factor, k 🎀

C.1. RTT-Dependence 🦋

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

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

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

C.2. Guidance on Controlling Throughput Equivalence

okay so the coupling factor, k, is basically the knob that decides how L4S and Classic flows share throughput 💅 (see Section 2.5.2.1 and equation (1) in Section 2.1). ✨

for the public Internet, a coupling factor of k = 2 is recommended, and I'll justify it below 🫶. for other scenarios, you can get a good coupling factor by plugging the right numbers into the same working. 🧮

to summarize the maths (no cap, it's kinda long), equation (7) shows that k = 1.64 would theoretically make L4S throughput roughly the same as Classic, _if their actual end-to-end RTTs were the same_ 👀. but even with the same base RTTs, the actual RTTs are unlikely to match, because Classic traffic needs a pretty big queue to avoid underutilization and excess drop, while L4S doesn't 😭.

so the operator needs to decide the base RTT where they want L4S and Classic flows to have roughly equal throughput, once the extra Classic queue's effect on Classic throughput is factored in 🎀. with this approach, a network operator can pick a good coupling factor without knowing the exact L4S algorithm for reducing RTT-dependence, or even if no such algorithm exists 🦋.

the following extra terminology is used, with the appropriate subscripts:

  • r: Packet rate [pkt/s]
  • R: RTT [s/round]
  • p: ECN-marking probability []

on the Classic side, we treat Reno as the most sensitive and therefore worst-case Classic congestion control 💀. we also look at CUBIC in its Reno-friendly mode ('CReno'), since it's the most prevalent congestion control according to the references and analysis in [PI2param] 👑. either way, the steady-state Classic packet rate follows the well-known square root formula for Reno congestion control:

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

on the L4S side, we use the Prague congestion control [PRAGUE-CC] as the reference for steady-state dependence on congestion 🌈. Prague follows the same equation as DCTCP, but we don't use the equation from the DCTCP paper, because that one is only appropriate for step marking 🙈. the coupled marking, p_CL, is the right one when we're checking throughput equivalence with Classic flows. unlike step marking, coupled markings are inherently spaced out, so we use the DCTCP packet rate formula with probabilistic marking derived in Appendix A of [PI2] ✨. we use it without RTT-independence enabled, and we'll explain why later 🧚.

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

for packet rate equivalence, we equate the two packet rates and rearrange them into the same form as equation (1) (copied from Section 2.1). then they can be equated and simplified to give a formula for a theoretical coupling factor, which we'll call k* 🍓:

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

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

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

we call this coupling factor theoretical because it's written in terms of two RTTs, and that raises two practical questions 🙃. first, for multiple flows with different RTTs, the RTT for each traffic class would have to be derived from the RTTs of all the flows in that class (in fact, the harmonic mean would be needed). second, a network node can't easily know the RTT of the flows anyway 😭.

RTT-dependence is caused by window-based congestion control, so it ought to be reversed there, not in the network 💅. that's why we use a fixed coupling factor in the network and reduce RTT-dependence in L4S senders. we can't expect every Classic sender to be updated to reduce its RTT-dependence 🥺. but solving it only in L4S senders at least makes RTT-dependence no worse, not just between L4S senders, but also between L4S and Classic senders 🫶.

throughput equivalence is defined for flows under comparable conditions, including the same base RTT [RFC2914] 🎀. so if we assume the same base RTT, R_b, for comparable flows, we can write both R_C and R_L in terms of R_b ✨.

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

taking PI2 as an example Classic AQM, you might think we could just use R_C = R_b + target (recommended at 15 ms by default in Appendix A.1). but target is roughly the queue depth reached by the tips of the congestion control sawteeth, not the average [PI2param] 😭. so R_max = R_b + target 🌸.

where the average sits compared with the max depends on the amplitude and geometry of the sawteeth 📈. we look at two examples: Reno [RFC5681], as the most sensitive worst case, and CUBIC [RFC8312] in its Reno-friendly mode ('CReno'), as the most prevalent congestion control algorithm on the Internet according to the references in [PI2param] 👑. both are Additive Increase Multiplicative Decrease (AIMD), so we generalize using b as the multiplicative decrease factor (b_r = 0.5 for Reno, b_c = 0.7 for CReno). then:

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

   R_reno = 0.75 * (R_b + target);    R_creno = 0.85 * (R_b + target).
                                                                     (8)

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

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

an operator can then pick the base RTT where it wants throughput to be equivalent 🎀. for instance, if we suggest the operator picks R_b = 25 ms, as a typical base RTT between Internet users and CDNs [PI2param], these coupling factors become:

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

the approximation applies to any of the example DualQ Coupled algorithms above, which use a coupling factor that's an integer power of 2 to make implementation efficient ⚡. it also fits best for the worst case (Reno) 💅.

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

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

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

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

see how, for base RTTs below target (15 ms), both the numerator and the denominator plateau? 🫠 that's exactly the effect we wanted, limiting RTT-dependence ✨.

remember the promise from earlier? we said we'd explain why the L4S throughput equation in equation (6) didn't need to model RTT-independence. the reason is that we only use one point, the typical base RTT where the operator picks to calculate the coupling factor 🎯. throughput equivalence will at least hold at that chosen point. and if Prague senders implement RTT-independence over a range of RTTs below it, the throughput equivalence will extend over that range too 🥹.

congestion control designers can pick different ways to reduce RTT-dependence 🧑‍🎨. and each operator can make its own policy choice about a different base RTT, and therefore a different k, where it wants throughput equivalence. still, for the Internet, it makes sense to choose the typical RTT most users experience, because a Classic AQM's target queuing delay is also derived from a typical RTT for the Internet 💖.

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

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

Acknowledgements

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

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

Contributors

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

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

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

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

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

Authors' Addresses

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

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

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

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