A New Approach for Accurate Modelling of Medium Access Control (MAC) Protocols
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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)
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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
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The Big Picture
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Traffic Modelling
Queueing Theory
PerformanceEvaluation
Simulations andFast Simulations
NumericalSolutions
Formulae inClosed Form
Traffic Measurements
Link and Network Design and Dimensioning
Traffic Prediction
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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.
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Classical Performance Models
Poisson Traffic Model
Many simplified assumptions on System/protocol operation
Inaccurate results
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We want
Realistic Traffic Model
No simplified assumptions on System/protocol operation
Accurate results
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Example 1: Ethernet
The Ethernet MAC protocol:
(1) Carrier Sensed Multiple Access with Collision Detection (CSMA/CD)
(2) The Binary Exponential Backoff (BEB) Algorithm
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Ethernet
Dtime
F G
The Big Bang of E, F & G
E
C D E F G
C D E F G
time
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Detailed Analysis
CSMA/CD
BEBcollided packets
LAN traffic Served
packets
Ethernet -or -
IEEE 802.3
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Classical Performance Models
retr
ansm
issi
onoffered load G
LAN traffic Served
packets
BEB collided packets
1-persistentCSMA/CD
PoissonPoisson
PoissonPoisson
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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
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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
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Detailed Analysis
CSMA/CA
BEBcollided packets
LAN traffic Served
packets
IEEE 802.11
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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
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How do we do it?
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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
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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
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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
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State dependent single Server queue
Markovian SRD arrival process
State dependent (n) service
For each n solve MAC under saturation
n stations
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What statistical traffic models we have considered?
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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
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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
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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
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Now let’s use the simpler problem
under saturation to model the service rate
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Saturation Traffic
n stations
arrival departure
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Service Process
Service Time (second)
Prob
abili
ty
ExponentialE8
E32
Simulation: IEEE 802.11for 20 saturated stations
E8 will be chosen
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Why we think it will work?
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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]
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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:
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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.
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How accurate are we?
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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
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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
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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
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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
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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
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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
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How inaccurate are classical performance models?
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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
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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
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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: