A New Approach for Accurate Modelling of Medium Access

Control (MAC) Protocols Presenter: Moshe Zukerman

ARC Centre for Ultra Broadband Information Networks

EEE Dept., The University of Melbourne

Presented at EE Dept., City University of Hong Kong, 11 April, 2002

Credit: Chuan Foh (EEE, Melbourne)

1. The big picture 2. Classical performance models3. Ethernet4. IEEE 802.35. How can we get performance statistics for a

complicated protocol6. Breaking the problem into two: Saturation and

SSQ fed by correlated SRD Markovian traffic7. Numerical results

OUTLINE

The Big Picture

Traffic Modelling

Queueing Theory

PerformanceEvaluation

Simulations andFast Simulations

NumericalSolutions

Formulae inClosed Form

Traffic Measurements

Link and Network Design and Dimensioning

Traffic Prediction

Research in Performance Evaluation

1. Exact analytical results (models)2. Exact numerical results (models)3. Approximations4. Simulations (slow and fast)5. Experiments6. Testbeds7. Deployment and measurements8. Typically, 4-7 validate 1-3.

Classical Performance Models

Poisson Traffic Model

Many simplified assumptions on System/protocol operation

Inaccurate results

We want

Realistic Traffic Model

No simplified assumptions on System/protocol operation

Accurate results

Example 1: Ethernet

The Ethernet MAC protocol:

(1) Carrier Sensed Multiple Access with Collision Detection (CSMA/CD)

(2) The Binary Exponential Backoff (BEB) Algorithm

Ethernet

Dtime

F G

The Big Bang of E, F & G

E

C D E F G

C D E F G

time

Detailed Analysis

CSMA/CD

BEBcollided packets

LAN traffic Served

packets

Ethernet -or -

IEEE 802.3

Classical Performance Models

retr

ansm

issi

onoffered load G

LAN traffic Served

packets

BEB collided packets

1-persistentCSMA/CD

PoissonPoisson

PoissonPoisson

Example 2: IEEE 802.11

The IEEE 802.11 MAC protocol:

(1) Carrier Sensed Multiple Access with Collision Avoidance (CSMA/CA)

(2) The Binary Exponential Backoff (BEB) Algorithm

Figure 1: The IEEE 802.11 access methods: (a) Basic access method. (b) Four-way handshaking access method

Data ACK

DIFS SIFS DIFS

idle slots

channel is busy idle

slots

(a)

time

DIFS SIFS SIFS SIFS DIFS

idle slots

idle slots

RTS CTS Data ACK

(b)

time

Detailed Analysis

CSMA/CA

BEBcollided packets

LAN traffic Served

packets

IEEE 802.11

Simplified Performance Models

fixe

d w

indo

w

retr

ansm

issi

onoffered load G

LAN traffic Served

packets

BEB collided packets

CSMA/CA

BernoulliBernoullior Poissonor Poisson

How do we do it?

Well, we know how to get:

Queueing performance of state dependent Markovian Single Server Queue (SSQ)

Performance results without simplified assumptions on System/protocol operation when system is saturated

so, we break the hard problem into two separate easy problems:

Queueing performance of a state dependent Markovian SSQ

Performance evaluation of the System/protocol operation when system is saturated

From saturation analysis without simplified assumptions on system/protocol operation, we can get:

The service rate, given that there are n saturated stations in the system.

Then using state dependent Markov Chain analysis, we get:

The performance results we are after

State dependent single Server queue

Markovian SRD arrival process

State dependent (n) service

For each n solve MAC under saturation

n stations

What statistical traffic models we have considered?

Source Traffic Arrival Model

time Data frame Data frame

Phase type distributed

transmission time

Phase type distributed

transmissiontime

Exp. distributed

gaps

Data frame = Packet

Train of packets

Source Traffic Arrival Model

time

A new data frame is generated, it is scheduled for transmission immediately

The data frame is transmitted successfully at this point of time

After an idle period, another new data frame is generated. It is scheduled for transmission immediately

Exp

onen

tial

ly

dist

ribu

ted

Another Traffic Model considered:Markov Modulated Poisson

Process (MMPP)

The number of active stations increases based on MMPPAnd decreases based on the MAC service process

Now let’s use the simpler problem

under saturation to model the service rate

Saturation Traffic

n stations

arrival departure

Service Process

Service Time (second)

Prob

abili

ty

ExponentialE8

E32

Simulation: IEEE 802.11for 20 saturated stations

E8 will be chosen

Why we think it will work?

Why E8 is good enough?

Let X exp(), E [X] = 1/

X8 E8, X32 E32 both with mean 1/ ,

Var [X] = 1/ 2

Var [X8] =8/(8)2=1/(82)

Var [X32] = 32/(32)2=1/(322)

Var [X32] = (1/4)Var [X8] = (1/32)Var [X]

2 [X32] = [X8] , 2.82 [X8] = [X]

Why E8 is good enough (cont.)?

12

22

22

SQ

S

Q: mean queue size: utilizationS:SD of the service time distributionS: mean service time

From M/G/1 mean queue size result:

Why E8 is good enough (cont.)?

Det. X32 X8X

SD/Mean 0 (1/32)(1/2)

= 0.176

(1/8)(1/2)

= 0.353

1

When the SD/mean is small (as for X32), doubling it does not significantly affect queueing performance for small . However, when it is already doubled, multiplying it further by 2.82, affects performance.

How accurate are we?

Mean delay under different payload sizes: simulation vs. analysis

Throughput

Mea

n da

ta f

ram

e de

lay

(mse

c) Payload:512 bits

2430 bits4348 bits8184 bits

Throughput

Mea

n da

ta f

ram

e de

lay

(mse

c) 512 bits (75%)8184 bits (25%)

512 bits (50%)8184 bits (50%)

Solid lines:dual fixed data frames

Dotted lines:fixed size data frames

Mean delay under different date frame distributions: simulation vs. analysis

Mean delay under different train arrival processes: simulation vs. analysis

Throughput

Mea

n m

essa

ge d

elay

(m

sec)

Hyper-geometricGeometricDual fixedFixed

Mean train size = 24576 bits

Delay performance: IEEE 802.11

Throughput

Mea

n da

ta f

ram

e de

lay

(mse

c)

M/M/1/50

M/E8/1/50 and M/E32/1/50

Simulation

Delay Performance: 802.11

M

ean

data

fra

me

dela

y (m

sec)

MMPP/E8/1/50

Simulation

Throughput

MMPP parameters 0=5

1

r0=0.00002 msec r1=0.00008 msec

Delay Performance: IEEE 802.3

Throughput

Mea

n da

ta f

ram

e de

lay

(slo

ts)

M/M/1/50

M/E8/1/50

Simulation

How inaccurate are classical performance models?

A ComparisonN

orm

aliz

ed m

ean

dela

y, D

/b1

100

50

20

10

5

2

1

0 0.2 0.4 0.6 0.8 1.0Throughput, S

a=0.1 a=0.01Lam’s resultsOur results

Lam’s results overestimate the performance. Our results indicate that the Ethernet protocol will be unstable at 30% for a=0.1 and 75% at a=0.01. Lam’s predictions (Computer Network 4, 1980) are much higher in the two cases. a = the signal propagation delay normalized to the data frame transmission time between any pair of stations. We assume a star network and the distance between any station and the hub (active or passive) is fixed. D/b1= the mean transmission delay normalized to the data frame transmission time. Traffic: Lam’s=Ours=Poisson trafficData frame size distribution: Lam’s=Ours=fixedRetransmission algorithm:Lam’s=An adaptive retransmission algorithm; Ours=BEB

Accurate MAC performance results under statistical traffic can be achieved by breaking up the original problem into two simpler easier problems:(1) SSQ(2) MAC under saturation

Conclusion: