Minimum Energy Reliable Minimum Energy Reliable Paths Using Unreliable Paths Using Unreliable

Wireless LinksWireless LinksQunfeng Dong, Suman Banerjee, Qunfeng Dong, Suman Banerjee,

Micah Adler, and Archan MisraMicah Adler, and Archan MisraMobihoc 2005Mobihoc 2005

OutlineOutline IntroductionIntroductionRelated workRelated workFormulationFormulationSingle-path min-energy routesSingle-path min-energy routesMulti-path min-energy routesMulti-path min-energy routesEvaluationEvaluationConclusionConclusion

IntroductionIntroductionTraditional power aware routing schemes Traditional power aware routing schemes

do not take do not take link losslink loss rates into account rates into accountEnergy efficient pathsEnergy efficient pathsAssume that every link is totally Assume that every link is totally reliablereliable

Too optimisticToo optimisticRight metricRight metric

All transmissions including retransmissionsAll transmissions including retransmissions

IntroductionIntroductionDesign of wireless communication Design of wireless communication

protocols are guided by two requirementsprotocols are guided by two requirementsEnergy efficiencyEnergy efficiencyResilience to packet lossesResilience to packet losses

Achieve end-to-end reliability on multi-hop Achieve end-to-end reliability on multi-hop pathspathsHop-by-hop retransmissionHop-by-hop retransmissionEnd-to-end retransmissionEnd-to-end retransmissionMixed methodMixed method

IntroductionIntroductionSolve the problem of computing minimum Solve the problem of computing minimum

energy paths for reliable communication in energy paths for reliable communication in End-to-end retransmission modelEnd-to-end retransmission modelMixed retransmission modelMixed retransmission model

Examine the problem of reliability through Examine the problem of reliability through utilization of multiple routesutilization of multiple routesThroughputThroughputReliabilityReliability

Related workRelated workFinding minimum cost pathFinding minimum cost path

Link costLink cost is set to the transmission power is set to the transmission powerResidual batteryResidual battery is used as a routing metri is used as a routing metri

ccNone of these papers considered the lossy None of these papers considered the lossy

property of wireless links.property of wireless links.

Related workRelated workMinimum energy paths for reliable commuMinimum energy paths for reliable commu

nication in multi-hop wireless networksnication in multi-hop wireless networksACM MobiHoc 2002ACM MobiHoc 2002BMABMA

pw1

Transmission power

Error rate of a hop by hop retransmission link

Related workRelated workNot true in the end-to-end retransmission Not true in the end-to-end retransmission

modelmodel

L>=2 makes lossy links appear to be even moL>=2 makes lossy links appear to be even more expensivere expensive

Reasonable but not optimalReasonable but not optimalMore general and realistic mixed retransmiMore general and realistic mixed retransmi

ssion model in not exploredssion model in not explored

lpw1

I >=2 is some constant

FormulationFormulationTwo metrics are used to calculate the lick Two metrics are used to calculate the lick

costcostWeight of link (Weight of link (ii,,jj): ): WW((ii,,jj))Expected number of transmissions of a succeExpected number of transmissions of a succe

ssful delivery over a link (ssful delivery over a link (ii,,jj): ): NN((ii,,jj))

FormulationFormulationWeight of link (Weight of link (ii,,jj): ): WW((ii,,jj))

FormulationFormulationExpected number of transmissions of a suExpected number of transmissions of a su

ccessful delivery over a ccessful delivery over a linklink ( (ii,,jj): ): NN((ii,,jj))Er(i, j) is the probability that a transmission ov

er link (i; j)Er(i, j) = 0: link (i, j) is considered reliable

FormulationFormulation

Cmin(u, v): expected energy consumption of a successful delivery along a minimum energy path from u to v.

Single-path min-energy routesSingle-path min-energy routesBasic Algorithm for Minimum Energy Basic Algorithm for Minimum Energy

Routing (BAMER)Routing (BAMER)General Algorithm for Minimum Energy General Algorithm for Minimum Energy

Routing (GAMER)Routing (GAMER)BAMER for the mixed retransmission BAMER for the mixed retransmission

modelmodelDistributed Algorithm for Minimum Energy Distributed Algorithm for Minimum Energy

Routing (DAMER)Routing (DAMER)

BAMERBAMERGeneralized extension of Dijkstra’s shortesGeneralized extension of Dijkstra’s shortes

t path algorithmt path algorithmEnd-to-end transmission modelEnd-to-end transmission model

BAMER-exampleBAMER-example

C(s)=0

GAMERGAMERFurther generalization of BAMERFurther generalization of BAMER

Each individual link may or may not provide Each individual link may or may not provide per hop reliabilityper hop reliability

GAMER-exampleGAMER-example

C(s)=0

Hop by hop retransmission

10+4*12=58

BAMER for the mixed BAMER for the mixed retransmission modelretransmission model

An appropriate preprocessing stage An appropriate preprocessing stage enable BAMER to solve the same problem enable BAMER to solve the same problem in mixed retransmission modelin mixed retransmission model

).('),(')( vuNvuWuC

GAMERGAMER

BAMERBAMER

BAMER for the mixed BAMER for the mixed retransmission model-exampleretransmission model-example

(48,1)

