Post on 04-Jan-2016
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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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Model A - numerical results
Aggregated throughput
(pkt/s)
Aggregated packet arrival rate (pkt/s), Λ
n = 10 stations – buffer size K = 20 – basic access scheme
540
560
580
600
620
640
660
680
550 600 650 700 750 800
mod Ans
mod Ans
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Model A - numerical results
Aggregated packet arrival rate (pkt/s), Λ
n = 10 stations – buffer size K = 20 – basic access scheme
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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Model A - numerical results
Number of backlogged stations
n = 10 stations – buffer size K = 20 – basic access scheme
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
Aggregated packet arrival rate (pkt/s), Λ
n = 10 stations – buffer size K = 20 – basic access scheme
0.1
1
10
400 450 500 550 600 650 700 750 800
mod B
ns
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Model B - numerical results
Aggregated packet arrival rate (pkt/s), Λ
n = 10 stations – buffer size K = 20 – basic access scheme
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
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Model B - numerical results
Number of packets in the queue
n = 10 stations – buffer size K = 20 – basic access scheme
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
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Model B - numerical results
Number of backlogged stations
n = 10 stations – buffer size K = 20 – basic access scheme
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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Multi-rate multi-hop environment
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)
Multi-rate multi-hop environment
(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
Number of stations at 2 Mb/s
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
Multi-rate multi-hop environment
(saturated case)
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Multi-rate multi-hop environment
(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)
Number of stations at 11 Mb/s
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)
Aggregated packet arrival rate (pkt/s), Λ
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…