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RFC 8033

Proportional Integral Controller Enhanced (PIE): A Lightweight Control Scheme to Address the Bufferbloat Problem

Pages: 30

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Internet Engineering Task Force (IETF)                            R. Pan
Request for Comments: 8033                                  P. Natarajan
Category: Experimental                                     Cisco Systems
ISSN: 2070-1721                                                 F. Baker
                                                                G. White
                                                           February 2017

            Proportional Integral Controller Enhanced (PIE):
    A Lightweight Control Scheme to Address the Bufferbloat Problem


Bufferbloat is a phenomenon in which excess buffers in the network cause high latency and latency variation. As more and more interactive applications (e.g., voice over IP, real-time video streaming, and financial transactions) run in the Internet, high latency and latency variation degrade application performance. There is a pressing need to design intelligent queue management schemes that can control latency and latency variation, and hence provide desirable quality of service to users. This document presents a lightweight active queue management design called "PIE" (Proportional Integral controller Enhanced) that can effectively control the average queuing latency to a target value. Simulation results, theoretical analysis, and Linux testbed results have shown that PIE can ensure low latency and achieve high link utilization under various congestion situations. The design does not require per-packet timestamps, so it incurs very little overhead and is simple enough to implement in both hardware and software.
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Status of This Memo

   This document is not an Internet Standards Track specification; it is
   published for examination, experimental implementation, and

   This document defines an Experimental Protocol for the Internet
   community.  This document is a product of the Internet Engineering
   Task Force (IETF).  It represents the consensus of the IETF
   community.  It has received public review and has been approved for
   publication by the Internet Engineering Steering Group (IESG).  Not
   all documents approved by the IESG are a candidate for any level of
   Internet Standard; see Section 2 of RFC 7841.

   Information about the current status of this document, any errata,
   and how to provide feedback on it may be obtained at

Copyright Notice

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

   This document is subject to BCP 78 and the IETF Trust's Legal
   Provisions Relating to IETF Documents
   ( in effect on the date of
   publication of this document.  Please review these documents
   carefully, as they describe your rights and restrictions with respect
   to this document.  Code Components extracted from this document must
   include Simplified BSD License text as described in Section 4.e of
   the Trust Legal Provisions and are provided without warranty as
   described in the Simplified BSD License.
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Table of Contents

1. Introduction ....................................................3 2. Terminology .....................................................5 3. Design Goals ....................................................5 4. The Basic PIE Scheme ............................................6 4.1. Random Dropping ............................................7 4.2. Drop Probability Calculation ...............................7 4.3. Latency Calculation ........................................9 4.4. Burst Tolerance ...........................................10 5. Optional Design Elements of PIE ................................11 5.1. ECN Support ...............................................11 5.2. Dequeue Rate Estimation ...................................11 5.3. Setting PIE Active and Inactive ...........................13 5.4. Derandomization ...........................................14 5.5. Cap Drop Adjustment .......................................15 6. Implementation Cost ............................................15 7. Scope of Experimentation .......................................17 8. Incremental Deployment .........................................17 9. Security Considerations ........................................18 10. References ....................................................18 10.1. Normative References .....................................18 10.2. Informative References ...................................18 Appendix A. The Basic PIE Pseudocode ..............................21 Appendix B. Pseudocode for PIE with Optional Enhancement ..........24 Contributors ......................................................29 Authors' Addresses ................................................30

1. Introduction

The explosion of smart phones, tablets, and video traffic in the Internet brings about a unique set of challenges for congestion control. To avoid packet drops, many service providers or data-center operators require vendors to put in as much buffer as possible. Because of the rapid decrease in memory chip prices, these requests are easily accommodated to keep customers happy. While this solution succeeds in assuring low packet loss and high TCP throughput, it suffers from a major downside. TCP continuously increases its sending rate and causes network buffers to fill up. TCP cuts its rate only when it receives a packet drop or mark that is interpreted as a congestion signal. However, drops and marks usually occur when network buffers are full or almost full. As a result, excess buffers, initially designed to avoid packet drops, would lead to highly elevated queuing latency and latency variation. Designing a queue management scheme is a delicate balancing act: it not only should allow short-term bursts to smoothly pass but also should control the average latency in the presence of long-running greedy flows.
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   Active Queue Management (AQM) schemes could potentially solve the
   aforementioned problem.  AQM schemes, such as Random Early Detection
   (RED) [RED] as suggested in [RFC2309] (which is now obsoleted by
   [RFC7567]), have been around for well over a decade.  RED is
   implemented in a wide variety of network devices, both in hardware
   and software.  Unfortunately, due to the fact that RED needs careful
   tuning of its parameters for various network conditions, most network
   operators don't turn RED on.  In addition, RED is designed to control
   the queue length, which would affect latency implicitly.  It does not
   control latency directly.  Hence, the Internet today still lacks an
   effective design that can control buffer latency to improve the
   quality of experience to latency-sensitive applications.  The more
   recently published RFC 7567 calls for new methods of controlling
   network latency.

   New algorithms are beginning to emerge to control queuing latency
   directly to address the bufferbloat problem [CoDel].  Along these
   lines, Proportional Integral controller Enhanced (PIE) also aims to
   keep the benefits of RED, including easy implementation and
   scalability to high speeds.  Similar to RED, PIE randomly drops an
   incoming packet at the onset of congestion.  Congestion detection,
   however, is based on the queuing latency instead of the queue length
   (as with RED).  Furthermore, PIE also uses the derivative (rate of
   change) of the queuing latency to help determine congestion levels
   and an appropriate response.  The design parameters of PIE are chosen
   via control theory stability analysis.  While these parameters can be
   fixed to work in various traffic conditions, they could be made
   self-tuning to optimize system performance.

   Separately, it is assumed that any latency-based AQM scheme would be
   applied over a Fair Queuing (FQ) structure or one of its approximate
   designs, Flow Queuing or Class-Based Queuing (CBQ).  FQ is one of the
   most studied scheduling algorithms since it was first proposed in
   1985 [RFC970].  CBQ has been a standard feature in most network
   devices today [CBQ].  Any AQM scheme that is built on top of FQ or
   CBQ could benefit from these advantages.  Furthermore, these
   advantages, such as per-flow or per-class fairness, are orthogonal to
   the AQM design whose primary goal is to control latency for a given
   queue.  For flows that are classified into the same class and put
   into the same queue, one needs to ensure that their latency is better
   controlled and that their fairness is not worse than those under the
   standard DropTail or RED design.  More details about the relationship
   between FQ and AQM can be found in [RFC7806].

   In October 2013, CableLabs' Data-Over-Cable Service Interface
   Specification 3.1 (DOCSIS 3.1) specification [DOCSIS_3.1] mandated
   that cable modems implement a specific variant of the PIE design as
   the active queue management algorithm.  In addition to cable-specific
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   improvements, the PIE design in DOCSIS 3.1 [RFC8034] has improved the
   original design in several areas, including derandomization of coin
   tosses and enhanced burst protection.

   This document describes the design of PIE and separates it into basic
   elements and optional components that may be implemented to enhance
   the performance of PIE.

2. Terminology

The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in RFC 2119 [RFC2119].

3. Design Goals

A queue management framework is designed to improve the performance of interactive and latency-sensitive applications. It should follow the general guidelines set by the AQM working group document "IETF Recommendations Regarding Active Queue Management" [RFC7567]. More specifically, the PIE design has the following basic criteria. * First, queuing latency, instead of queue length, is controlled. Queue sizes change with queue draining rates and various flows' round-trip times. Latency bloat is the real issue that needs to be addressed, as it impairs real-time applications. If latency can be controlled, bufferbloat is not an issue. In fact, once latency is under control, it frees up buffers for sporadic bursts. * Secondly, PIE aims to attain high link utilization. The goal of low latency shall be achieved without suffering link underutilization or losing network efficiency. An early congestion signal could cause TCP to back off and avoid queue buildup. On the other hand, however, TCP's rate reduction could result in link underutilization. There is a delicate balance between achieving high link utilization and low latency. * Furthermore, the scheme should be simple to implement and easily scalable in both hardware and software. PIE strives to maintain design simplicity similar to that of RED, which has been implemented in a wide variety of network devices. * Finally, the scheme should ensure system stability for various network topologies and scale well across an arbitrary number of streams. Design parameters shall be set automatically. Users only need to set performance-related parameters such as target queue latency, not design parameters.
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   In the following text, the design of PIE and its operation are
   described in detail.

4. The Basic PIE Scheme

As illustrated in Figure 1, PIE is comprised of three simple basic components: a) random dropping at enqueuing, b) periodic drop probability updates, and c) latency calculation. When a packet arrives, a random decision is made regarding whether to drop the packet. The drop probability is updated periodically based on how far the current latency is away from the target value and whether the queuing latency is currently trending up or down. The queuing latency can be obtained using direct measurements or using estimations calculated from the queue length and the dequeue rate. The detailed definition of parameters can be found in Appendix A of this document ("The Basic PIE Pseudocode"). Any state variables that PIE maintains are noted using "PIE->". For a full description of the algorithm, one can refer to the full paper [HPSR-PIE]. Random Drop / -------------- -------/ --------------> | | | | | --------------> /|\ | | | | | | -------------- | Queue Buffer \ | | \ | |Queue \ | |Length \ | | \ | \|/ \/ | ----------------- ------------------- | | Drop | | | -----<-----| Probability |<---| Latency | | Calculation | | Calculation | ----------------- ------------------- Figure 1: The PIE Structure
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4.1. Random Dropping

PIE randomly drops a packet upon its arrival to a queue according to a drop probability, PIE->drop_prob_, that is obtained from the drop-probability-calculation component. The random drop is triggered by a packet's arrival before enqueuing into a queue. * Upon a packet enqueue: randomly drop the packet with a probability of PIE->drop_prob_. To ensure that PIE is "work conserving", we bypass the random drop if the latency sample, PIE->qdelay_old_, is smaller than half of the target latency value (QDELAY_REF) when the drop probability is not too high (i.e., PIE->drop_prob_ < 0.2), or if the queue has less than a couple of packets. * Upon a packet enqueue, PIE does the following: //Safeguard PIE to be work conserving if ( (PIE->qdelay_old_ < QDELAY_REF/2 && PIE->drop_prob_ < 0.2) || (queue_.byte_length() <= 2 * MEAN_PKTSIZE) ) return ENQUE; else randomly drop the packet with a probability of PIE->drop_prob_. PIE optionally supports Explicit Congestion Notification (ECN); see Section 5.1.

4.2. Drop Probability Calculation

The PIE algorithm periodically updates the drop probability based on the latency samples -- not only the current latency sample but also whether the latency is trending up or down. This is the classical Proportional Integral (PI) controller method, which is known for eliminating steady-state errors. This type of controller has been studied before for controlling the queue length [PI] [QCN]. PIE adopts the PI controller for controlling latency. The algorithm also auto-adjusts the control parameters based on how heavy the congestion is, which is reflected in the current drop probability. Note that the current drop probability is a direct measure of the current congestion level; there is no need to measure the arrival rate and dequeue rate mismatches. When a congestion period ends, we might be left with a high drop probability with light packet arrivals. Hence, the PIE algorithm includes a mechanism by which the drop probability decays
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   exponentially (rather than linearly) when the system is not
   congested.  This would help the drop probability converge to 0 more
   quickly, while the PI controller ensures that it would eventually
   reach zero.  The decay parameter of 2% gives us a time constant
   around 50 * T_UPDATE.

   Specifically, the PIE algorithm periodically adjusts the drop
   probability every T_UPDATE interval:

   *  calculate drop probability PIE->drop_prob_, and autotune it as

         p = alpha * (current_qdelay - QDELAY_REF) +
                beta * (current_qdelay - PIE->qdelay_old_);

         if (PIE->drop_prob_ < 0.000001) {
             p /= 2048;
         } else if (PIE->drop_prob_ < 0.00001) {
             p /= 512;
         } else if (PIE->drop_prob_ < 0.0001) {
             p /= 128;
         } else if (PIE->drop_prob_ < 0.001) {
             p /= 32;
         } else if (PIE->drop_prob_ < 0.01) {
             p /= 8;
         } else if (PIE->drop_prob_ < 0.1) {
             p /= 2;
         } else {
             p = p;
         PIE->drop_prob_ += p;

   *  decay the drop probability exponentially:

         if (current_qdelay == 0 && PIE->qdelay_old_ == 0) {
             PIE->drop_prob_ = PIE->drop_prob_ * 0.98;
                                                 //1 - 1/64 is

   *  bound the drop probability:

         if (PIE->drop_prob_ < 0)
                  PIE->drop_prob_ = 0.0
         if (PIE->drop_prob_ > 1)
                  PIE->drop_prob_ = 1.0
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   *  store the current latency value:

         PIE->qdelay_old_ = current_qdelay.

   The update interval, T_UPDATE, is defaulted to be 15 milliseconds.
   It MAY be reduced on high-speed links in order to provide smoother
   response.  The target latency value, QDELAY_REF, SHOULD be set to 15
   milliseconds.  The variables current_qdelay and PIE->qdelay_old_
   represent the current and previous samples of the queuing latency,
   which are calculated by the "latency calculation" component (see
   Section 4.3).  The variable current_qdelay is actually a temporary
   variable, while PIE->qdelay_old_ is a state variable that PIE keeps.
   The drop probability is a value between 0 and 1.  However,
   implementations can certainly use integers.

   The controller parameters, alpha and beta (expressed in Hz), are
   designed using feedback loop analysis, where TCP's behaviors are
   modeled using the results from well-studied prior art [TCP-Models].
   Note that the above adjustment of 'p' effectively scales the alpha
   and beta parameters based on the current congestion level indicated
   by the drop probability.

   The theoretical analysis of PIE can be found in [HPSR-PIE].  As a
   rule of thumb, to keep the same feedback loop dynamics, if we cut
   T_UPDATE in half, we should also cut alpha by half and increase beta
   by alpha/4.  If the target latency is reduced, e.g., for data-center
   use, the values of alpha and beta should be increased by the same
   order of magnitude by which the target latency is reduced.  For
   example, if QDELAY_REF is reduced and changed from 15 milliseconds to
   150 microseconds -- a reduction of two orders of magnitude -- then
   alpha and beta values should be increased to alpha * 100 and
   beta * 100.

4.3. Latency Calculation

The PIE algorithm uses latency to calculate drop probability in one of two ways: * It estimates the current queuing latency using Little's law (see Section 5.2 for details): current_qdelay = queue_.byte_length()/dequeue_rate; * It may use other techniques for calculating queuing latency, e.g., time-stamp the packets at enqueue, and use the timestamps to calculate latency during dequeue.
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4.4. Burst Tolerance

PIE does not penalize short-term packet bursts as suggested in [RFC7567]. PIE allows bursts of traffic that create finite-duration events in which current queuing latency exceeds QDELAY_REF without triggering packet drops. This document introduces a parameter called "MAX_BURST"; MAX_BURST defines the burst duration that will be protected. By default, the parameter SHOULD be set to 150 milliseconds. For simplicity, the PIE algorithm MAY effectively round MAX_BURST up to an integer multiple of T_UPDATE. To implement the burst tolerance function, two basic components of PIE are involved: "random dropping" and "drop probability calculation". The PIE algorithm does the following: * In the "random dropping" block and upon packet arrival, PIE checks the following: Upon a packet enqueue: if PIE->burst_allowance_ > 0 enqueue packet; else randomly drop a packet with a probability of PIE->drop_prob_. if (PIE->drop_prob_ == 0 and current_qdelay < QDELAY_REF/2 and PIE->qdelay_old_ < QDELAY_REF/2) PIE->burst_allowance_ = MAX_BURST; * In the "drop probability calculation" block, PIE additionally calculates: PIE->burst_allowance_ = max(0,PIE->burst_allowance_ - T_UPDATE); The burst allowance, noted by PIE->burst_allowance_, is initialized to MAX_BURST. As long as PIE->burst_allowance_ is above zero, an incoming packet will be enqueued, bypassing the random drop process. During each update instance, the value of PIE->burst_allowance_ is decremented by the update period, T_UPDATE, and is bottomed at 0. When the congestion goes away -- defined here as PIE->drop_prob_ equals 0 and both the current and previous samples of estimated latency are less than half of QDELAY_REF -- PIE->burst_allowance_ is reset to MAX_BURST.
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5. Optional Design Elements of PIE

There are several enhancements that are added to further augment the performance of the basic algorithm. For purposes of clarity, they are included in this section.

