The Delay Distribution of IEEE 802.11e EDCA and 802.11 DCF IPCCC 2006 April 10 - 12, 2006 - Phoenix, Arizona Paal E. Engelstad UniK / Telenor R&D Olav

The Delay Distribution of IEEE 802.11e EDCA and 802.11 DCF

IPCCC 2006 April 10 - 12, 2006 - Phoenix, Arizona

Paal E. Engelstad UniK / Telenor R&D

Olav N. Østerbø (presenter)

Telenor R&D

Agenda

• Introduction

• A non-saturation model for 802.11e EDCA

– ... and for 802.11 DCF as a special case

• Finding the z-transform of the MAC delay

• Deriving the z-transform of queueing delay from the z-transform

• Finding the delay distribution and precentiles

• Numerical examples

Introduction

• Fact 1: IEEE 802.11 WLAN standard widely deployed as wireless access technology in

– office environments

– public hot-spots

– in the homes.

• Fact 2: WLAN easily becomes bottleneck for communication. (shared medium with limited capacity, overhead etc..)

• Fact 3: Standard IEEE 802.11 WLAN lacks QoS differentiation

• Fact 4: IEEE 802.11e Enhanced Distributed Channel Access (EDCA) allows for differentiation between four different access categories (ACs) at each station

– relative QoS differentiations between ACs

Wireless Channel

Why is the queueing delay so important?

• Delay consists of two major parts:

– Queuing Delay

– Transmit queues

– IP buffering

– Medium Access Delay (”MAC delay”)

AC[0](AC_BK)

AC[1](AC_BE)

AC[2](AC_VI)

AC[3](AC_VO)

The problem...

• Analytical work on the performance of 802.11e EDCA (Bianchi models) assume saturation conditions and focuses on predicting the

– throughput

– mean delay of the medium access

• Current analytical Bianchi models assume saturation conditions

– The queue lengths and the queueing delay are assumed to be infinite !

– Not a realistic transmission scenario

– No protocols will work under those circumstances!

• A non-saturation model is needed

The objective...• Finding the MAC delay, by itself, is normally not so

interesting

• The queueing delay can be significant

– moments of the delay

– full distribution of the delay, for instance to obtain various delay percentiles

• Important is to find the point when saturation occurs, i.e. when:

– the queueing delay goes to infinity, and

– the transmission of the flow breaks down

Uplink throughput example

QSTA 1

QSTA 2

QSTA 3

QSTA 4

QSTA 5

QAP

QSTA 1 QSTA 1

QSTA 2 QSTA 2

QSTA 3 QSTA 3

QSTA 4 QSTA 4

QSTA 5 QSTA 5

QAP

0

500

1000

1500

2000

2500

3000

3500

4000

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

Traffic generated per AC [Kb/s]

Thro

ughput per

AC

[K

b/s

]

AC[3]: Simulations AC[2]: Simulations AC[1]: Simulations

AC[0]: Simulations Input = Output

AC[0] (AC_BK)

AC[1] (AC_BE)

AC[2] (AC_VI)

AC[3] (AC_VO)

Agenda

• Introduction







IEEE 802.11e EDCA channel access

• Differentiation parameters:

– Contention Windows:

– Arbitration IFS (AIFS):

– (TXOP lengths)

ii

i

iim

ij

ji Lmj

mj

CWW

WW

i ,....,

1,....,1,0

12

2

max,0,

0,,

]1[][ NAIFSNiAIFSNAi

A bi-dimensional Markov chain representing backoff stage and backoff counter

inS

•Embedded Markov chain

•Post-backoff included

•Adding “extra” row representing the case where the post-backoff starts with an empty queue

•The state space where

representing the backoff stage

is the backoff counter

in

in BS ,

inS

inB

Markov chain- parameters

-the probability that there is a packet waiting in the transmission queue at the time a transmission is completed

i

-the collision probabilityip

-the probability that there is at least one packet arrives in the idle state (-1,0) during a generic time slot

iq

-the countdown blocking probabilityip

-the probability that at one packet arrives during the time the system is in post-backoff state (-1,j)

iq

... some calculations ...

- the steady state distributions,

Chain regularities gives a power-law expression

- probability of a transmission attempt in a generic time slot

Solving for bijk gives

))p(

pq)W((

qW

)q(

qp

W

kW

pb i

ii,i

i,i

Wi

i

iji

L

j

W

k j,i

j,i

i,,i

,ii j,i

12

11

111

1

11

1 0

00

1

100

0

000 ,,ij

i,j,i bpb

kjib ,,

i

.1

1 1

0,0,0

0,,i

Li

i

L

jjii p

pbb

ii

The transmission probability

• Before solving the equations, we first need to determine the remaining parameters

– ρi*, pi, pi*, qi and qi* in terms of i

)1(2

)21(1*

*

i

i

i p

p

)1)(21)(1(2

)1()2)(21())2(1)(1(1*

10,

i

iiii

Liii

mLi

mii

miii

ppp

pppppW

))p(

pq)W((

qW

)q(

q)

p

p(

i

ii,i

i,i

Wi

i

iLi

i,i

i

12

11

111

1

1 0

01

0

Non-Saturation part

The collision probabilities pi, pi*

• The probability of a busy slot:

• The collision probability of AC[i]- pi :

– Without Virtual Collisions:

– With Virtual Collisions:

• Countdown blocking probability:

– Bianchi:

– pi* = 0

– Xiao:

– pi* = pi

– Incorporating AIFS differentiation:

–

1

0

)1(1N

i

nib

ip

i

bi

pp

1

11

i

cc

bi

pp

0

)1(

11

)1

)2][(,1min(

i

bii

piAIFSNpp

Assuming Poisson arrivals of packets with rate i

• qi –prob. that at least one packet will arrive in the transmission queue during generic time slot

• ps -prob. that a time slot contains a successfully

transmitted packet with

• pb -prob. of busy channel

– Te duration of an empty slot,

– Ts a slot containing a successfully transmitted packet and

– Tc of a slot containing two or more colliding packets

• qi* -prob. that a packet arrives during countdown blocking.

Expressions for qi and qi*

.)()1(1 cieisi Tsb

Tb

Tsi eppepepq

.1

0,

N

isis pp .)1(, iiisi pnp

1

0

.)1(1N

i

nib

ip

.

)1(1

)1(1

*

**

cisi

ei

T

b

sT

b

si

iT

i

ep

pe

p

pp

peq

Expressions for the load i and i*

CA Tr PB

Packet 1:

CA Tr PB

Packet 2:

CA Tr PB

Packet 3:

BUSY IDLE BUSY IDLE

CA Tr PB

Packet 1:

CA Tr PB

Packet 1:

CA Tr PB

Packet 2:

CA Tr PB

Packet 2:

CA Tr PB

Packet 3:

CA Tr PB

Packet 3:

BUSY IDLE BUSY IDLE

Backoff instance is busy:

•while contending for channel access ("CA")

•while the packet is being transmitted ("Tr"),

•and during post-backoff ("PB") of the packet.

The post-backoff period should be associated as part of the processing of the packet that has been transmitted, and not the next packet to be transmitted and therefore

represents the mean service time (including CA,TR and PB)

The following relation yields:

PiPB-prob. of not receiving any packets in the transmission queue while

performing a complete empty-queue post-backoff procedure.

SATiD

,),1min( SATiii D

.P)( PBiii

11

Agenda

• Introduction







z-tranform of the MAC delay

cs T

b

sT

b

s zp

pz

p

pzD )1()(

)()( zDzzD ibl

Tistate

e

)(1

1)(

*

*

zDp

pzD

i

iibl

)(1

))((11)(, zD

zD

WzD

istate

Wistate

ij

ijstage

ij

i

cs

L

j

ijlevel

jTTjii

iSat zDzppzD

00,, )()1()(

*

)(0,,)1(1 *

zDzp iLlevel

TLLi i

cii

j

sl

ilstage

isjlevel zDzD )()( ,,, s=0

s=1

z-transform of the MAC delay• With post-backoff (Saturation case)

• Without post-backoff (Non-saturation case)

i

cs

L

j

ijlevel

jTTjii

iSatNon zDzppzD

01,, )()1()(

*

)(1,,)1(1 *

zDzp iLlevel

TLLi i

cii

i

cs

L

j

ijlevel

jTTjii

iSat zDzppzD

00,, )()1()(

*

)(0,,)1(1 *

zDzp iLlevel

TLLi i

cii

Exact form of the z-transform of the MAC delay by considering three cases:

1. The queue is non-empty when the post-backoff starts.



2. The queue is empty when the post-backoff starts and with no arrivals during the whole post-backoff period.



2. The queue is empty when the post-backoff starts and with no arrivals during the whole post-backoff period.

3. The queue is empty when the post-backoff starts, there is at least one packet arrival during the post-backoff period.

)z(D)q(

)z(D)q(

WP)z(D

istate

*i

Wistate

W*i

,iPB

i

i,stage

,i,i

1

11 00

0

0

))}z(D)z(D(p)z(D))z(D){(()z(D)z(D iSatNon

iSati

iSatNon

i,stagei

iSat

i

011

where

Mean Medium Access Delay• Diffrentiation of z-tramsforms gives:

• Mean Medium Access Delay:

• Higher order moments may also be found (e.g second order)

,2

)1

)(1()1( 1*1)1(i

statei

i

ics

LiSat

SATi

RD

p

pTTpDD i

i

,)1(

)1()1(*

*)1(

i

ic

b

ss

b

se

istate

statei p

pT

p

pT

p

pTDD

)W(pR ij

L

j

ji

ii

10

1 .p

p

p

pp

p

)p(W

i

Li

i

Li

mim

i

mi

i

iii

i

i

1

1

12

21

21 1111

0

,)1( PBii

SATii DDD

.DW

pPq

PD state

i,i

iPBii

PBiPB

i

2

11 0 (+ should be – in paper)

Agenda

• Introduction







Z-transform of the queueing delay

• Queueing delay is obtained by consider an M/G/1 queue with Di

SAT as service time with z-transform Dsati(z):

• Total delay is sum of queueing delay and MAC delay

• z-transforms of complementary (tail) distributions

obtain through

)z(Dz

)z)(()z(

iSatii

ii

1

11

).z()z(D)z(T iii

.1

)(1~)(

~

0 z

zDzdzD

i

m

mim

i

...~

21 im

im

im ddd

Agenda

• Introduction







Numerical procedure for obtaining tail distributions

• Inversion of the z-transforms by applying Cauchys integral formula

• By using the trapezoidal rule with step size /m of the inversion integral becomes:

• Discretization error:

du))re(D~

Im()musin())re(D~

Re()mucos(r

dzz

)z(D~

id~ iuiiui

mC

m

iim

r

2

01 2

1

2

1

1

1

1212

1 m

j

m/ijimimim

Num,im

im ))re(D

~Re()()r(D

~)()r(D

~

rd~

d~

.1

~~2

2,

m

mNumi

mim r

rdd

Agenda

• Introduction







Numerical parameters• Numerical computations in Mathematica.

• Applying 802.11b with long preamble and without the RTS/CTS-mechanism with time parameters

• Parameters CWmin and CWmax are overridden using 802.11e values

• Five different stations, QSTAs, contending for channel access.

– Each QSTA uses all four ACs, and virtual collisions therefore occur.

• Poisson distributed traffic consisting of 1024-bytes packets was generated at equal amounts to each AC.

sTe 20 sTT cs 1321 sTT MSDUi 5201024,

The complimentary distribution of the MAC delay of AC[3]

at a generated traffic rate of 1250 kbps

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 5 5,5 6 6,5 7

Delay [ms]

Ac

cu

mu

late

d T

ail

Pro

ba

bili

ty

The complimentary distribution of the queueing delay of

AC[3] at 1250 kbps

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

0 0,5 1 1,5 2 2,5

Delay [ms]

Acc

um

ula

ted

Tai

l P

rob

abil

ity

The complimentary distribution of the total delay of AC[3]

at 1250 kbps

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 5 5,5 6 6,5 7

Delay [ms]

Acc

um

ula

ted

Ta

il P

rob

ab

ilit

y

The complimentary distribution of the MAC delay of AC[3]

at a generated traffic rate of 1750 kbps

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 5 5,5 6 6,5 7

Delay [ms]

Ac

cu

mu

late

d T

ail

Pro

ba

bili

ty

Percentiles of the MAC

0

5

10

15

20

25

30

35

40

45

50

0 500 1000 1500 2000


Me

diu

m a

cc

es

s d

ela

y (

ms

)

AC[3] - 90 percentile AC[3] - 95 percentile AC[3] - 99 percentile

Percentiles of the queueing delay

0

2

4

6

8

10

0 500 1000 1500 2000


Qu

eu

ein

g d

ela

y (

ms

)


Percentiles of the total delay

0

2

4

6

8

10

0 500 1000 1500 2000


To

tal d

ela

y (

ms

)


Summary• We have argued why the queuing delay is important.

• Describing the queueing delay requires a non-saturation model

• Based on an analytical model for the IEEE 802.11e the z-transform of the MAC delay is obtained in closed form

• The queueing delay and total delay is obtained by applying a slotted version of Pollaczek-Khintchine formula.

• The corresponding distributions are obtained by numerical inversion (by applying the trapezoidal rule), and different percentiles are calculated.

• The numerical results show that the complementary distribution of the MAC delay has a typical stepwise form where the levels of the steps are related to the probability and duration of a transmission.

• In a following up paper "Analysis of the Total Delay of IEEE 802.11e EDCA", Accepted for IEEE International Conference on Communication (ICC'2006), Istanbul, June 11-15, 2006 the mean and second order moments of the MAC delay and mean queueing delay is obtained

Backup slides...

Throughput

• We have shown that this expression is valid also under non-saturation

csbsseb

MSDUisii TppTpTp

BTpS

)()1(,,

)1(, iiisi pnp

1

0,

N

isis pp

AIFS Differentiation

• We “scale down” the collision probability during countdown, depending on the AIFS setting:

• Starvation is thus predicted to occur when:

n*pb

busy slots

n*(Ai*pb)blocked slots

n*(1-pb)empty slots

n slots(n is large)n*(1- (Ai +1)*pb)

unblocked empty slots

n*pb

busy slots

n*(Ai*pb)blocked slots

n*(1-pb)empty slots

n slots(n is large)n*(1- (Ai +1)*pb)

unblocked empty slots

)1

,1min(i

biii

pApp

ib A

p

1

1where: ]1[][ NAIFSNiAIFSNAi

Preliminary Throughput Validations: Setup I

• 802.11b with long preamble and without RTS/CTS

• Poisson distributed traffic – 1024B packets

QSTA 1

QSTA 2

QSTA 3

QSTA 4

QSTA 5

QAP

QSTA 1 QSTA 1

QSTA 2 QSTA 2

QSTA 3 QSTA 3

QSTA 4 QSTA 4

QSTA 5 QSTA 5

QAP

sTe 20

sT MSDUi 520,

sTc 1.1321

sTs 1.1321

Preliminary Throughput Validations: Setup II

• We use the recommended (default) parameter settings of 802.11e EDCA:

• Simulations:

– ns-2

– with TKN implementation of 802.11e from TUB

• Numerical computations:

– Mathematica

AC[3] AC[2] AC[1] AC[0]AIFSN 2 2 3 7CWmin 3 7 15 15CWmax 15 31 1023 1023

Retry Limit (long/short) 7/4 7/4 7/4 7/4

Preliminary Throughput Validation: The non-saturation analysis

802.11b/802.11e: Analysis vs. Simulations (250 Kb/s per AC per station)

0

500

1000

1500

2000

2500

3000

0 2 4 6 8 10 12 14 16 18 20

Number of stations

Th

rou

gh

pu

t per

AC

[Kb

/s]

Generated Traffic (pr. AC)

AC[3] (Simulation)

AC[2] (Simulation)

AC[1] (Simulation)

AC[0] (Simulation)

AC[3] (Numerical)

AC[2] (Numerical)

AC[1] (Numerical)

AC[0] (Numerical)

Preliminary Throughput Validation: The starvation predictions

Fixed number of nodes (n=5)

0

500

1000

1500

2000

2500

3000

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000


Thro

ughput per A

C [K

b/s

]

AC[3]: Simulations AC[2]: Simulations AC[1]: Simulations AC[0]: Simulations

AC[3]: Numerical AC[2]: Numerical AC[1]: Numerical AC[0]: Numerical

The effect of AIFS differentiation during countdown

Packet Packet

Slots that AC[3]can use for countdown

Packet Packet


• A higher AIFS value translates into a lower average countdown rate

AC[3]’s perspective:


Medium Access Starvation

Packet Packet


Packet Packet

No slots for AC[0]’s countdown

• AIFS differentiation leads to starvation at high traffic loads



Packet

Packet

How to incorporate this effect into the analytical model?

AIFSN[0]

Packet Packet

Ai = AIFSN[i] - AIFSN[0](i.e. defined such that always A0 = 0)

Packet Packet

Ai blocked slots

unblockedempty slotsone busy slot

Documents

The Delay Distribution of IEEE 802.11e EDCA and 802.11 DCF IPCCC 2006 April 10 - 12, 2006 - Phoenix, Arizona Paal E. Engelstad UniK / Telenor R&D Olav