DAMERDAMERBoth BAMER and GAMER are centralized Both BAMER and GAMER are centralized

algorithmsalgorithmsHas to be implemented as a distributed Has to be implemented as a distributed

protocol in a lightweight fashionprotocol in a lightweight fashion

(1,0)

(1,0)

(1,0)(1,0)

(12,0)

(1,0)

(0, 4)

(0, 4)

(0, 4)

15

12

4

DAMERDAMERComputes an energy efficient path from ea

ch node to every other node.uw

vMv.C(w)

N(u.v)W(u.v) Mv.R(w)

C(w)

DAMER-exampleDAMER-example

0+1*2*8=16

0+1*2*5=16

16+2*2*6=40

40+4*2*5=16

10+2*2*8=42

Multi-path min-energy routesMulti-path min-energy routesMulti-path routing is considered beneficial fMulti-path routing is considered beneficial f

or improved throughput and reliabilityor improved throughput and reliabilityCost more energy consumptionCost more energy consumption

In the presence of such noisy routing inforIn the presence of such noisy routing informationmationMulti-path routing may outperform Dijkstra’s sMulti-path routing may outperform Dijkstra’s s

hortest path routinghortest path routing

Multi-path min-energy routesMulti-path min-energy routesReveal thatReveal that

If If perfect routing informationperfect routing information is given and is given and link link loss ratesloss rates are taken into account, multi-path are taken into account, multi-path routing can still potentially routing can still potentially reducereduce the the expected energy consumption of one-to-one expected energy consumption of one-to-one communication.communication.

Multi-path min-energy routesMulti-path min-energy routes

(1,2)

(1,2) (1,2)

(0,0) (0,0)

2

8/7

““Should the intermediate node forward Should the intermediate node forward every copy of the packet? “every copy of the packet? “NoNo

Formally analyze the complexity of finding Formally analyze the complexity of finding minimum energy multi-path routes and minimum energy multi-path routes and prove that it is prove that it is NP-hardNP-hardBy reducing form the By reducing form the 3-dimensional 3-dimensional

matching problemmatching problem

Multi-path min-energy routesMulti-path min-energy routes

Multi-path min-energy routesMulti-path min-energy routes

jijijijjjjiiii zzyywwMzywmzywm ,,,),,('),,,('

Multi-path min-energy routesMulti-path min-energy routes W = {w1,w2} X = {x1, x2} Y = {y1, y2}: M = {m1,m2,m3,m4} m1 = (w1, x2, y2) m2 = (w1, x1, y1) m3 = (w2, x2, y2) m4 = (w1, x1, y2)

Weight 0, error rate p=e-1/3q

Weight 1, error rate 0

Weight c=(e-1)q, error rate=0

Multi-path min-energy routesMulti-path min-energy routesM contains a 3-DM of size q if and only if t

he minimum expected energy consumption to deliver a packet from s to t is

Multi-path min-energy routesMulti-path min-energy routes ““Only if” directionOnly if” direction

S->m: qS->m: qM->w,x.y; 3qM->w,x.y; 3qEnergy consumptionEnergy consumption

c+qc+qProbabilityProbability

1-p1-p3q3q

Weight 0, error rate p=e-1/3q

Weight 1, error rate 0

Weight c=(e-1)q, error rate=0

Multi-path min-energy routesMulti-path min-energy routes ““if” directionif” direction

The number of triplet nodes that participate to forward packets in this routing scheme n0, 1<= n0<= n

The number of element nodes that participate to forward packets in this routing scheme, q0. 1<= q0 <= min(3q, 3n0).

Prove by contradictionAssume that M does not contain a matching of

size q

Multi-path min-energy routesMulti-path min-energy routes

n0 > qn0 = q, q0 < 3qn0 < q then q0 < min(3q, 3n0) = 3n0

EvaluationEvaluation100 nodes100 nodes10*10 square fields 10*10 square fields Link error rate 0<=Link error rate 0<=MaxLER<=1MaxLER<=1

Link error rate of link(u,v) and link(v,u) is differLink error rate of link(u,v) and link(v,u) is differentent

Normalized energy efficiency (NEE)Normalized energy efficiency (NEE)The ratio of its average energy consumption tThe ratio of its average energy consumption t

o that of BAMER and GAMERo that of BAMER and GAMER

EvaluationEvaluation

a = 2, 3, 4

EvaluationEvaluationUPGrate: percentage of links supporting h

op-by-hop retransmission

UPGrate

NEE MaxLER = 0.1, 0.4, 0.7

EvaluationEvaluation

30, 150, 250 nodes,

UPGrate

NEE

ConclusionConclusionStudy the problem of minimum energy routStudy the problem of minimum energy rout

ing for reliable one-to-one communication iing for reliable one-to-one communication in the presence of lossy linksn the presence of lossy linksEach link support link layer hop-by-hop retranEach link support link layer hop-by-hop retran

smission and guarantee reliable deliverysmission and guarantee reliable deliveryBAMERBAMERGAMERGAMERDAMER DAMER

ConclusionConclusionOur another interesting finding

In some cases multi-path routing may reduce the expected energy consumption in the presence of lossy links.

Formally analyze the problem of finding the minimum energy multi-path routing scheme and prove that it is actually NP-hard.

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