On the Capacity of Wireless CSMA/CA Multihop Networks

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COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED.

On the Capacity ofWireless CSMA/CA Multihop NetworksRafael Laufer and Leonard KleinrockBell Labs, UCLAIEEE INFOCOM 2013

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• 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

INTRODUCTIONWireless CSMA/CA Multihop Networks

U2(t)

t

21 3

1

1

3


• 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

INTRODUCTIONWireless CSMA/CA Multihop Networks

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• 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

INTRODUCTIONGoals

f2

f1

f3

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• 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

INTRODUCTIONKey Contributions

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• 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

MODEL AND ASSUMPTIONSSystem Model

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THROUGHPUT MODELING

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SATURATED SINGLE-HOP FLOWSAll Nodes Within Carrier Sense Range

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SATURATED SINGLE-HOP FLOWSAll Nodes Within Carrier Sense RangeU1(t)

t

1

U2(t)

tU3(t)

t

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• By definition, the steady-state solution is

• Ratio between and


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• System of linear equations

• Steady-state solution

• Throughput of each flow


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SATURATED SINGLE-HOP FLOWSNot All Nodes Within Carrier Sense Range

2

1

3

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SATURATED SINGLE-HOP FLOWSNot All Nodes Within Carrier Sense RangeU1(t)

tU2(t)

tU3(t)

t

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• Steady-state solution for this case

• General solution

• Throughput of each flow

SATURATED SINGLE-HOP FLOWSNot All Nodes Within Carrier Sense Range

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UNSATURATED SINGLE-HOP FLOWSIdle TimeU1(t)

t1

U2(t)

tU3(t)

t

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• Steady-state solution

• Source behavior Injecting too little traffic: 0 Injecting too much traffic: 1

UNSATURATED SINGLE-HOP FLOWS

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• 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/

UNSATURATED SINGLE-HOP FLOWS

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UNSATURATED SINGLE-HOP FLOWSPrimal Unsaturated NetworkU1(t)

t1

U2(t)

tU3(t)

t

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UNSATURATED SINGLE-HOP FLOWS Dual Saturated NetworkU1(t)

tU2(t)

tU3(t)

t

1

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CAPACITY REGION CHARACTERIZATION

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• Normalized throughput of transmitter i

• Express as a function of

• Find the inverse

• Limit the stability factors to the range

CAPACITY REGIONCharacterization Algorithm

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CAPACITY REGIONTwo Transmitters Within Carrier Sense Range

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CAPACITY REGIONTwo Transmitters Within Carrier Sense Range

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y1

y2

1

1

1

2

2

1

121

2

1

21

1

1

12

22 1

1yy

21

11 1

1yy

01

11

02 12

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CAPACITY REGIONThree Transmitters Within Carrier Sense Range

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CAPACITY REGIONThree Transmitters Within Carrier Sense Range

1y1

y21

y31

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CAPACITY REGIONThree Transmitters Not Within Carrier Sense Range

2

1

3

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1

y1

y2

1

1

1

2

2

1

111121

2

1

11121

111

1

11

112

21

22

2

yyyy

21

11 1

1yy

Capacity lost due to the lack of synchronization between

nodes

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1y1

y21

y31

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FEASIBILITY TEST

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• 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

FEASIBILITY TESTFeasibility of Input Rates

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SIMULATION RESULTS

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SIMULATION SCENARIOMIT Roofnet Network: Single-Hop Flows

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SIMULATION RESULTSSingle-Hop Flows (ρ = 1.00)

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• 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

CONCLUSIONS

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On the Capacity ofWireless CSMA/CA Multihop NetworksRafael Laufer and Leonard KleinrockBell Labs, UCLAIEEE INFOCOM 2013

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On the Capacity of Wireless CSMA/CA Multihop Networks