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)
OUTLINE
1.
2.
3.
4.
5.
The big picture
Classical performance models
Ethernet
IEEE 802.3
How can we get performance statistics for a
complicated protocol
6. Breaking the problem into two: Saturation and
SSQ fed by correlated SRD Markovian traffic
7. Numerical results
The Big Picture
Link and Network Design
and Dimensioning
Traffic
Modelling
Performance
Evaluation
Traffic
Queueing
Measurements Theory
Formulae in
Closed Form
Traffic
Prediction
Simulations and
Fast Simulations
Numerical
Solutions
Research in Performance Evaluation
1. Exact analytical results (models)
2. Exact numerical results (models)
3. Approximations
4. Simulations (slow and fast)
5. Experiments
6. Testbeds
7. Deployment and measurements
8. 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
C
D
E
F
G
time
C D
E
F G
The Big Bang
of E, F & G
D
time
E
F
G
Detailed Analysis
LAN
traffic
CSMA/CD
Served
packets
BEB
collided
packets
Ethernet
-or IEEE 802.3
Classical Performance Models
offered load G
1-persistent
CSMA/CD
retransmission

Poisson
LAN
traffic
BEB
Poisson
collided
packets

Served
packets
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
channel
is busy
idle
slots
Data
ACK
idle slots
time
DIFS
(a)
idle
RTS
slots
CTS
Data
SIFS
DIFS
idle
slots
ACK
time
DIFS
SIFS
SIFS
(b)
SIFS
DIFS
Figure 1: The IEEE 802.11 access methods: (a) Basic
access method. (b) Four-way handshaking access method
Detailed Analysis
LAN
traffic
CSMA/CA
Served
packets
BEB
collided
packets
IEEE 802.11
Simplified Performance Models
offered load G
CSMA/CA
fixed window
retransmission

Bernoulli
or Poisson
LAN
traffic

BEB
collided
packets
Served
packets
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
State dependent (n) service
Markovian SRD arrival process
For each n solve MAC under saturation
n stations
What statistical traffic models
we have considered?
Source Traffic Arrival Model
Phase type
distributed
transmission
time
Exp.
distributed
gaps
Data frame
Phase type
distributed
transmission
time
Data frame
Packet
Data frame =
Train of packets
time
Source Traffic Arrival Model
A new data frame is generated, it is
scheduled for transmission immediately
Exponentially
distributed
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
time
Another Traffic Model considered:
Markov Modulated Poisson
Process (MMPP)
The number of active stations increases
based on MMPP
And 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

Probability
Exponential
E8
E32

E8 will be chosen
Simulation: IEEE 802.11
for 20 saturated stations


     
Service Time (second)
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/(82)
Var [X32] = 32/(32)2=1/(322)
Var [X32] = (1/4)Var [X8] = (1/32)Var [X]
2 [X32] =  [X8] , 2.82 [X8] =  [X]
Why E8 is good enough (cont.)?
From M/G/1 mean queue size result:
S 
2      
S 

Q
21   
2
2
2
Q: mean queue size
: utilization
S:SD of the service time distribution
S: mean service time
Why E8 is good enough (cont.)?
Det.
SD/Mean
0
X32
X8
(1/32)(1/2) (1/8)(1/2)
= 0.176
X
1
= 0.353
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 data frame delay (msec)
Mean delay under different payload sizes:
simulation vs. analysis

Payload:
512 bits
2430 bits
4348 bits
8184 bits










Throughput


Mean data frame delay (msec)
Mean delay under different date frame
distributions: simulation vs. analysis




512 bits (75%)
8184 bits (25%)
Solid lines:
dual fixed data frames
512 bits (50%)
8184 bits (50%)
Dotted lines:
fixed size data frames







Throughput


Mean delay under different train arrival
processes: simulation vs. analysis
Mean message delay (msec)


Hyper-geometric
Geometric
Dual fixed
Fixed






Mean train size = 24576 bits



Throughput


Mean data frame delay (msec)
Delay performance: IEEE 802.11

Simulation


M/M/1/50

M/E8/1/50 and M/E32/1/50





Throughput


Mean data frame delay (msec)
Delay Performance: 802.11








Simulation
MMPP/E8/1/50
MMPP parameters
0=51
r0=0.00002 msec
r1=0.00008 msec



Throughput


Mean data frame delay (slots)
Delay Performance: IEEE 802.3


Simulation

M/M/1/50





M/E8/1/50



Throughput


How inaccurate are
classical performance
models?
A Comparison
Lam’s results
Our results
Normalized mean delay, D/b1
100
a=0.1
a=0.01
50
20
10
5
2
1
0
0.2
0.4
0.6
Throughput, S
0.8
1.0
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 traffic
Data frame size distribution: Lam’s=Ours=fixed
Retransmission algorithm:
Lam’s=An adaptive retransmission algorithm;
Ours=BEB
Conclusion:
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