1 performance analysis of the 802.11 distributed coordination function under sporadic traffic joint...

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Performance Analysis of the 802.11 Distributed CoordinationFunction under Sporadic Traffic

joint work with

C.-F. Chiasserini(Politecnico di Torino)

(Submitted for publication)

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Motivation

The bulk of literature on analytical models of 802.11 considers only saturated sources

Saturated conditions are not a desirable operating point for many applications, because of large queueing delays and/or packet losses

We need to develop sound models to understand the behavior of 802.11 networks under not-saturated conditions

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Network scenario

We consider n contending stations using the standard DCF mechanism of 802.11

The MAC buffer of each station receives data packets according to an external, stationary arrival

process of rate MAC buffers have finite capacity, equal to K packets Stations are within radio proximity of each other,

there are no hidden terminals, no capture effects, … The communication channel is error-free

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Our contribution We identify the critical assumptions in the

development of an analytical model of the system

We obtain an accurate model which is able to predict

Network throughput Distribution of the MAC queue length Average packet delay Packet loss probability

Our approach can account for: Burstiness in the arrival process of packets Variable packet sizes Transmission of multiple packets when a station seizes the

channel (802.11e) Multirate environment (802.11b)

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Saturated sources (Bianchi’s model)

Description of the channel occupation:

… …

successful transmission idle slot collision

t

Discrete-time embedded Markov Chain

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Basic model for saturated sources

Embedded Markov Chain (simplified version of Bianchi’s model)

probability that a (tagged) station sends out a packet at the beginning of an (arbitrary) time step

=stage 0

stage 1

…

stage m

Independence assumption:

The probability of successful transmission of a packet is computed as:

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Numerical results for saturated sources

300

350

400

450

500

550

600

650

700

0 5 10 15 20 25 30 35 40 45 50

Basic Access - CWmin = 32mod

ns

300

350

400

450

500

550

600

650

700

0 5 10 15 20 25 30 35 40 45 50

Ag

gre

gate

d p

ack

et

thro

ug

hp

ut

Number of Wireless Stations (n)

RTS/CTS - CWmin = 128

modns

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Numerical results for saturated sources

1e-07

1e-06

1e-05

0.0001

0.001

0.01

0.1

0 10 20 30 40 50 60

Number of Wireless Stations

modsim b0sim b1sim b2sim b3sim b4sim b5

Probability

of states

bi

sim b6

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From the model solution we can compute The probability that a stations sends out a packet in an

arbitrary step The probability that the station is backlogged (at least

one packet in the queue)

Modeling not-saturated sourcesFirst attempt: model “A”

We incorporate in the description of the state of the tagged station the information of the number of packets in the queue:

States:i = backoff stage

j = packets in the queue

# states = O(mK)

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First attempt: model “A”

Relying on the same independence assumption used for saturated sources, we can compute the collision probability, the successful probability, etc., and solve the system iteratively

The model provides all performance metrics of interest (throughput, queue length distribution, queueing delay, packet loss probability, etc…)

Note: the distribution of the number of backlogged stations is assumed to be binomial: ~ Binom

e.g.: successful transmission probability:

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Model A - numerical results

0.1

1

10

400 450 500 550 600 650 700 750 800

Average number of packets in the queue

Aggregated packet arrival rate (pkt/s), Λ

mod A

ns

n = 10 stations – buffer size K = 20 – basic access scheme

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Aggregated throughput

(pkt/s)



540

560

580

600

620

640

660

680

550 600 650 700 750 800

mod Ans

mod Ans

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0

1

2

3

4

5

6

7

8

9

10

200 300 400 500 600 700 800

mod A

ns

Average number of backlogged

queues

650

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Number of backlogged stations


pdf

0.001

0.01

0.1

1

0 1 2 3 4 5 6 7 8 9 10

Λ = 650 pkt/s

mod A

ns

Binomial

Not binomial !

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Model A - conclusions

The independence assumption among stations does not hold in 802.11 networks under not-saturated conditions

it is not possible to just analyze the behavior of a tagged station in isolation

This fact has been neglected by most analytical approaches proposed so far in the literature:

e.g.: O. Tickoo and B. Sikdar, ``Queueing Analysis and Delay Mitigation in IEEE 802.11 Random Access MAC based Wireless Networks,'‘ INFOCOM 2004, Hong Kong, China, March 2004.

Note: the independence assumption would indeed hold in a hypothetical system in which

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We compute transmission probabilities, collision probabilities, etc, conditioned to the number C of backlogged queues in the system)

Modeling not-saturated sourcesSecond attempt: model “B”

We enrich the description of the tagged station with the number of backlogged queues (belonging to other stations):

States:i = backoff stage

j = packets in the queue

# states = O(mKn)

k = backlogged queues

e.g. = P { send out a packet | c backlogged queues }

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Model B - numerical results

Average number of packets in the queue



0.1

1

10

400 450 500 550 600 650 700 750 800

mod B

ns

18




Average number of backlogged

queues

0

1

2

3

4

5

6

7

8

9

10

200 300 400 500 600 700 800

mod B

ns

19


Number of packets in the queue


pdf

0.001

0.01

0.1

1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

mod B

ns - Λ = 720

ns - Λ = 640

20


Number of backlogged stations


pdf

0.0001

0.001

0.01

0.1

1

0 1 2 3 4 5 6 7 8 9 10

ns - Λ = 640

ns - Λ = 550

mod B

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Multi-rate multi-hop environment

Assumptions: All nodes can hear each other (no hidden nodes, etc…) Stations can choose their data sending rate (2 or 11 Mb/s) Error free channel (within transmission range, no matter

the distance)

Dilemma: In terms of overall network performance, it is better to

make a single hop at low rate, or two hops at high rate ?

A B

C

2 Mb/s

11 Mb/s 11 Mb/s

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0

1

2

3

4

5

6

0 2 4 6 8 10 12 14 16 18 20

Number of stations at 2 Mb/s

modns - 1500 bytesns - 1000 bytes

ns - 500 bytesns - 250 bytes

Total number of stations = 20 (basic access scheme)

(saturated case)

Aggregated data

throughput (Mb/s)

3.1 Mb/s

5.5 * (1 – 4/20) = 4.4 Mb/s

1.3 Mb/s

2 * (1 – 8/20)

= 1.2 Mb/s

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Aggregated data

throughput (Mb/s)


(saturated case)

Total number of stations = 20 (RTS/CTS scheme)

0

1

2

3

4

5

6

0 2 4 6 8 10 12 14 16 18 20

modns - 1500 bytesns - 1000 bytes

ns - 500 bytesns - 250 bytes


Region where best choice is two-hops

at 11 Mb/s

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The optimal choice of data rate jointly depends on:

Access scheme (basic or RTS/CTS) Payload size Fraction of stations switching from 11 to 2

Mb/s

… and on Physical and MAC layer parameters


(saturated case)

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(not saturated case)

1

10

100

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

modns - n_low = 0ns - n_low = 1ns - n_low = 2ns - n_low = 3ns - n_low = 4

Average queueing

delay (ms)


Variable number of stations, each generating 50 pkt/s

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Power consumption

(saturated conditions)

Number of Wireles Stations

1.42

1.44

1.46

1.48

1.5

1.52

1.54

1.56

1.58

1.6

1 2 3 4 5 6 7 8 9 10

Avera

ge P

ow

er

Consu

mpti

on (

W)

mod - RTS/CTSns - RTS/CTS

mod - basicns - basic

P_tx = 1.65 W – P_overhearing = 1.4 W – P_idle = 1.15 W

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Power consumption(non-saturated conditions)


Avera

ge P

ow

er

Consu

mpti

on (

W)

1.15

1.2

1.25

1.3

1.35

1.4

1.45

100 200 300 400 500 600 700 800

n = 10 stations – buffer size K = 20

ns - RTS/CTSmod - basic

ns - basic

mod - RTS/CTS

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Final remarks

We have found an accurate analytical model with O(mKn) states

Es: m = 7, K = 20, n = 10 1400 states

The behavior of stations is highly correlated independence assumption does not

hold

The key point is modeling the number of competing (backlogged) stations

Model limitation: we analyze only a

symmetrical system (i= )

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The End

Thanks for your attention

questions & comments…

1 performance analysis of the 802.11 distributed coordination function under sporadic traffic joint...

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