PIE: A Lightweight Control Scheme To Address the Bufferbloat Problem
draft-ietf-aqm-pie-09

Internet Draft                                                    R. Pan
Active Queue Management                                    Cisco Systems
Working Group                                               P. Natarajan
Intended Status: Experimental Track                        Cisco Systems
                                                                F. Baker
                                                           Cisco Systems
                                                                G. White
                                                               CableLabs

Expires: February 03, 2017                               August 02, 2016

           PIE: A Lightweight Control Scheme To Address the 
                          Bufferbloat Problem 

                      draft-ietf-aqm-pie-09

Abstract

   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 queueing 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. 

Status of this Memo

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

   Internet-Drafts are working documents of the Internet Engineering
   Task Force (IETF), its areas, and its working groups.  Note that
   other groups may also distribute working documents as
   Internet-Drafts.
 

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   Internet-Drafts are draft documents valid for a maximum of six months
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   Copyright (c) 2012 IETF Trust and the persons identified as the
   document authors. All rights reserved.

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   described in the Simplified BSD License.

Table of Contents

   1. Introduction  . . . . . . . . . . . . . . . . . . . . . . . . .  4
   2. Terminology . . . . . . . . . . . . . . . . . . . . . . . . . .  5
   3. Design Goals  . . . . . . . . . . . . . . . . . . . . . . . . .  5
   4. The Basic PIE Scheme  . . . . . . . . . . . . . . . . . . . . .  6
     4.1 Random Dropping(ECN Support is described later in this
         document)  . . . . . . . . . . . . . . . . . . . . . . . . .  7
     4.2 Drop Probability Calculation . . . . . . . . . . . . . . . .  8
     4.3 Latency Calculation  . . . . . . . . . . . . . . . . . . . . 10
     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 De-randomization . . . . . . . . . . . . . . . . . . . . . . 14
     5.5 Cap Drop Adjustment  . . . . . . . . . . . . . . . . . . . . 15
   6. Implementation Cost . . . . . . . . . . . . . . . . . . . . . . 15
   7. Scope of Experimentation  . . . . . . . . . . . . . . . . . . . 16
 

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   8. Incremental Deployment  . . . . . . . . . . . . . . . . . . . . 17
   9. Security Considerations . . . . . . . . . . . . . . . . . . . . 18
   10. IANA Considerations  . . . . . . . . . . . . . . . . . . . . . 18
   11. References . . . . . . . . . . . . . . . . . . . . . . . . . . 18
     11.1  Normative References . . . . . . . . . . . . . . . . . . . 18
     11.2  Informative References . . . . . . . . . . . . . . . . . . 18
     11.3  Other References . . . . . . . . . . . . . . . . . . . . . 19
   12. The Basic PIE pseudo Code  . . . . . . . . . . . . . . . . . . 20
   13. Pseudo code for PIE with optional enhancement  . . . . . . . . 23

 

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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. The TCP protocol 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 queueing latency and latency variation. Designing
   a queue management scheme is a delicate balancing act: it not only
   should allow short-term burst to smoothly pass, but also should
   control the average latency in the presence of long-running greedy
   flows.

   AQM schemes could potentially solve the aforementioned problem.
   Active queue management (AQM) schemes, such as Random Early Detection
   (RED [RED] as suggested in RFC2309[RFC2309], 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. Recently, a new IETF RFC7567
   [RFC7567] calls for new methods of controlling network latency. 

   New algorithms are beginning to emerge to control queueing latency
   directly to address the bufferbloat problem [CoDel]. Along these
   lines, 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 the congestion. The
   congestion detection, however, is based on the queueing latency
   instead of the queue length like RED. Furthermore, PIE also uses the
   derivative (rate of change) of the queueing 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. 

 

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   Separately, it is assumed that any latency-based AQM scheme would be
   applied over a Fair Queueing (FQ) structure or one of its approximate
   designs, Flow Queueing or Class Based Queueing (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/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 their latency is better controlled and 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 IETF draft [FQ-Implement]. 

   In October 2013, CableLabs' 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 improvements, the PIE design in DOCSIS 3.1 [DOCSIS-PIE] has
   improved the original design in several areas, including de-
   randomization of coin tosses and enhanced burst protection.