5.1. ECN Support

PIE MAY support ECN by marking (rather than dropping) ECN-capable packets [ECN]. This document introduces an additional threshold called "mark_ecnth", which acts as a safeguard: if the calculated drop probability exceeds mark_ecnth, PIE reverts to packet-dropping for ECN-capable packets. The variable mark_ecnth SHOULD be set to 0.1 (10%). * To support ECN, the "random drop with a probability of PIE->drop_prob_" function in the "random dropping" block is changed to the following: * Upon a packet enqueue: if rand() < PIE->drop_prob_: if PIE->drop_prob_ < mark_ecnth && ecn_capable_packet == TRUE: mark packet; else drop packet;

5.2. Dequeue Rate Estimation

Using timestamps, a latency sample can only be obtained when a packet reaches the head of a queue. When a quick response time is desired or a direct latency sample is not available, one may obtain latency through measuring the dequeue rate. The draining rate of a queue in the network often varies either because other queues are sharing the same link or because the link capacity fluctuates. Rate fluctuation is particularly common in wireless networks. One may measure directly at the dequeue operation. Short, non-persistent bursts of packets result in empty queues from time to time; this would make the measurement less accurate. PIE only measures latency when there is sufficient data in the buffer, i.e., when the queue length is over a
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   certain threshold (DQ_THRESHOLD).  PIE measures how long it takes to
   drain DQ_THRESHOLD packets.  More specifically, the rate estimation
   can be implemented as follows:

      current_qdelay = queue_.byte_length() *

   *  Upon a packet dequeue:

      if PIE->in_measurement_ == FALSE and queue.byte_length() >=
         PIE->in_measurement_ = TRUE;
         PIE->measurement_start_ = now;
         PIE->dq_count_ = 0;

      if PIE->in_measurement_ == TRUE:
         PIE->dq_count_ = PIE->dq_count_ + deque_pkt_size;
         if PIE->dq_count_ >= DQ_THRESHOLD then
            weight = DQ_THRESHOLD/2^16
            PIE->avg_dq_time_ = (now - PIE->measurement_start_) *
                                weight + PIE->avg_dq_time_ *
                                (1 - weight);
            PIE->dq_count_ = 0;
            PIE->measurement_start_ = now
            PIE->in_measurement_ = FALSE;

   The parameter PIE->dq_count_ represents the number of bytes departed
   since the last measurement.  Once PIE->dq_count_ is over
   DQ_THRESHOLD, a measurement sample is obtained.  It is recommended
   that the threshold be set to 16 KB, assuming a typical packet size of
   around 1 KB or 1.5 KB.  This threshold would allow sufficient data to
   obtain an average draining rate but would also be fast enough (< 64
   KB) to reflect sudden changes in the draining rate.  If DQ_THRESHOLD
   is smaller than 64 KB, a small weight is used to smooth out the
   dequeue time and obtain PIE->avg_dq_time_.  The dequeue rate is
   simply DQ_THRESHOLD divided by PIE->avg_dq_time_.  This threshold is
   not crucial for the system's stability.  Please note that the update
   interval for calculating the drop probability is different from the
   rate measurement cycle.  The drop probability calculation is done
   periodically per Section 4.2, and it is done even when the algorithm
   is not in a measurement cycle; in this case, the previously latched
   value of PIE->avg_dq_time_ is used.
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            Random Drop
                /                     --------------
        -------/  -------------------->    | | | | | -------------->
               /|\             |           | | | | |
                |              |      --------------
                |              |       Queue Buffer
                |              |             |
                |              |             |Queue
                |              |             |Length
                |              |             |
                |             \|/           \|/
                |          ------------------------------
                |          |     Dequeue Rate           |
                -----<-----|  & Drop Probability        |
                           |        Calculation         |

                 Figure 2: The Enqueue-Based PIE Structure

   In some platforms, enqueuing and dequeuing functions belong to
   different modules that are independent of each other.  In such
   situations, a pure enqueue-based design can be developed.  An
   enqueue-based design is depicted in Figure 2.  The dequeue rate is
   deduced from the number of packets enqueued and the queue length.
   The design is based on the following key observation: over a certain
   time interval, the number of dequeued packets = the number of
   enqueued packets minus the number of remaining packets in the queue.
   In this design, everything can be triggered by packet arrival,
   including the background update process.  The design complexity here
   is similar to the original design.

5.3. Setting PIE Active and Inactive

Traffic naturally fluctuates in a network. It would be preferable not to unnecessarily drop packets due to a spurious uptick in queuing latency. PIE has an optional feature of automatically becoming active/inactive. To implement this feature, PIE may choose to only become active (from inactive) when the buffer occupancy is over a certain threshold, which may be set to 1/3 of the tail drop threshold. PIE becomes inactive when congestion ends; i.e., when the drop probability reaches 0, current and previous latency samples are all below half of QDELAY_REF. Ideally, PIE should become active/inactive based on latency. However, calculating latency when PIE is inactive would introduce unnecessary packet-processing overhead. Weighing the trade-offs, we decided to compare against the tail drop threshold to keep things simple.
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   When PIE optionally becomes active/inactive, the burst protection
   logic described in Section 4.4 is modified as follows:

   *  "Random dropping" block: PIE adds the following:

      Upon packet arrival:

      if PIE->active_ == FALSE && queue_length >= TAIL_DROP/3:
         PIE->active_ = TRUE;
         PIE->burst_allowance_ = MAX_BURST;

      if PIE->burst_allowance_ > 0
         enqueue packet;
         randomly drop a packet with a probability of

      if (PIE->drop_prob_ == 0 and current_qdelay < QDELAY_REF/2 and
          PIE->qdelay_old_ < QDELAY_REF/2)
          PIE->active_ = FALSE;
          PIE->burst_allowance_ = MAX_BURST;

