On the Capacity of
Wireless CSMA/CA Multihop Networks
Rafael Laufer and Leonard Kleinrock
Bell Labs, UCLA
IEEE INFOCOM 2013
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INTRODUCTION
Wireless CSMA/CA Multihop Networks
• Carrier sense multiple access with collision avoidance (CSMA/CA)
- Before transmitting, the node verifies if the medium is idle via carrier sensing
- If idle, sample a random back-off interval and starts counting down
- Whenever busy, freeze the counter and wait for ongoing transmission to finish
1
2
3
U2(t)
1
1
t
2
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INTRODUCTION
Wireless CSMA/CA Multihop Networks
• Considered unpredictable with unknown throughput limitations
- Distributed nature of CSMA/CA: nodes should back off from each other
- Buffer dynamics of unsaturated sources: time-varying subset of transmitters
- Dependence of downstream links on upstream traffic: coupled queue state
• Strong dependence among the state of transmitters
- Physical proximity and traffic pattern induce correlation across the network
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INTRODUCTION
Goals
• Understand throughput limits of wireless CSMA/CA multihop networks
• Provide answers to specific questions regarding the network capacity
- If the rate of f1 increases by 10%, how much can f2 still achieve?
- If f3 starts, by how much must f1 and f2 slow down to keep the network stable?
• Determine the capacity region of arbitrary wireless networks
f2
f3
f1
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INTRODUCTION
Key Contributions
• Theory to model the behavior of wireless CSMA/CA multihop networks
- Handle buffer dynamics of unsaturated traffic sources and multihop flows
- Respect interference constraints imposed by the wireless medium
• Characterization of the capacity region of any wireless network
- No restrictions on node placement: suitable for arbitrary networks
- Agnostic to the distribution of network parameters: only averages are relevant
- Convex only when nodes are within range: nonconvex in general
• Feasibility test
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MODEL AND ASSUMPTIONS
System Model
• Single-path routing, with routes and bit rates assumed fixed
• Omnidirectional antenna communicating in a single channel
• CSMA/CA for medium access control
• Network state S composed of links transmitting
- Knowledge of the feasible link sets in the network
•
: fraction of time that all links in S are transmitting
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THROUGHPUT MODELING
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SATURATED SINGLE-HOP FLOWS
All Nodes Within Carrier Sense Range
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SATURATED SINGLE-HOP FLOWS
All Nodes Within Carrier Sense Range
U1(t)
1
t
U2(t)
t
U3(t)
t
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SATURATED SINGLE-HOP FLOWS
All Nodes Within Carrier Sense Range
• By definition, the steady-state solution is
• Ratio between
and
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SATURATED SINGLE-HOP FLOWS
All Nodes Within Carrier Sense Range
• System of linear equations
• Steady-state solution
• Throughput of each flow
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SATURATED SINGLE-HOP FLOWS
Not All Nodes Within Carrier Sense Range
1
3
2
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SATURATED SINGLE-HOP FLOWS
Not All Nodes Within Carrier Sense Range
U1(t)
t
U2(t)
t
U3(t)
t
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SATURATED SINGLE-HOP FLOWS
Not All Nodes Within Carrier Sense Range
• Steady-state solution for this case
• General solution
• Throughput of each flow
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UNSATURATED SINGLE-HOP FLOWS
Idle Time
U1(t)
1
t
U2(t)
t
U3(t)
t
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UNSATURATED SINGLE-HOP FLOWS
• Steady-state solution
• Source behavior
- Injecting too little traffic:
- Injecting too much traffic:
0
1
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UNSATURATED SINGLE-HOP FLOWS
• Why the solution is similar to the saturated case?
• Statistically equivalent to a saturated network
- Average transmission times are the same
- Average backoff times are larger by 1/
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UNSATURATED SINGLE-HOP FLOWS
Primal Unsaturated Network
U1(t)
1
t
U2(t)
t
U3(t)
t
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UNSATURATED SINGLE-HOP FLOWS
Dual Saturated Network
U1(t)
1
t
U2(t)
t
U3(t)
t
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CAPACITY REGION CHARACTERIZATION
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CAPACITY REGION
Characterization Algorithm
• Normalized throughput of transmitter i
• Express
as a function of
• Find the inverse
• Limit the stability factors to the range
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CAPACITY REGION
Two Transmitters Within Carrier Sense Range
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CAPACITY REGION
Two Transmitters Within Carrier Sense Range
y1
1
y2 
2
12
1 
y1 
1
1  1
1  1
1
1  1   2
y1 
2  0
1
1  1
1 
y2 
2  1
1  0
2
2
1  1   2
12
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1
y2
CAPACITY REGION
Three Transmitters Within Carrier Sense Range
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CAPACITY REGION
Three Transmitters Within Carrier Sense Range
y1
1
1
y3
1
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y2
CAPACITY REGION
Three Transmitters Not Within Carrier Sense Range
1
3
2
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CAPACITY REGION
Three Transmitters Not Within Carrier Sense Range
y1
1
 1


 2
 y 2 1  y 2 

1
2

 1  y 1  y 2 
1
 1   1 1 1   1
Capacity lost due to the lack of
synchronization between nodes
1   1   2   1   1 1
y1 
2
2
1   1   2   1   1 1
12
1
1  1
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1
1 
y2 
y2
CAPACITY REGION
Three Transmitters Not Within Carrier Sense Range
y1
1
1
y3
1
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y2
FEASIBILITY TEST
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FEASIBILITY TEST
Feasibility of Input Rates
• Does the network support a given rate vector
• Normalized throughput
-
depends only on average values
approximates the total transmission time as
approximates the total time as
• Plug into the expression
and check if
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?
SIMULATION RESULTS
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SIMULATION SCENARIO
MIT Roofnet Network: Single-Hop Flows
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SIMULATION RESULTS
Single-Hop Flows (ρ = 1.00)
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SIMULATION RESULTS
Single-Hop Flows (ρ = 0.50)
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SIMULATION RESULTS
Single-Hop Flows (ρ = 0.25)
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SIMULATION RESULTS
Single-Hop Flows (ρ = 0.01)
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CONCLUSIONS
• Capacity of wireless CSMA/CA multihop networks poorly understood
• Theory able to model the network behavior
- Buffer dynamics of unsaturated sources and multihop flows
- Wireless CSMA/CA multihop networks are not erratic, but predictable
• System of nonlinear equations characterizes the network capacity
- Agnostic to the distribution of network parameters, only averages relevant
• Knowledge of the underlying process governing CSMA/CA networks
- Opens up new areas of research
- Routing optimization and network provisioning
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COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED.
On the Capacity of
Wireless CSMA/CA Multihop Networks
Rafael Laufer and Leonard Kleinrock
Bell Labs, UCLA
IEEE INFOCOM 2013
38
COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED.