Internet Draft R. Pan, P. Natarajan, F. Baker
Active Queue Management G. White, B. VerSteeg, M.S. Prabhu
Working Group C. Piglione, V. Subramanian
Intended Status: Standards Track
Expires: February 11, 2016 August 10, 2015
PIE: A Lightweight Control Scheme To Address the
Bufferbloat Problem
draft-ietf-aqm-pie-02
Abstract
Bufferbloat is a phenomenon where excess buffers in the network cause
high latency and jitter. 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 jitter degrade
application performance. There is a pressing need to design
intelligent queue management schemes that can control latency and
jitter; 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 timestamp, so it incurs very small 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
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Internet-Drafts are draft documents valid for a maximum of six months
and may be updated, replaced, or obsoleted by other documents at any
time. It is inappropriate to use Internet-Drafts as reference
material or to cite them other than as "work in progress."
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Copyright and License Notice
Copyright (c) 2012 IETF Trust and the persons identified as the
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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) . . . . . . . . . . . . . . . . . . . . . . . . . 6
4.2 Drop Probability Calculation . . . . . . . . . . . . . . . . 7
4.3 Latency Calculation . . . . . . . . . . . . . . . . . . . . 8
4.4 Protecting Bursts . . . . . . . . . . . . . . . . . . . . . 9
4.5 Exponential Decay Drop Probability . . . . . . . . . . . . . 9
5. Optional Design Elements of PIE . . . . . . . . . . . . . . . . 9
5.1 ECN Support . . . . . . . . . . . . . . . . . . . . . . . . 10
5.2 Departure Rate Estimation . . . . . . . . . . . . . . . . . 10
5.3 Turning PIE on and off . . . . . . . . . . . . . . . . . . . 12
5.4 De-randomization . . . . . . . . . . . . . . . . . . . . . . 12
6. Implementation Cost . . . . . . . . . . . . . . . . . . . . . . 13
7. Future Research . . . . . . . . . . . . . . . . . . . . . . . . 14
8. Incremental Deployment . . . . . . . . . . . . . . . . . . . . 14
9. IANA Considerations . . . . . . . . . . . . . . . . . . . . . . 14
10. References . . . . . . . . . . . . . . . . . . . . . . . . . . 14
10.1 Normative References . . . . . . . . . . . . . . . . . . . 15
10.2 Informative References . . . . . . . . . . . . . . . . . . 15
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10.3 Other References . . . . . . . . . . . . . . . . . . . . . 15
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 16
11. The Basic PIE pseudo Code . . . . . . . . . . . . . . . . . . 17
12. Pseudo code for PIE with optional enhancement . . . . . . . . 19
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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. With
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 jitter. It is a delicate balancing act
to design a queue management scheme that not only allows short-term
burst to smoothly pass, but also controls the average latency in the
presence of long-running greedy flows.
Active queue management (AQM) schemes, such as Random Early Discard
(RED), have been around for well over a decade. AQM schemes could
potentially solve the aforementioned problem. RFC 2309[RFC2309]
strongly recommends the adoption of AQM schemes in the network to
improve the performance of the Internet. 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 delay 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. Notably, a recent IETF
AQM working group draft [IETF-AQM] 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: such as 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 delay-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: de-randomization of
coin tosses, enhanced burst protection and expanded range of auto-
tuning.
This draft separates the PIE design into the basic elements that are
MUST to be implemented and optional SHOULD/MAY enhancement elements.
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 delay-sensitive applications. It should follow the
general guidelines set by the AQM working group document "IETF
Recommendations Regarding Active Queue Management" [IETF-AQM]. 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. Delay 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 with arbitrary number streams.
Design parameters shall be set automatically. Users only need to
set performance-related parameters such as target queue delay,
not design parameters.
In the following, the design of PIE and its operation are described in
deta.
4. The Basic PIE Scheme
As illustrated in Fig. 1, PIE conceptually comprises three simple MUST
components: a) random dropping at enqueing; b) periodic drop probability
update; c) latency calculation. The following sections describe these
components in further detail, and explain how they interact with each
other.
4.1 Random Dropping (ECN Support is described later in this document)
PIE MUST drop packets randomly according to a drop probability, p, that
is obtained from the drop-probability-calculation component:
* upon a packet arrival MUST
randomly drop a packet with a probability p.
Random Drop
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/ --------------
-------/ --------------> | | | | | -------------->
/|\ | | | | |
| --------------
| Queue Buffer \
| | \
| |queue \
| |length \
| | \
| \|/ \/
| ----------------- -------------------
| | Drop | | |
-----<-----| Probability |<---| Latency |
| Calculation | | Calculation |
----------------- -------------------
Figure 1. The PIE Structure
PIE optionally supports ECN and will be discussed in Section 5.1.
4.2 Drop Probability Calculation
The PIE algorithm MUST periodically adjust the drop probability every
Tupdate interval:
* MUST calculate drop probability p as:
p = p + alpha*(est_del-target_del) + beta*(est_del-est_del_old);
est_del_old = est_del.
* MUST autotune the alpha and beta parameters based on drop
probability p:
if (drop_prob_ < 0.000001) {
p /= 2048;
} else if (drop_prob_ < 0.00001) {
p /= 512;
} else if (drop_prob_ < 0.0001) {
p /= 128;
} else if (drop_prob_ < 0.001) {
p /= 32;
} else if (drop_prob_ < 0.01) {
p /= 8;
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} else if (drop_prob_ < 0.1) {
p /= 2;
} else {
p = p;
}
Here, the current queue length is denoted by qlen. The update interval
is denoted as Tupdate. Tupdate is defaulted to be 16ms. It can b reduced
on high speed links in order to provide smoother response. The target
latency value is expressed in target_del, which SHOULD be set to 15ms.
Variables, est_del and est_del_old represent the current and previous
estimation of the queueing delay.
Note that the adjustment to drop probability is based not only on the
current estimation of the queueing delay, but also on the rate of change
of queueing delay. This rate of change can simply be measured as the
difference between est_del and est_del_old. The result is the classical
Proportional Integral (PI) controller design which is known for
eliminating steady state errors. It is adopted here to control queueing
latency so that, at the steady state, the difference between the
queueing latency and the target value is zero even under heavy load. The
controller parameters, 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].
This type of controller has been studied before for controlling the
queue length [PI, QCN]. PIE adopts the Proportional Integral controller
for controlling delay and makes the scheme auto-tuning. The theoretical
analysis of PIE can be found in [HPSR-PIE]. As a rule of thumb, if we
cut Tupdate in half, we should also cut alpha by half and increase beta
by alpha/4 in order to keep the same feedback loop dynamics.
4.3 Latency Calculation
The PIE algorithm MUST use latency to calculate drop probability.
* It MAY estimate current queueing delay using Little's law:
est_del = qlen/depart_rate;
* or MAY use other techniques for calculating queueing delay, ex:
timestamp packets at enqueue and use the same to calculate delay
during dequeue.
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4.4 Protecting Bursts
PIE MUST NOT penalize short-term packet bursts [IETF-AQM]. PIE MUST give
users precise control of how much burst to allow without penalty. A
parameter, max_burst, is introduced that is similar to the burst
tolerance in the token bucket design. By default, the parameter SHOULD
be set to be 150ms (MUST be > 0). The PIE algorithm MUST do the
following:
* if p == 0 and est_del < del_ref and est_del_old < del_ref
burst_allowance = max_burst;
* upon packet arrival
if burst_allowance > 0 enqueue packet;
* upon probability update
burst_allowance = burst_allowance - Tupdate;
The burst allowance, noted by burst_allowance, is initialized to
max_burst. As long as burst_allowance is above zero, an incoming packet
will be enqueued bypassing the random drop process. During each update
instance, the value of burst_allowance is decremented by the update
period, Tupdate. When the congestion goes away, defined here as p equals
to 0 and both the current and previous samples of estimated delay are
less than target_del, burst_allowance is reset to max_burst.