   *  "Drop probability calculation" block: PIE does the following:
      if PIE->active_ == TRUE:
         PIE->burst_allowance_ =
            max(0,PIE->burst_allowance_ - T_UPDATE);

5.4. Derandomization

Although PIE adopts random dropping to achieve latency control, independent coin tosses could introduce outlier situations where packets are dropped too close to each other or too far from each other. This would cause the real drop percentage to temporarily deviate from the intended value PIE->drop_prob_. In certain scenarios, such as a small number of simultaneous TCP flows, these deviations can cause significant deviations in link utilization and queuing latency. PIE may use a derandomization mechanism to avoid such situations. A parameter called "PIE->accu_prob_" is reset to 0 after a drop. Upon packet arrival, PIE->accu_prob_ is incremented by the amount of drop probability, PIE->drop_prob_. If PIE->accu_prob_ is less than a low threshold, e.g., 0.85, the arriving packet is enqueued; on the other hand, if PIE->accu_prob_ is more than a high threshold, e.g., 8.5, and the queue is congested, the arrival packet is forced to be dropped. A packet is only randomly dropped if PIE->accu_prob_ falls between the two thresholds. Since PIE->accu_prob_ is reset to 0 after a drop, another drop will not happen until 0.85/PIE->drop_prob_ packets later. This avoids packets being dropped too close to each other. In the other extreme case
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   where 8.5/PIE->drop_prob_ packets have been enqueued without
   incurring a drop, PIE would force a drop in order to prevent the
   drops from being spaced too far apart.  Further analysis can be found
   in [RFC8034].

5.5. Cap Drop Adjustment

In the case of a single TCP flow, during the slow-start phase the queue could quickly increase, which could result in a very rapid increase in drop probability. In order to prevent an excessive ramp-up that could negatively impact the throughput in this scenario, PIE can cap the maximum drop probability increase in each step. * "Drop probability calculation" block: PIE adds the following: if (PIE->drop_prob_ >= 0.1 && p > 0.02) { p = 0.02; }

6. Implementation Cost

PIE can be applied to existing hardware or software solutions. There are three steps involved in PIE, as discussed in Section 4. Their complexities are examined below. Upon packet arrival, the algorithm simply drops a packet randomly, based on the drop probability. This step is straightforward and requires no packet header examination and manipulation. If the implementation doesn't rely on packet timestamps for calculating latency, PIE does not require extra memory. Furthermore, the input side of a queue is typically under software control while the output side of a queue is hardware based. Hence, a drop at enqueuing can be readily retrofitted into existing or software implementations. The drop probability calculation is done in the background, and it occurs every T_UPDATE interval. Given modern high-speed links, this period translates into once every tens, hundreds, or even thousands of packets. Hence, the calculation occurs at a much slower time scale than the packet-processing time -- at least an order of magnitude slower. The calculation of drop probability involves multiplications using alpha and beta. Since PIE's control law is robust to minor changes in alpha and beta values, an implementation MAY choose these values to the closest multiples of 2 or 1/2 (e.g., alpha = 1/8, beta = 1 + 1/4) such that the multiplications can be done using simple adds and shifts. As no complicated functions are required, PIE can be easily implemented in both hardware and
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   software.  The state requirement is only three variables per queue:
   burst_allowance_, PIE->drop_prob_, and PIE->qdelay_old_.  Hence, the
   memory overhead is small.

   If one chooses to implement the departure rate estimation, PIE uses a
   counter to keep track of the number of bytes departed for the current
   interval.  This counter is incremented per packet departure.  Every
   T_UPDATE, PIE calculates latency using the departure rate, which can
   be implemented using a single multiply operation.  Note that many
   network devices keep track of an interface's departure rate.  In this
   case, PIE might be able to reuse this information and simply skip the
   third step of the algorithm; hence, it would incur no extra cost.  If
   a platform already leverages packet timestamps for other purposes,
   PIE can make use of these packet timestamps for latency calculation
   instead of estimating the departure rate.

   Flow queuing can also be combined with PIE to provide isolation
   between flows.  In this case, it is preferable to have an independent
   value of drop probability per queue.  This allows each flow to
   receive the most appropriate level of congestion signal and ensures
   that sparse flows are protected from experiencing packet drops.
   However, running the entire PIE algorithm independently on each queue
   in order to calculate the drop probability may be overkill.
   Furthermore, in the case where departure rate estimation is used to
   predict queuing latency, it is not possible to calculate an accurate
   per-queue departure rate upon which to implement the PIE drop
   probability calculation.  Instead, it has been proposed [DOCSIS-AQM]
   that a single implementation of the PIE drop probability calculation
   based on the overall latency estimate be used, followed by a
   per-queue scaling of drop probability based on the ratio of
   queue depth between the queue in question and the current largest
   queue.  This scaling is reasonably simple and has a couple of nice

   *  If a packet is arriving to an empty queue, it is given immunity
      from packet drops altogether, regardless of the state of the other

   *  In the situation where only a single queue is in use, the
      algorithm behaves exactly like the single-queue PIE algorithm.

