1 COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED. On the Capacity of Wireless CSMA/CA Multihop Networks Rafael Laufer and Leonard Kleinrock Bell

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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

10


• 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


12


SATURATED SINGLE-HOP FLOWSNot All Nodes Within Carrier Sense Range

2

1

3

13


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

tU2(t)

tU3(t)

t

14


• 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

16


• 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

19


UNSATURATED SINGLE-HOP FLOWS Dual Saturated NetworkU1(t)

tU2(t)

tU3(t)

t

1

20


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

1

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

1

y1

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

yy

yy

21

11 1

1yy

Capacity lost due to the lack of synchronization between

nodes

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1

y1

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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1 COPYRIGHT © 2011 ALCATEL-LUCENT. ALL RIGHTS RESERVED. On the Capacity of Wireless CSMA/CA Multihop Networks Rafael Laufer and Leonard Kleinrock Bell