4.5 Exponential Decay Drop Probability
The PIE algorithm MUST include 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 much
faster than the PI controller dictates. The decay parameter of 2% gives
us around 750ms time constant, a few RTT.
* upon probability update (Tupdate interval):
if (est_delay == 0 && est_delay_old_ == 0) {
p = p*0.98; //1- 1/64 is sufficient
}
5. Optional Design Elements of PIE
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The above forms the basic MUST have elements of the PIE algorithm. There
are several enhancements that are added to further augment the
performance of the basic algorithm. For clarity purpose, they are
included in this section.
5.1 ECN Support
PIE SHOULD support ECN by marking (rather than dropping) ECN capable
packets. However, as a safeguard, an additional threshold, mark_ecnth,
is introduced. If the calculated drop probability exceeds mark_ecnth,
PIE MUST revert to packet drop for ECN capable packets. The variable
mark_ecnth SHOULD be set at 10%.
* if rand() < p
if p < mark_ecnth && ecn_capable_packet == TRUE:
mark packet;
else:
drop packet;
5.2 Departure Rate Estimation
One way to calculate latency is to obtain an estimation of the departure
rate as discussed in Section 4.3. 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. Hence, one MAY decide to measure the
departure rate directly as follows.
* if rate_measurement == FALSE and qlen > dq_threshold:
rate_measurement = TRUE;
start = now;
* if rate_measurement == TRUE:
upon a packet departure:
dq_count = dq_count + deque_pkt_size;
if dq_count > dq_threshold then
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depart_rate = dq_count/(now-start);
dq_count=0;
start = now
The departure rate is measured when there are sufficient data in the
buffer, i.e., when the queue length is over a certain threshold,
DQ_THRESHOLD. Short, non-persistent bursts of packets result in empty
queues from time to time, this would make the measurement less accurate.
The parameter, dq_count, represents the number of bytes departed since
the last measurement. Once dq_count is over a certain threshold,
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 us a long enough period to
obtain an average draining rate but also fast enough to reflect sudden
changes in the draining rate. 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 depart_rate is used.
Random Drop
/ --------------
-------/ --------------------> | | | | | -------------->
/|\ | | | | | |
| | --------------
| | Queue Buffer
| | |
| | |queue
| | |length
| | |
| \|/ \|/
| ------------------------------
| | Departure Rate |
-----<-----| & Drop Probability |
| Calculation |
------------------------------
Figure 2. The Enque-based PIE Structure
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In some platforms, enqueueing and dequeueing functions belong to
different modules that are independent to each other. In such
situations, a pure enque-based design MAY be designed. As shown in
Figure 2, an enque-based design is depicted. The departure 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 departure 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 Turning PIE on and off
Traffic naturally fluctuates in a network. It would be preferable not to
unnecessarily drop packets due to a spurious uptick in queueing latency.
PIE can be optionally turned on and off. IT SHOULD only be turned on
(from off) when the buffer occupancy is over a certain threshold, which
SHOULD be set to 1/3 of the tail drop threshold. If it is on, PIE SHOULD
be turned off when congestion is over, i.e. when the drop probability,
queue length and estimated queue delay all reach 0.
Ideally PIE should be turned on or off based on the latency. However,
calculating latency when PIE is off 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 turned on and off, the burst protection logic is
modified as follows:
* if PIE_active == FALSE
burst_allowance = MAX_BURST;
* upon packet arrival
if burst_allowance > 0 enqueue packet;
* upon probability update when PIE_active == TRUE
burst_allowance = burst_allowance - Tupdate;
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
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would cause real drop percentage to temporarily deviate from the
intended drop probability p. 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 scenarios. A parameter, called
accu_prob, is reset to 0 after a drop. Upon a packet arrival, accu_prob
is incremented by the amount of drop probability, p. If accu_prob is
less than a low threshold, e.g. 0.85, the arriving packet is enqued; on
the other hand, if accu_prob is more than a high threshold, e.g. 8.5, a
packet is forced to be dropped. A packet is only randomly dropped if
accu_prob falls in between the two thresholds. Since accu_prob is reset
to 0 after a drop, another drop will not happen until 0.85/p packets
later. This avoids packets being dropped too close to each other. In the
other extreme case where 8.5/p packets have been enqued without
incurring a drop, PIE would force a drop that prevents much fewer drops
than desired. Further analysis can be found in [DOCSIS-PIE].
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 p. 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 hardware or software implementations.
The drop probability calculation is done in the background and it occurs
every Tudpate 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,
an implementation MAY choose these values to the closest multiples of 2
or 1/2 (ex: alpha=0.125, beta=1.25) 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 two variables per queue: est_del and
est_del_old. Hence the memory overhead is small.
If one chooses to implement the departure rate estimation, PIE uses a
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counter to keep track of the number of bytes departed for the current
interval. This counter is incremented per packet departure. Every
Tupdate, 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.
Since the PIE design is separated into data path and control path, if
control path is implemented in software, any further improvement in
control path can be easily accommodated.
In summary, PIE is simple to implement. SFQ can be combined with PIE to
provide further improvement of latency for various flows with different
priorities.
7. Future Research
The design of the PIE algorithm is presented in this document. It
effectively controls the average queueing latency to a target value. The
following areas can be further studied:
* Autotuning of target delay without losing utilization;
* Autotuning for average RTT of traffic;
8. Incremental Deployment
PIE scheme can be independently deployed and managed without any
need for interoperability.
Although all network nodes cannot be changed altogether to adopt
latency-based AQM schemes, a gradual adoption would eventually lead
to end-to-end low latency service for all applications.
9. IANA Considerations
There are no actions for IANA.
10. References
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10.1 Normative References
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119, March 1997.
10.2 Informative References
[RFC970] Nagle, J., "On Packet Switches With Infinite
Storage",RFC970, December 1985.
10.3 Other References
[IETF-AQM] Baker, F. and Fairhurst, G., "IETF Recommendations
Regarding Active Queue Management", draft-ietf-aqm-recommendation-11.
[CoDel] Nichols, K., Jacobson, V., "Controlling Queue Delay",
ACM Queue. ACM Publishing. doi:10.1145/2209249.22W.09264.
[CBQ] Cisco White Paper,
"http://www.cisco.com/en/US/docs/12_0t/12_0tfeature/guide/cbwfq.html".
[FQ-Implement] Baker, F. and Pan, R. "On Queueing, Marking and
Dropping", IETF draft-ietf-aqm-fq-implementation.
[DOCSIS_3.1] http://www.cablelabs.com/wp-content/uploads/specdocs
/CM-SP-MULPIv3.1-I01-131029.pdf.
[DOCSIS-PIE] White, G. and Pan, R., "A PIE-Based AQM for DOCSIS
Cable Modems", IETF draft-white-aqm-docsis-pie-00.
[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.
[AQM DOCSIS] http://www.cablelabs.com/wp-
content/uploads/2014/06/DOCSIS-AQM_May2014.pdf
[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
[PI] Hollot, C.V., Misra, V., Towsley, D. and Gong, W., "On
Designing Improved Controller for AQM Routers Supporting TCP Flows",
Infocom 2001.
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[QCN] "Data Center Bridging - Congestion Notification",
http://www.ieee802.org/1/pages/802.1au.html.
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
Fred Baker
Cisco Systems
725 Alder Drive,
Milpitas, CA 95035, USA
Email: fred@cisco.com
Bill Ver Steeg
Cisco Systems
5030 Sugarloaf Parkway
Lawrenceville, GA, 30044, USA
Email: versteb@cisco.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
Pan et al. Expires February 11, 2016 [Page 16]
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Greg White
CableLabs
858 Coal Creek Circle
Louisville, CO 80027, USA
Email: g.white@cablelabs.com
* Formerly at Cisco Systems
11. The Basic PIE pseudo Code
Configurable Parameters:
- QDELAY_REF. AQM Latency Target (default: 16ms)
- 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)
- T_UPDATE: a period to calculate drop probability (default:16ms)
Table which stores status variables (ending with "_"):
- burst_allowance_: current burst_allowance
- drop_prob_: The current packet drop probability. reset to 0
- current_qdelay_: The current queue delay. 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 && PIE->current_qdelay_ < del_ref
&& PIE->qdelay_old < del_ref) {
burst_allowance = MAX_BURST;
}
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if (PIE->burst_allowance_ < 0 && drop_early() == DROP
&& PIE->burst_allowance_ <= 0) {
drop(packet);
} else {
queue_.enque(packet);
}
}
===========================
drop_early() {
//Safeguard PIE to be work conserving
if ( (PIE->qdelay_old_ < QDELAY_REF/2 && PIE->drop_prob_ < 20%)
|| (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 pseudo code
deque(Packet packet) {
PIE->current_qdelay_ = packet.timestamp_delay();
}
============================
//update periodically, T_UPDATE = 16ms
calculate_drop_prob() {
//can be implemented using integer multiply,
qdelay = PIE->current_qdelay_;
p = alpha*(qdelay - QDELAY_REF) + \
beta*(qdelay-PIE->qdelay_old_);
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//Expanding scaling range can help improve performance.
//Please see DOCSIS-PIE design.
//We keep it simple here
if (PIE->drop_prob_ < 0.1%) {
p = p/128
} else if (PIE->drop_prob_ < 1%) {
p = p/16;
} else if (PIE->drop_prob_ < 10%) {
p = p/2;
} else {
p = p;
}
PIE->drop_prob_ += p;
//Exponentially decay drop prob when congestion goes away
if (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
if (PIE->drop_prob_ > 1)
PIE->drop_prob_ = 1
PIE->qdelay_old_ = qdelay;
PIE->last_timestamp_ = now;
if (PIE->burst_allowance_ > 0) {
PIE->burst_allowance_ = PIE->burst_allowance_ - T_UPDATE;
}
}
}
12. Pseudo code for PIE with optional enhancement
Configurable Parameters:
- QDELAY_REF. AQM Latency Target (default: 16ms)
- 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)
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- DQ_THRESHOLD: (in bytes, default: 2^14 (in a power of 2) )
- T_UPDATE: a period to calculate drop probability (default:16ms)
- 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 avg_dq_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
============================
//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) {
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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
&& queue_.byte_length() == 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_ < 20%)
|| (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;
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double u = random();
if (u < PIE->drop_prob_) {
PIE->accu_prob_ = 0;
return DROP;
} else {
return ENQUE;
}
}
============================
//update periodically, T_UPDATE = 16ms
calculate_drop_prob() {
if ( (now - PIE->last_timestampe_) >= T_UPDATE &&
PIE->active_ == ACTIVE) {
//can be implemented using integer multiply,
//DQ_THRESHOLD is power of 2 value
qdelay = queue_.byte_length() * avg_dq_time_/DQ_THRESHOLD;
p = alpha*(qdelay - QDELAY_REF) + \
beta*(qdelay-PIE->qdelay_old_);
//Expanding scaling range can help improve performance.
//Please see DOCSIS-PIE design.
//We keep it simple here
if (PIE->drop_prob_ < 0.1%) {
p = p/128
} else if (PIE->drop_prob_ < 1%) {
p = p/16;
} else if (PIE->drop_prob_ < 10%) {
p = p/2;
} else {
p = p;
}
if (PIE->drop_prob_ >= 10% && p > 2%) {
p = 0.02;
}
PIE->drop_prob_ += p;
//Exponentially decay drop prob when congestion goes away
if (qdelay == 0 && PIE->qdelay_old_ == 0) {
PIE->drop_prob_ *= 0.98; //1- 1/64 is sufficient
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}
//bound drop probability
if (PIE->drop_prob_ < 0)
PIE->drop_prob_ = 0
if (PIE->drop_prob_ > 1)
PIE->drop_prob_ = 1
PIE->qdelay_old_ = qdelay;
PIE->last_timestamp_ = now;
if (PIE->burst_allowance_ > 0) {
PIE->burst_allowance_ = PIE->burst_allowance_ - T_UPDATE;
}
}
}
==========================
//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 cycle 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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