   This draft describes the design of PIE and separates it into basic
   elements that SHOULD be implemented 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 "
   Recommendations Regarding Active Queue Management" [RFC7567]. More
   specifically PIE design has the following basic criteria.  

        * First, queueing 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.
 

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        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 under-
        utilization or losing network efficiency. An early congestion
        signal could cause TCP to back off and avoid queue building up.
        On the other hand, however, TCP's rate reduction could result in
        link under-utilization. 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 similar design simplicity to 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. 

In the following, the design of PIE and its operation are described in
detail.

4. The Basic PIE Scheme

As illustrated in Fig. 1, PIE is comprised of three simple basic
components: a) random dropping at enqueueing; b) periodic drop
probability update; 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 and whether the queueing latency is currently
trending up or down. The queueing 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 the pseudo code
section of this document (Section 11). Any state variables that PIE
maintains are noted using "PIE->". For full description of the
algorithm, one can refer to the full paper [HPSR-PIE]. 

 

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        Random Drop 
             /               --------------
     -------/  -------------->    | | | | | -------------->     
            /|\                   | | | | |         
             |               --------------         
             |             Queue Buffer   \      
             |                     |       \    
             |                     |queue   \    
             |                     |length   \   
             |                     |          \  
             |                    \|/         \/ 
             |          -----------------    -------------------
             |          |     Drop      |    |                 |
             -----<-----|  Probability  |<---| Latency         | 
                        |  Calculation  |    | Calculation     |
                        -----------------    ------------------- 

                      Figure 1. The PIE Structure

4.1 Random Dropping(ECN Support is described later in this document)

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 arrival before enqueueing into a queue. 

    * Upon a packet enqueue, PIE:

      randomly drops the packet with a probability 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,
PIE->drop_prob_ < 0.2; or if the queue has less than a couple of
packets.

    * Upon a packet enqueue, PIE:

      //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 PIE->drop_prob_. 

 

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PIE optionally supports ECN and 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 the trend
where the latency is going, 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 Proportional Integral 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 current
congestion level, no need to measure the arrival rate and dequeue rate
mismatches.

When a congestion period goes away, 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 decay exponentially
(rather than linearly) when the system is not congested. This would help
the drop probability converge to 0 faster while the PI controller
ensures that it would eventually reaches zero. The decay parameter of 2%
gives us a time constant around 50*T_UPDATE.

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

    * calculate drop probability PIE->drop_prob_ and auto-tune 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;
 

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        } 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 sufficient

        }

    * bound the drop probability
       if (PIE->drop_prob_ < 0) 
                PIE->drop_prob_ = 0.0
       if (PIE->drop_prob_ > 1) 
                PIE->drop_prob_ = 1.0  

    * store current latency value:

        PIE->qdelay_old_ = current_qdelay. 

The update interval, T_UPDATE, is defaulted to be 15ms. It MAY be
reduced on high speed links in order to provide smoother response. The
target latency value, QDELAY_REF, SHOULD be set to 15ms. Variables,
current_qdelay and PIE->qdelay_old_ represent the current and previous
samples of the queueing 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(in the unit of 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 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 MUST be increased by the same order of magnitude that the
target latency is reduced. For example, if QDELAY_REF is reduced changed
 

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from 15ms to 150us, 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 MUST use latency to calculate drop probability.

    * It MAY estimate current queueing latency using Little's law:

        current_qdelay = queue_.byte_length()/dequeue_rate; 

      Details can be found in Section 5.2.

    * or MAY use other techniques for calculating queueing latency, ex:
    timestamp packets at enqueue and use the same to calculate latency
    during dequeue.

4.4 Burst Tolerance

PIE does NOT penalize short-term packet bursts as suggested in RFC7567
[RFC7567]. PIE allows bursts of traffic that create finite-duration
events in which current queueing latency exceeds the QDELAY_REF, without
triggering packet drops. A parameter, MAX_BURST, is introduced that
defines the burst duration that will be protected. By default, the
parameter SHOULD be set to be 150ms. 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 "Random Dropping" block and upon a packet arrival , PIE checks:

      Upon a packet enqueue:
      if PIE->burst_allowance_ > 0 enqueue packet;
      else randomly drop a packet with a probability 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 "Drop Probability Calculation" block, PIE additionally
    calculates:

          PIE->burst_allowance_ = max(0,PIE->burst_allowance_ -
 

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          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. 

5. Optional Design Elements of PIE

The above forms the basic elements of the PIE algorithm. There are
several enhancements that are added to further augment the performance
of the basic algorithm. For clarity purposes, they are included in this
section. An implementer MAY implement any of the following options. 

5.1 ECN Support

PIE MAY support ECN by marking (rather than dropping) ECN capable
packets [IETF-ECN].  As a safeguard, an additional threshold,
mark_ecnth, is introduced.  If the calculated drop probability exceeds
mark_ecnth, PIE reverts to packet drop for ECN capable packets. The
variable mark_ecnth MAY be set at 0.1(10%). 

    * To support ECN, the "random drop with a probability
      PIE->drop_prob_" function in "Random Dropping" block are
      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

 

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Using the timestamps, a latency sample can only be obtained when a
packet reaches at 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 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 measures when a sufficient data in the buffer, i.e., when
the queue length is over a certain threshold (DQ_THRESHOLD). PIE
measures how long it takes to drain DQ_THRESHOLD of packets. More
specifically, PIE MAY implement the rate estimation as follows: 

    current_qdelay = queue_.byte_length() *
                     PIE->avg_dq_time_/DQ_THRESHOLD;

    * Upon a packet deque:

      if PIE->in_measurement_ == FALSE and queue.byte_length() >=
      DQ_THRESHOLD:
         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
         else
            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. The threshold is recommended to be set
to 16KB assuming a typical packet size of around 1KB or 1.5KB. This
threshold would allow sufficient data to obtain an average draining rate
but also fast enough (< 64KB) to reflect sudden changes in the draining
rate. IF DQ_THRESHOLD is smaller than 64KB, 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
 

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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. 

         Random Drop 
             /                     --------------
     -------/  -------------------->    | | | | | -------------->     
            /|\             |           | | | | |         
             |              |      --------------         
             |              |       Queue Buffer         
             |              |             |                 
             |              |             |queue           
             |              |             |length           
             |              |             |                
             |             \|/           \|/              
             |          ------------------------------    
             |          |     Dequeue Rate           |    
             -----<-----|  & Drop Probability        |
                        |        Calculation         |   
                        ------------------------------    

               Figure 2. The Enqueue-based PIE Structure

In some platforms, enqueueing and dequeueing functions belong to
different modules that are independent of each other. In such
situations, a pure enqueue-based design MAY be designed. As shown in
Figure 2, an enqueue-based design is depicted. 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 - the number of remaining packets in queue. In this design,
everything can be triggered by a 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 queueing 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
 

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MAY be set to 1/3 of the tail drop threshold. PIE becomes inactive when
congestion is over, 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 the latency.
However, calculating latency when PIE is inactive would introduce
unnecessary packet processing overhead. Weighing the trade-offs, it is
decided to compare against tail drop threshold to keep things simple. 

When PIE is optionally becomes active/inactive, the burst protection
logic in Section 4.4 are modified as follows:

    * "Random Dropping" block, PIE adds:

      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;
      else randomly drop a packet with a probability PIE->drop_prob_.

      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 MAY do the following: 
      if PIE->active_ == TRUE:
        PIE->burst_allowance_ = max(0,PIE->burst_allowance_ - T_UPDATE);

                
5.4 De-randomization

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 real drop percentage to temporarily deviate from the
intended value PIE->drop_prob_. In certain scenarios, such as small
number of simultaneous TCP flows, these deviations can cause significant
deviations in link utilization and queueing latency. PIE MAY introduce a
de-randomization mechanism to avoid such situations. A parameter, called
PIE->accu_prob_, is reset to 0 after a drop. Upon a 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
 

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arrival packet is forced to be dropped. A packet is only randomly
dropped if PIE->accu_prob_ falls in 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 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 [DOCSIS-PIE].   

5.5 Cap Drop Adjustment

In the case of one single TCP flow during slow start phase in the
system, queue could quickly increase during slow start and demands high
drop probability. In some environments such as Cable Modem Speed Test,
one could not afford triggering timeout and lose throughput as
throughput is shown to customers who are testing his/her connection
speed. We MAY cap the maximum drop probability increase in each step.

    * "Drop Probability Calculation" block, PIE MAY add:

      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 enqueueing 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 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,
 

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an implementation MAY choose these values to the closest multiples of 2
or 1/2 (ex: 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 software.
The state requirement is only one variables per queue: 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 multiplication. Note that many network devices keep
track of an interface's departure rate. In this case, PIE might be able
to reuse this information, simply skip the third step of the algorithm
and hence incurs no extra cost. If platform already leverages packet
timestamps for other purposes, PIE MAY make use of these packet
timestamps for latency calculation instead of estimating 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 that
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
properties.  One, if a packet is arriving to an empty queue, it is given
immunity from packet drops altogether, regardless of the state of the
other queues. Two, 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.

7. Scope of Experimentation

The design of the PIE algorithm is presented in this document. It
 

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effectively controls the average queueing latency to a target value. The
following areas can be further studied and experimented: 

    * Autotuning of target latency without losing utilization;

    * Autotuning for average RTT of traffic;

    * The proper threshold to transition smoothly between ECN marking
    and dropping;

    * The enhancements in Section 5 can be experimented to see if they
    would bring more value in the real world. If so, they will be
    incorporated into the basic PIE algorithm;

    * The PIE design is separated into data path and control path, and
    the control path can be implemented in software. Field tests of
    other control laws can be experimented to further improve 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.
Further study and experiments will be presented once available.

8. Incremental Deployment

From testbed experiments and large scale simulations of PIE so far, PIE
has been shown to be effective across 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
co-exist with existing AQM schemes such as 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
15ms and 150ms for non datacenter network devices and to 15us and 150us
for datacenter switches, respectively.

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 forsee any scaling issues associated with the algorithm as the
 

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link speed scales up.

9. Security Considerations

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

10. IANA Considerations

There are no actions for IANA.

11. References

11.1  Normative References

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

11.2  Informative References

   [RFC970]   Nagle, J., "On Packet Switches With Infinite
              Storage",RFC970, December 1985.

   [RFC2309]  Braden, B., Clark, D., Crowcroft, J., Davie, B., Deering,
              S., Estrin, D., Floyd, S., Jacobson, V., Minshall, G.,
              Patridge, C., Peterson, L., Ramakrishnan, K., Shenker, S.,
              Wroclawski, J. and Zhang, L., "Recommendations on Queue
              Management and Congestion Avoidance in the Internet",
              April, 1998.

   [RFC7567]  Baker, F. and Fairhurst, G., "Recommendations Regarding
              Active Queue Management", July, 2015.

   [CBQ]      Cisco White Paper,
   "http://www.cisco.com/en/US/docs/12_0t/12_0tfeature/guide/cbwfq.html".

   [CoDel]    Nichols, K., Jacobson, V., "Controlling Queue Delay", ACM
   Queue. ACM Publishing. doi:10.1145/2209249.22W.09264.

   [DOCSIS_3.1]   http://www.cablelabs.com/wp-content/uploads/specdocs  
                  /CM-SP-MULPIv3.1-I01-131029.pdf. 

 

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   [DOCSIS-PIE]   White, G. and Pan, R., "A PIE-Based AQM for DOCSIS    
                  Cable Modems", IETF draft-white-aqm-docsis-pie-02.

   [FQ-Implement] Baker, F. and Pan, R. "On Queueing, Marking and
   Dropping", IETF draft-ietf-aqm-fq-implementation. 

   [HPSR-PIE]     Pan, R., Natarajan, P. Piglione, C., Prabhu, M.S.,
   Subramanian, V., Baker, F. Steeg and B. V., "PIE: A Lightweight
   Control Scheme to Address the Bufferbloat Problem", IEEE HPSR 2013.
   https://www.researchgate.net/publication/261134127_PIE_A_lightweight
   _control_scheme_to_address_the_bufferbloat_problem?origin=mail.

   [IETF-ECN]     Briscoe, B. Kaippallimalil, J and Phaler, P.,
   "Guidelines for Adding Congestion Notification to Protocols that
   Encapsulate IP", draft-ietf-tsvwg-ecn-encap-guidelines.

11.3  Other References

   [PI]   Hollot, C.V., Misra, V., Towsley, D. and Gong, W., "On
   Designing Improved Controller for AQM Routers Supporting TCP Flows",
   Infocom 2001.

   [QCN]          "Data Center Bridging - Congestion Notification",
   http://www.ieee802.org/1/pages/802.1au.html.

   [RED]          Floyd, S. and Jacobson V., "Random Early Detection (RED)
   Gateways for Congestion Avoidance", IEEE/ACM Transactions on
   Networking, August, 1993.

   [TCP-Models]   Misra, V., Gong, W., and Towsley, D., "Fluid-base
   Analysis of a Network of AQM Routers Supporting TCP Flows with an
   Application to RED", SIGCOMM 2000.

   Authors' Addresses

   Rong Pan
   Cisco Systems
   3625 Cisco Way, 
   San Jose, CA 95134, USA
   Email: ropan@cisco.com

   Preethi Natarajan, 
   Cisco Systems
   725 Alder Drive, 
   Milpitas, CA 95035, USA
   Email: prenatar@cisco.com

 

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   Fred Baker
   Cisco Systems
   725 Alder Drive, 
   Milpitas, CA 95035, USA
   Email: fred@cisco.com

   Greg White
   CableLabs
   858 Coal Creek Circle
   Louisville, CO 80027, USA
   Email: g.white@cablelabs.com

   Other Contributor's Addresses

   Bill Ver Steeg
   Comcast Cable
   Email: William_VerSteeg@comcast.com

   Mythili Prabhu*
   Akamai Technologies
   3355 Scott Blvd
   Santa Clara, CA - 95054
   Email: mythili@akamai.com

   Chiara Piglione*
   Broadcom Corporation
   3151 Zanker Road
   San Jose, CA 95134
   Email: chiara@broadcom.com

   Vijay Subramanian*
   PLUMgrid, Inc. 
   350 Oakmead Parkway, 
   Suite 250
   Sunnyvale, CA 94085
   Email: vns@plumgrid.com
   * Formerly at Cisco Systems 

12. The Basic PIE pseudo Code

  Configurable Parameters:
       - QDELAY_REF. AQM Latency Target (default: 15ms)
       - MAX_BURST. AQM Max Burst Allowance (default: 150ms)

  Internal Parameters:
       - Weights in the drop probability calculation (1/s):
         alpha (default: 1/8), beta(default: 1 + 1/4)  
 

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       - T_UPDATE: a period to calculate drop probability (default:15ms)

  Table which 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);
       }
  }

===========================

  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();   
 

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      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 pseudo code

  deque(Packet packet) {

    current_qdelay = packet.timestamp_delay();

  }

============================
//update periodically, T_UPDATE = 15ms

  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;
       } else if (PIE->drop_prob_ < 0.1) {
            p /= 2;
       } else {
            p = p;
       } 

       PIE->drop_prob_ += p;

       //Exponentially decay drop prob when congestion goes away
 

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

       //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);

        
    }
}

13. Pseudo code for PIE with optional enhancement

  Configurable Parameters:
       - QDELAY_REF. AQM Latency Target (default: 15ms)
       - MAX_BURST. AQM Max Burst Allowance (default: 150ms)
       - 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:15ms)
       - TAIL_DROP: each queue has a tail drop threshold, pass it to PIE

  Table which 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:
 

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       - 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

============================
//called on each packet arrival
  enque(Packet packet) {
       if (queue_.byte_length()+packet.size() > TAIL_DROP) {       
        drop(packet);
        PIE->accu_prob_ = 0;
       } else if (PIE->active_ == TRUE && drop_early() == DROP
                  && PIE->burst_allowance_ == 0) {  
        if (PIE->drop_prob_ < MAX_ECNTH && packet.ecn() == TRUE) 
                mark(packet);
        else
                drop(packet);
                PIE->accu_prob_ = 0;
       } else {
        queue_.enque(packet);
       }

       //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
 

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            && current_qdelay == 0) {
            PIE->active_ = INACTIVE; 
            PIE->in_measurement_ = FALSE;
       } 
  }

===========================

  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 need 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;
      }
   }

============================
 

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 //update periodically, T_UPDATE = 15ms
 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() * PIE-
     >avg_dq_time_/DQ_THRESHOLD;

       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 sufficient
       }

       //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;
 

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       PIE->burst_allowance_ = max(0,PIE->burst_allowance_ - T_UPDATE); 
    }
}

==========================
//called on each packet departure
  deque(Packet packet) {

     //deque 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;
     }
  }

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