   In summary, PIE is simple enough to be implemented in both software
   and hardware.
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7. Scope of Experimentation

The design of the PIE algorithm is presented in this document. The PIE algorithm effectively controls the average queuing latency to a target value. The following areas can be used for further study and experimentation: * Autotuning of target latency without losing utilization. * Autotuning for the average round-trip time of traffic. * The proper threshold to transition smoothly between ECN marking and dropping. * The enhancements described in Section 5, which can be used in experiments to see if they would be of more value in the real world. If so, they will be incorporated into the basic PIE algorithm. * The PIE design, which is separated into the data path and the control path. The control path can be implemented in software. Field tests of other control laws can be performed to experiment with further improvements to PIE's performance. Although all network nodes cannot be changed altogether to adopt latency-based AQM schemes such as PIE, a gradual adoption would eventually lead to end-to-end low-latency service for all applications.

8. Incremental Deployment

From testbed experiments and large-scale simulations of PIE so far, PIE has been shown to be effective across a diverse range of network scenarios. There is no indication that PIE would be harmful to deploy. The PIE scheme can be independently deployed and managed without a need for interoperability between different network devices. In addition, any individual buffer queue can be incrementally upgraded to PIE, as it can coexist with existing AQM schemes such as Weighted RED (WRED). PIE is intended to be self-configuring. Users should not need to configure any design parameters. Upon installation, the two user-configurable parameters -- QDELAY_REF and MAX_BURST -- will be defaulted to 15 milliseconds and 150 milliseconds for non-data-center network devices and to 15 microseconds and 150 microseconds for data-center switches, respectively.
Top   ToC   RFC8033 - Page 18
   Since the data path of the algorithm needs only a simple coin toss
   and the control-path calculation happens in a much slower time scale,
   we don't foresee any scaling issues associated with the algorithm as
   the link speed scales up.

9. Security Considerations

This document describes PIE, an active queue management algorithm based on implementations in different products. The PIE algorithm introduces no specific security exposures.

10. References

10.1. Normative References

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

10.2. Informative References

[RFC970] Nagle, J., "On Packet Switches With Infinite Storage", RFC 970, DOI 10.17487/RFC0970, December 1985, <>. [RFC2309] Braden, B., Clark, D., Crowcroft, J., Davie, B., Deering, S., Estrin, D., Floyd, S., Jacobson, V., Minshall, G., Partridge, C., Peterson, L., Ramakrishnan, K., Shenker, S., Wroclawski, J., and L. Zhang, "Recommendations on Queue Management and Congestion Avoidance in the Internet", RFC 2309, DOI 10.17487/RFC2309, April 1998, <>. [RFC7567] Baker, F., Ed., and G. Fairhurst, Ed., "IETF Recommendations Regarding Active Queue Management", BCP 197, RFC 7567, DOI 10.17487/RFC7567, July 2015, <>. [RFC7806] Baker, F. and R. Pan, "On Queuing, Marking, and Dropping", RFC 7806, DOI 10.17487/RFC7806, April 2016, <>.
Top   ToC   RFC8033 - Page 19
   [RFC8034]  White, G. and R. Pan, "Active Queue Management (AQM) Based
              on Proportional Integral Controller Enhanced (PIE) for
              Data-Over-Cable Service Interface Specifications (DOCSIS)
              Cable Modems", RFC 8034, DOI 10.17487/RFC8034,
              February 2017, <>.

   [CBQ]      Cisco, "Class-Based Weighted Fair Queueing",

   [CoDel]    Nichols, K. and V. Jacobson, "Controlling Queue Delay",
              Communications of the ACM, Volume 55, Issue 7, pp. 42-50,
              DOI 10.1145/2209249.2209264, July 2012.

              CableLabs, "MAC and Upper Layer Protocols Interface
              Specification", DOCSIS 3.1, January 2017,

              White, G., "Active Queue Management in DOCSIS 3.x Cable
              Modems", May 2014, <

   [ECN]      Briscoe, B., Kaippallimalil, J., and P. Thaler,
              "Guidelines for Adding Congestion Notification to
              Protocols that Encapsulate IP", Work in Progress,
              draft-ietf-tsvwg-ecn-encap-guidelines-07, July 2016.

   [HPSR-PIE] Pan, R., Natarajan, P., Piglione, C., Prabhu, M.S.,
              Subramanian, V., Baker, F., and B. Ver Steeg, "PIE: A
              lightweight control scheme to address the bufferbloat
              problem", IEEE HPSR, DOI 10.1109/HPSR.2013.6602305, 2013,

   [PI]       Hollot, C.V., Misra, V., Towsley, D., and W. Gong, "On
              designing improved controllers for AQM routers supporting
              TCP flows", INFOCOM 2001, DOI 10.1109/INFCOM.2001.916670,
              April 2001.

   [QCN]      IEEE, "IEEE Standard for Local and Metropolitan Area
              Networks--Virtual Bridged Local Area Networks -
              Amendment: 10: Congestion Notification", IEEE 802.1Qau,
Top   ToC   RFC8033 - Page 20
   [RED]      Floyd, S. and V. Jacobson, "Random Early Detection (RED)
              Gateways for Congestion Avoidance", IEEE/ACM Transactions
              on Networking, Volume 1, Issue 4, DOI 10.1109/90.251892,
              August 1993.

