Modeling Media Access in Embedded Two-Flow Topologies of Multi-hop Wireless Networks
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Transcript of Modeling Media Access in Embedded Two-Flow Topologies of Multi-hop Wireless Networks
Rice Networks Grouphttp://www.ece.rice.edu/networks
Michele GarettoJingpu Shi
Edward W. Knightly
Modeling Media Access in Embedded Two-Flow Topologies of Multi-hop Wireless Networks
MobiCom 2005
Garetto, Shi, Knightly
Motivation
Multi-hop wireless networks employing CSMA/CA protocols exhibit complex behavior and are difficult to analyze– Root cause: different and incomplete channel state
information among flows– Most of existing modeling techniques only consider the
case in which all stations are in radio range
When stations are not all in radio range, severe unfairness can occur among flows:– Long-term unfairness : some flows can starve
completely– Short-term unfairness : flows alternate phases in which
dominate each other in terms of throughput
Garetto, Shi, Knightly
Our contribution
We decompose a large-scale network into embedded subgraphs, each consisting of four nodes and two flow pairs
We identify all possible two-flow scenarios and propose a novel classification of them
We compute the occurrence probability of each scenario under random nodes deployment
We accurately study the performance of random access in all cases not analyzed so far in the literature
Garetto, Shi, Knightly
Basic two-flow, four-node layout
A
ba
BAB
Ab
aB
AB
Senders A, B Receivers a, b A-a, B-b must be connected
(= in radio range)
Nodes from one flow may hear nodes from the other
Four possible connections that can exist – or not
24 = 16 combinations Ab, Ba interchangeable 4 redundant scenarios
Garetto, Shi, Knightly
Twelve possible scenarios
A
ba
BA
ba
BA
ba
BA
ba
BAb
A
ba
B
ab
A
ba
BAb
A
ba
BABA
ba
BAB
A
ba
B
ab
A
ba
BA
ba
B
ab
Ab
aB
A
ba
BAB AB AB
AB
Ab Ab
aB
aB aBaB
ab
ab ab
aB aB
Garetto, Shi, Knightly
Example topologies
bB
aA
bBaA bB aA
bB aA
bB
aAbBa A
bBaA
b B
aAbBaA b
B
aAbBaA
Garetto, Shi, Knightly
Spatial analysis We assume nodes uniformly distributed in the area We compute the occurrence probability of each
scenario We discard the case in which flows are completely
isolated from each other normalized probabilities – insensitive to area size (no border effects)– insensitive to node density
Garetto, Shi, Knightly
0
0.1
0.2
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0.7
0.8
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Prob
abili
ty (c
ondi
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d)
Normalized distance between tx and rx
scenario 2scenario 3scenario 4scenario 5scenario 6
scenario 7scenario 8scenario 9
scenario 10scenario 11scenario 12
Scenario Likelihood
Garetto, Shi, Knightly
Performance simulations with CSMA/CA protocol
Throughput measurements every 400 ms X = two-way handshake = four-way handshake
Garetto, Shi, Knightly
Scenarios classification : 3 groups
A
ba
BAb
aB
A
ba
BA
ba
BAb
aBab
A
ba
BA
ba
B
aBaB
ab
A
ba
BAB
Senders Connected (SC)
Symmetric Incomplete State
(SIS)
Asymmetric Incomplete State
(AIS)
Garetto, Shi, Knightly
00.10.20.30.40.50.60.70.80.9
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0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Prob
abili
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ondi
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d)
Normalized distance between tx and rx
SCAISSIS
Probabilities of 3 groups of scenarios
Garetto, Shi, Knightly
Hop distance distribution in a multi-hop network
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Prob
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Hop distance / TX range
300 nodes - 2000 m x 2000 m – Random waypoint – DSDV
Most of actively used hops are close to the maximum
TX range !
Garetto, Shi, Knightly
Probabilities of 3 groups of scenarios
00.10.20.30.40.50.60.70.80.9
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1 1.5 2 2.5 3
Prob
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d)
Ratio between sensing range and transmission range
SCAISSIS
Hop distance = TX range ; variable Sensing Range
Garetto, Shi, Knightly
Analysis of Asimmetric Incomplete State scenarios (AIS)
Known to be highly problematic for random access protocols: flow A a starves – V. Bharghavan, A. J. Demers, S. Shenker, L. Zhang, MACAW: A Media Access Protocol for Wireless LAN's, SIGCOMM ‘94
RTS/CTS does not solve the problem RRTS does not help Not yet modeled analytically
bB
aAbB
aA aA Aa
B b b
B
Garetto, Shi, Knightly
Decoupling technique (valid for general topologies)
The channel “private view” of a node:
… …
Node’s transmission is
successfulidle slot
Node’s transmission
collides
t
channel is busy because of activity
of other nodes
Modelled as a renewal-reward process
Throughput (pkt/s) = P [event Ts occurs]
Average duration of an event (s)
Garetto, Shi, Knightly
Analysis of Asimmetric Incomplete State scenarios (AIS)
Flow A a does not know when to contend: it has to discover an available gap in the activity of flow B b randomly, where to place an entire RTS or DATA packet
B b…t
…B b B b B b
A a ?
bB
aAbB
aA aA Aa
B b b
B
RTS/DATA
Garetto, Shi, Knightly
Analysis of Asimmetric Incomplete State scenarios (AIS)
B bA a
B b B b
B bA a
B b B b
B b A a B b B b
• The collision probability of flow A a can be accurately computed assuming that the first packet arrives at a random point in time • The collision probability of flow B b is zero
Garetto, Shi, Knightly
AIS scenario – model vs simulation
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800
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200 400 600 800 1000 1200 1400
Pack
et T
hrou
ghpu
t (pk
t/s)
Data Payload Size (bytes)
ns - Flow Bmodel - Flow B
ns - Flow Amodel - Flow A
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200
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600
800
1000
200 400 600 800 1000 1200 1400
ns - Flow Bmodel - Flow B
ns - Flow Amodel - Flow A
with RTS/CTS basic access (no RTS/CTS)
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AIS scenario – model vs simulation
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0 100 200 300 400 500 600
Pack
et T
hrou
ghpu
t (pk
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Arrival rate of flow B (pkt/s)
Flow A backlogged – Flow B not backlogged
ns - Flow Bmodel - Flow B
ns - Flow Amodel - Flow A
Garetto, Shi, Knightly
Analysis of Symmetric Incomplete State scenarios (SIS)
Long term fair, but short term unfair One flow dominates over the other, until they switch
their role (randomly) RTS/CTS does not help, and can even make things
worse Not yet modeled analytically As a special case, the receiver can be in common:
b B
aAbB
aAb BaA
AP= the classic “hidden-terminal” scenario
Garetto, Shi, Knightly
Simulation of short term unfairness – SC vs SIS
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thro
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0 m
s
Time (s)
Time (s)
RTS/CTS – 7 backoff stages
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s basic access – 4 backoff stages
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basic access – 7 backoff stages
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RTS/CTS – 9 backoff stages
Garetto, Shi, Knightly
Analysis of Symmetric Incomplete State scenarios (SIS)
To capture short-term behavior, we cannot apply the decoupling technique (independent states) States of the two flows are tightly correlated !
We use a markov model in which the state is:
The computation of the collision probability is the key point
b B
aAbB
aAb BaA
{ backoff stage of A, backoff stage of B }
Garetto, Shi, Knightly
Analysis of Symmetric Incomplete State scenarios (SIS)
Steady-state distribution of Markov Chain:
01
23
45
6
0 1 2 3 4 5 6stage A
00.020.040.060.08
0.10.12
Prob
abili
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stage B
0.140.16
Time-scale of short term unfairness
Garetto, Shi, Knightly
SIS scenario – model vs simulation
Case Throughput(pkt/s)
Collision probability
Time scale of unfairness (ms)
RTS/CTS7 stages
218216
0.250.25
235223
RTS/CTS9 stages
229230
0.110.09
9821156
Basic access4 stages
125107
0.690.75
1515
Basic access7 stages
222220
0.370.38
5960
nsmodel
nsmodel
nsmodel
nsmodel
Thanks !
Backup slides
Garetto, Shi, Knightly
Modeling Media Access
Event probabilities:
… …t
Define the probabilities = probability that the node sends out a packet in a slot= conditional collision probability= conditional busy channel probability
Garetto, Shi, Knightly
The unknown variables are:
(a decreasing function of p )
The throughput of a node decreases if either: is large (if so, is small, also) is large (large fraction of busy time)
Throughput formula:
Modeling Media Access
Garetto, Shi, Knightly
Short term unfairness – simulation
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SCSIS
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