              Misra, V., Gong, W., and D. Towsley, "Fluid-based analysis
              of a network of AQM routers supporting TCP flows with an
              application to RED", SIGCOMM 2000, Volume 30, Issue 4,
              pp. 151-160, DOI 10.1145/347057.347421, October 2000.
Top   ToC   RFC8033 - Page 21

Appendix A. The Basic PIE Pseudocode

Configurable parameters: - QDELAY_REF. AQM Latency Target (default: 15 milliseconds) - MAX_BURST. AQM Max Burst Allowance (default: 150 milliseconds) Internal parameters: - Weights in the drop probability calculation (1/s): alpha (default: 1/8), beta (default: 1 + 1/4) - T_UPDATE: a period to calculate drop probability (default: 15 milliseconds) Table that stores status variables (ending with "_"): - burst_allowance_: current burst allowance - drop_prob_: The current packet drop probability. Reset to 0 - qdelay_old_: The previous queue delay. Reset to 0 Public/system functions: - queue_. Holds the pending packets - drop(packet). Drops/discards a packet - now(). Returns the current time - random(). Returns a uniform r.v. in the range 0 ~ 1 - queue_.byte_length(). Returns current queue_ length in bytes - queue_.enque(packet). Adds packet to tail of queue_ - queue_.deque(). Returns the packet from the head of queue_ - packet.size(). Returns size of packet - packet.timestamp_delay(). Returns timestamped packet latency ============================ //Called on each packet arrival enque(Packet packet) { if (PIE->drop_prob_ == 0 && current_qdelay < QDELAY_REF/2 && PIE->qdelay_old_ < QDELAY_REF/2) { PIE->burst_allowance_ = MAX_BURST; } if (PIE->burst_allowance_ == 0 && drop_early() == DROP) { drop(packet); } else { queue_.enque(packet); } } ============================
Top   ToC   RFC8033 - Page 22
     drop_early() {

         //Safeguard PIE to be work conserving
         if ( (PIE->qdelay_old_ < QDELAY_REF/2 && PIE->drop_prob_ < 0.2)
               || (queue_.byte_length() <= 2 * MEAN_PKTSIZE) ) {
              return ENQUE;

         double u = random();
         if (u < PIE->drop_prob_) {
              return DROP;
         } else {

              return ENQUE;


   //We choose the timestamp option of obtaining latency for clarity
   //Rate estimation method can be found in the extended PIE pseudocode

     deque(Packet packet) {

       current_qdelay = packet.timestamp_delay();


   //Update periodically, T_UPDATE = 15 milliseconds

     calculate_drop_prob() {

          //Can be implemented using integer multiply

          p = alpha * (current_qdelay - QDELAY_REF) + \
              beta * (current_qdelay - PIE->qdelay_old_);

          if (PIE->drop_prob_ < 0.000001) {
              p /= 2048;
          } else if (PIE->drop_prob_ < 0.00001) {
              p /= 512;
          } else if (PIE->drop_prob_ < 0.0001) {
              p /= 128;
          } else if (PIE->drop_prob_ < 0.001) {
              p /= 32;
          } else if (PIE->drop_prob_ < 0.01) {
              p /= 8;
Top   ToC   RFC8033 - Page 23
          } else if (PIE->drop_prob_ < 0.1) {
              p /= 2;
          } else {
              p = p;

          PIE->drop_prob_ += p;

          //Exponentially decay drop prob when congestion goes away
          if (current_qdelay == 0 && PIE->qdelay_old_ == 0) {
              PIE->drop_prob_ *= 0.98;           //1 - 1/64 is

          //Bound drop probability
          if (PIE->drop_prob_ < 0)
                   PIE->drop_prob_ = 0.0
          if (PIE->drop_prob_ > 1)
                   PIE->drop_prob_ = 1.0

          PIE->qdelay_old_ = current_qdelay;

          PIE->burst_allowance_ =
             max(0,PIE->burst_allowance_ - T_UPDATE);
Top   ToC   RFC8033 - Page 24

Appendix B. Pseudocode for PIE with Optional Enhancement

Configurable parameters: - QDELAY_REF. AQM Latency Target (default: 15 milliseconds) - MAX_BURST. AQM Max Burst Allowance (default: 150 milliseconds) - MAX_ECNTH. AQM Max ECN Marking Threshold (default: 10%) Internal parameters: - Weights in the drop probability calculation (1/s): alpha (default: 1/8), beta (default: 1 + 1/4) - DQ_THRESHOLD: (in bytes, default: 2^14 (in a power of 2) ) - T_UPDATE: a period to calculate drop probability (default: 15 milliseconds) - TAIL_DROP: the tail drop threshold (max allowed queue depth) for the queue Table that stores status variables (ending with "_"): - active_: INACTIVE/ACTIVE - burst_allowance_: current burst allowance - drop_prob_: The current packet drop probability. Reset to 0 - accu_prob_: Accumulated drop probability. Reset to 0 - qdelay_old_: The previous queue delay estimate. Reset to 0 - last_timestamp_: Timestamp of previous status update - dq_count_, measurement_start_, in_measurement_, avg_dq_time_. Variables for measuring average dequeue rate Public/system functions: - queue_. Holds the pending packets - drop(packet). Drops/discards a packet - mark(packet). Marks ECN for a packet - now(). Returns the current time - random(). Returns a uniform r.v. in the range 0 ~ 1 - queue_.byte_length(). Returns current queue_ length in bytes - queue_.enque(packet). Adds packet to tail of queue_ - queue_.deque(). Returns the packet from the head of queue_ - packet.size(). Returns size of packet - packet.ecn(). Returns whether packet is ECN capable or not ============================
Top   ToC   RFC8033 - Page 25
   //Called on each packet arrival
     enque(Packet packet) {
          if (queue_.byte_length() + packet.size() > TAIL_DROP) {
                 PIE->accu_prob_ = 0;
          } else if (PIE->active_ == TRUE && drop_early() == DROP
                     && PIE->burst_allowance_ == 0) {
                 if (PIE->drop_prob_ < MAX_ECNTH && packet.ecn() ==
                       PIE->accu_prob_ = 0;
          } else {

          //If the queue is over a certain threshold, turn on PIE
          if (PIE->active_ == INACTIVE
              && queue_.byte_length() >= TAIL_DROP/3) {
               PIE->active_ = ACTIVE;
               PIE->qdelay_old_ = 0;
               PIE->drop_prob_ = 0;
               PIE->in_measurement_ = TRUE;
               PIE->dq_count_ = 0;
               PIE->avg_dq_time_ = 0;
               PIE->last_timestamp_ = now;
               PIE->burst_allowance_ = MAX_BURST;
               PIE->accu_prob_ = 0;
               PIE->measurement_start_ = now;

          //If the queue has been idle for a while, turn off PIE
          //Reset counters when accessing the queue after some idle
          //period if PIE was active before
          if ( PIE->drop_prob_ == 0 && PIE->qdelay_old_ == 0
               && current_qdelay == 0) {
               PIE->active_ = INACTIVE;
               PIE->in_measurement_ = FALSE;


Top   ToC   RFC8033 - Page 26
     drop_early() {

         //PIE is active but the queue is not congested: return ENQUE
         if ( (PIE->qdelay_old_ < QDELAY_REF/2 && PIE->drop_prob_ < 0.2)
               || (queue_.byte_length() <= 2 * MEAN_PKTSIZE) ) {
              return ENQUE;

         if (PIE->drop_prob_ == 0) {
                  PIE->accu_prob_ = 0;

         //For practical reasons, drop probability can be further scaled
         //according to packet size, but one needs to set a bound to
         //avoid unnecessary bias

         //Random drop
         PIE->accu_prob_ += PIE->drop_prob_;
         if (PIE->accu_prob_ < 0.85)
             return ENQUE;
         if (PIE->accu_prob_ >= 8.5)
             return DROP;
                 double u = random();
         if (u < PIE->drop_prob_) {
                      PIE->accu_prob_ = 0;
                      return DROP;
         } else {
                      return ENQUE;

Top   ToC   RFC8033 - Page 27
    //Update periodically, T_UPDATE = 15 milliseconds
    calculate_drop_prob() {
        if ( (now - PIE->last_timestamp_) >= T_UPDATE &&
                PIE->active_ == ACTIVE) {

          //Can be implemented using integer multiply
          //DQ_THRESHOLD is power of 2 value
          current_qdelay = queue_.byte_length() *

          p = alpha * (current_qdelay - QDELAY_REF) + \
              beta * (current_qdelay - PIE->qdelay_old_);

          if (PIE->drop_prob_ < 0.000001) {
              p /= 2048;
          } else if (PIE->drop_prob_ < 0.00001) {
              p /= 512;
          } else if (PIE->drop_prob_ < 0.0001) {
              p /= 128;
          } else if (PIE->drop_prob_ < 0.001) {
              p /= 32;
          } else if (PIE->drop_prob_ < 0.01) {
              p /= 8;
          } else if (PIE->drop_prob_ < 0.1) {
              p /= 2;
          } else {
              p = p;

          if (PIE->drop_prob_ >= 0.1 && p > 0.02) {
              p = 0.02;
          PIE->drop_prob_ += p;

          //Exponentially decay drop prob when congestion goes away
          if (current_qdelay < QDELAY_REF/2 && PIE->qdelay_old_ <
              QDELAY_REF/2) {
                 PIE->drop_prob_ *= 0.98;        //1 - 1/64 is
Top   ToC   RFC8033 - Page 28
          //Bound drop probability
          if (PIE->drop_prob_ < 0)
                   PIE->drop_prob_ = 0
          if (PIE->drop_prob_ > 1)
                   PIE->drop_prob_ = 1

          PIE->qdelay_old_ = current_qdelay;
          PIE->last_timestamp_ = now;
          PIE->burst_allowance_ = max(0,PIE->burst_allowance_ -


   //Called on each packet departure
     deque(Packet packet) {

        //Dequeue rate estimation
        if (PIE->in_measurement_ == TRUE) {
             PIE->dq_count_ = packet.size() + PIE->dq_count_;
             //Start a new measurement cycle if we have enough packets
             if ( PIE->dq_count_ >= DQ_THRESHOLD) {
               dq_time = now - PIE->measurement_start_;
               if (PIE->avg_dq_time_ == 0) {
                   PIE->avg_dq_time_ = dq_time;
               } else {
                   weight = DQ_THRESHOLD/2^16
                   PIE->avg_dq_time_ = dq_time * weight +
                      PIE->avg_dq_time_ * (1 - weight);
               PIE->in_measurement_ = FALSE;

        //Start a measurement if we have enough data in the queue
        if (queue_.byte_length() >= DQ_THRESHOLD &&
            PIE->in_measurement_ == FALSE) {
               PIE->in_measurement_ = TRUE;
               PIE->measurement_start_ = now;
               PIE->dq_count_ = 0;
Top   ToC   RFC8033 - Page 29


Bill Ver Steeg Comcast Cable Email: Mythili Prabhu* Akamai Technologies 3355 Scott Blvd. Santa Clara, CA 95054 United States of America Email: Chiara Piglione* Broadcom Corporation 3151 Zanker Road San Jose, CA 95134 United States of America Email: Vijay Subramanian* PLUMgrid, Inc. 350 Oakmead Parkway Suite 250 Sunnyvale, CA 94085 United States of America Email: * Formerly at Cisco Systems
Top   ToC   RFC8033 - Page 30

Authors' Addresses

Rong Pan Cisco Systems 3625 Cisco Way San Jose, CA 95134 United States of America Email: Preethi Natarajan Cisco Systems 725 Alder Drive Milpitas, CA 95035 United States of America Email: Fred Baker Santa Barbara, CA 93117 United States of America Email: Greg White CableLabs 858 Coal Creek Circle Louisville, CO 80027 United States of America Email: