DTM: A Distributed Traffic Management Algorithm for Sensor Networks

Transcription

1 8 IJCSNS International Journal of Computer Science Network Security, VOL6 No8A, Augut 6 DM: A Ditributed raffic Management Algorithm for Senor Network Yantao Pan, Xicheng Lu, Peidong Zhu School of Computer, National Unierity of Defene echnology, Changha, P R China Summary Lifetime optimization i a key challenge of enor network Since data tranmiion i the main energy conumer, it i important to make ue of energy efficient routing protocol We regard the lifetime optimization problem a a multi-ource ingle-ink flow problem in a directed graph with capacity power on ertice hen we propoe a ditributed algorithm to ole thi problem he method gie the alue of imum lifetime exactly Key word: Senor Network, raffic Management, Lifetime imization 1 Introduction he deelopment of enor network proide u a new way to interact with phyical enironment It i a key challenge to imize the lifetime of a enor network, which i uually defined a the time from it deployment to it partition when there exit a node that cannot end data to the ink Literature [1-4] inetigate the upper bound the expectation of a enor network imum lifetime Literature [5-8] propoe heuritic algorithm to imize the lifetime approximately Howeer, none of thoe approache proide the imum lifetime exactly In thi paper, we exploit thi problem by flow model propoe a ditributed algorithm to achiee a imum lifetime routing he ret of thi paper i organized a follow In ection, we propoe the formulation of the problem We gie a centralized algorithm in ection 3 then a ditributed algorithm in ection 4 In ection 5, ome concluding remark are made Problem Statement Formulation Conider a group of wirele tatic enor node V romly ditributed in a region Each node V ha a limited battery energy upply which i mainly ued for data communication Aume that each node ha a fixed communication power a fixed tranmiion radiu Let p () be the total quantity of data that ertex can end It i a function of the initial energy upply the communication power Let w () be the data-generating rate at a ource node A enor network can be defined a a directed graph with power on ertice Definition-1 A enor tranportation network (It will be howed a SenorNet for hort in the ret of thi paper) i defined a the form of N = ( V, A, p, X, t), where 1 GV (, A) i a connected imple directed graph, p (): Va i the reiduary tranmiion capacity of ertex, 3 X i the ource et t i the ink Let ( H) = ( u, ) A H, u V \ H} ( H) = (, u) A H, u V \ H} be the et of arc entering leaing a node et H For a function f( a): Aa, we denote f ( H) = ˆ f( a) f ( H) = ˆ f( a) a ( H) a ( H) Definition- f( a): Aa i defined a a flow of N if f () p(), V f () = f (), I Let al( f ) = ˆ f ( X ) f ( X ) be the alue of f Definition-3 Let N be a SenorNet Flow f i defined a a routing of N if there i a uch that f ( x) f ( x) = w( x), p () f = (), V i called the lifetime of N under the routing f If there i no f it correponding o a to >, f i a imum lifetime routing i the imum lifetime For a SenorNet N = ( V, A, p, X, t), we may add a irtual ource to it add a irtual arc from it to each ource Additionally, we et the capacity of a irtual arc to be w() correponding to ertex, where i a alue not more than the imum lifetime hen we can tranfer the imum flow problem from a multi-ource network to a ingle-ource network Manucript receied Augut 5, 6 Manucript reied Augut 5, 6

2 IJCSNS International Journal of Computer Science Network Security, VOL6 No8A, Augut 6 9 Definition-4 Let N = ( V, A, p, X, t) be a SenorNet aume > N = ( V, A, p, c,, t) i defined a the tranformed network of N about, if following 4 condition are atified 1 V = V U } A = AU A, where A = (, x) } 3 p (), V, p () =, otherwie 4 w(), u =, c ( u, ) =, otherwie Lemma-1 Let N be a SenorNet let be it imum lifetime Suppoe N i the tranformed network of N about, f i a imum flow of N hen, al( f ) = w( x) heorem-1 Suppoe N i the tranformed network of N about f i a imum flow of N hen i the imum that atifie al( f ) = w( x) Suppoe i }, i =,1,, i a equence, where = 1 i an upper bound of the imum lifetime he ret element are generated by BS algorithm, where ξ i the gien preciion 1, al( f ) = w( x), θ ( ) =, al( f ) < w( x) BS (, 1 ) 1 low up 1 i while up low > ξ 3 i ( up low ) 4 ifθ ( i ) = 5 up i 6 ele 7 low i 8 i= i 1 9 } 1 return ( ) up low Fig1 BS algorithm From heorem-1 BS algorithm, we obtain lim i } = herefore, we can take a binary i earch between the lower upper bound of the imum lifetime finally achiee a alue exactly enough if only we could find the imum flow of N In order to tranfer the contraint of N from ertice to arc, we diide a ertex into two irtual ertice add a irtual arc between them he capacity of a irtual arc i et to the reidual tranmiion capacity of the correponding ertex For a SenorNet N = ( V, A, p, X, t), we may add a irtual ource to it add a irtual arc from it to each ource Additionally, we et the capacity of a irtual arc to be w() correponding to ertex Definition-5 Let N = ( V, A, p, c,, t) be a tranformed network of N hen N = ( V, A, c,, t) i defined a the VA (Vertex to Arc) network of N, if the following condition are atified 1 V = V U V, uch that V V for each V A = AA U AV, uch that 1) ( u, ) A, (, ) (, ) A c u = c u for ( u, ) A ) (, ) A, (, ) ( ) V c = p for V heorem- Let N = ( V, A, c,, t) be a VA network N = ( V, A, p, c,, t) be a tranformed network of N = ( V, A, p, X, t) Aume f to be a imum flow of N hen f i a imum flow of N, where f ( u, ) = ˆ f ( u, ), ( u, ) A And f i a imum flow of N, ' where f( u, ) = ˆ f( u, ), ( u, ) A Centralized Algorithm In thi ection, we propoe a centralized algorithm baed on preflow-puh method introduced by Golberg-arjan [9] to ole the imum flow problem in N Since there i only N in conideration in thi ection, we denote it a N = ( V, A, c,, t) for hort denote the reidual network of it a N ( f) = ( V, A, c,, t) For a node V, we call ex() f = () f () the exce of It i the difference between the total flow entering leaing node he flow coneration contraint i atified when all node hae zero excee except the ource the ink Definition-6 A function ζ : A a i defined a a preflow if 1 ex( ) for V \, t}, ζ ( a) c( a) for a A A node i actie if it exce i poitie he baic idea i to puh the exce flow to the neighbor that are cloer to the ink o do thi, a height

3 1 IJCSNS International Journal of Computer Science Network Security, VOL6 No8A, Augut 6 function h: V a i aigned to each node A alid height function atify: ht () = hu ( ) h ( ) 1 for ( u, ) A We only puh flow from a higher node to a lower node Definition-7 A reidual arc ( u, ) A, u i admiible if hu ( ) = h ( ) 1 Let u be an actie node uppoe ( u, ) i admiible We puh Δ unit flow from u to through ( u, ), Δ= min ex, c ( u, ) hen ex = ex Δ where } ex() = ex() Δ If no more admiible arc exit, we perform lift proce to create admiible arc In thi tage, a node that ha no admiible outward arc et it height to min h ( ) 1 ( u, ) A } he algorithm end when there i no actie node At that tage the flow i feaible for the firt time alo imized CA( N ) 1 h ( ) V ht () Compute h ( ) for other node 3 ex( ), V ζ ( a), a A 4 for u Adj ( ) = ˆ u (, u) A } 5 ζ ( u, ) cu (, ), exu ( ) cu (, ) 6 while there exit actie node 7 elect an actie node u 8 if there i admiible arc 9 elect an admiible arc (, u ) 1 Δ min ex, c ( u, )} 11 ex ex( u ) Δ 1 ex( ) ex( ) Δ 13 ζ(, u) ζ(, u ) Δ 14 c (, u ) c (, u ) Δ 15 c (, u) c (, u ) Δ 16 }ele 17 hu ( ) min h ( ) 1( u, ) A } 18 }//while 19 return ζ Fig CA algorithm Lemma- Let h be a alid height function hen hu ( ) i a lower bound on the ditance from u to t in N ( ζ ) heorem-3he CA algorithm i finite terminate with the imum -t flow Proof he algorithm i finite becaue the height alue can increae at mot V time each he algorithm end with a flow f = ζ becaue if there were any actie node, the algorithm would not end At the end, h () = V Since h () i a lower bound on the hortet t path in N ( f ), there i no tpath in N( f ) hen there i no t admiible path in N ( f) the flow i imized 3 heorem-4he time complexity of CA i OV ( ) for N = ( V, A, p, X, t) 4 Ditributed Algorithm In thi ection, we propoe an aynchronouly ditributed algorithm DA baed on CA he baic idea i introduced by [1] he difference i that our approach can ole the imum flow problem in multi-ource network with capacity contraint on ertice We aume that each node in the network execute a ditributed program aynchronouly Each link i bidirectional All procee are eent-drien work on local data Communication are meage baed We aume that any ource node know the number of ource X he execution of algorithm alo proceed in two phae he firt phae et height of all node he econd phae etablihe the imum flow Different from the centralized algorithm preented in ection 3, a reidual arc ( u, ) i admiible for node u if hu ( ) h ( ) 1 Additionally, in lift proce, we increae a node height to a alue which i jut enough for it to puh all it exce out Conider a SenorNet N = ( V, A, p, X, t) We regard a node V a two irtual node i called In-node i called Out-node hey are connected to the neighbor of node by incoming arc outgoing arc repectiely At each node, the program maintain the following information 1 Adj () = Adj ( ) U Adj ( ) i the neighbor et, Adj( ) = u ( u, ) A where } Adj( ) = u (, u) A} h± ( ) i the height of ± 3 ex( ± ) i the exce of ± 4 h ± i u height from the point of iew of ± 5 ty() i the node type 6 c± i the reidual capacity of arc (, u ) or (, u ) Epecially c () = p() at the beginning If i a ource, it ha to maintain following information about the irtual ource 1 InitOk denote if all ource are initialized already

4 IJCSNS International Journal of Computer Science Network Security, VOL6 No8A, Augut 6 11 h () c () for 3 ex( ) h ( ) 4 h c for all u V he algorithm terminate at any of two ituation he firt i when all node are inactie hi mean there are no more meage will be exchanged he econd i when a ource puhe it exce back to the irtual ource hi mean the ource cannot tranmit wdata to the ink A to BS algorithm, i larger than the imum flow more computation i uele herefore, we terminate the algorithm he detail of DA are decribed a follow MainOnNode( ) 1 Initialization( ) while (1) 3 wait for incoming mg 4 proce mg 5 }//while Fig3 MainOnNode Initialization( ) 1 ex( ) ex( ) h ( ), h ( ) h ( ), h ( ) 3 for all u Adj( ) 4 c M 1 5 for all u Adj( ) 6 c ( u ) 7 c ( ) p( ) c ( ) 8 h ( u ), h for allu V 9 if ty( )= Source 1 InitOk 11 Adj( ) Adj( ) U } 1 h ( ) c ( ) 13 ex( ) h ( ) 14 h ( u ), c for allu V 15 }//if 16 if ty( )= Sink 17 h ( ) 18 InitHight( ) 19 }//if Fig4 Initialization InitHight( ) 1 for all u Adj( ) Send(NEW-HEIGH, h ( )) to u 3 for all u Adj( ) 4 Send(INI-HEIGH, h ( ) ) to u 5 if ty( )= Source 6 ex( ) w ( ) 7 c ( ) w( ) 1 M i a poitie real number that i large enough 8 Broadcat(ADD-SOURCE, h ( ) )to all 9 ReAS( h, ( ), ) 1 }//if Fig5 InitHight //when receie(new-heigh, h )fromw ReNH( hw),, 1 if w Adj( ) h ( w) h 3 if w Adj( ) 4 h ( w) h Fig6 ReNH //when receie(ini-heigh, h )fromw ReIH( hw),, 1 ReNH( hw),, if ( h ( ) = h ( ) > h 1) 3 h ( ), h ( ) h 1 h ( ), h ( ) h 4 InitHight( ) Fig7 ReIH //when receie(add-source, h )fromw ReAS( hw),, 1 if ty( )= Source InitOk InitOk 1 3 h ( w) h 4 if InitOk = X 5 h ( ) V 6 h ( ) V 7 PuhLiftIn(,,) 8 }//if 9 }//if Fig8 ReAS PuhLiftIn(,w, Δ ) 1 c ( w) c ( w ) Δ ex( ) ex( ) Δ while ( u t c > h( ) > h ( u )) ex( ) > 3 min ( ), ( )} Δ ex c u 4 ex( ) ex( ) Δ c c( u ) Δ 5 if u= 6 PuhLiftOut(,, Δ ) 7 ele 8 Send(PUSH-REQUES, Δ )tou 9 }//while 1 if ex( ) > 11 min ( ) ( ) uc ( ) ( ) } u > h u < h h h c u ex 1 h ( ), h ( ) h

5 1 IJCSNS International Journal of Computer Science Network Security, VOL6 No8A, Augut 6 13 if( ty( ) = Source h( ) > h ( )) 14 terminate 15 for all u Adj( ) 16 Send(NEW-HEIGH, h ( ) ) to u 17 }//for 18 PuhLiftIn(,,) 19 }//if Fig9 PuhLiftIn PuhLiftOut(,w, Δ ) 1 c ( w) c ( w ) Δ ex( ) ex( ) Δ while ( u t c > h( ) > h ( u )) ex( ) > 3 min ( ), ( )} Δ ex c u 4 ex( ) ex( ) Δ c c ( u ) Δ 5 if u= 6 PuhLiftIn(,, Δ ) 7 ele 8 Send(PUSH-REQUES, Δ )tou 9 }//while 1 if ex( ) > 11 min ( ( ) ( ) uc ( ) ( ) ) u > h u < h h h c u ex 1 h ( ), h ( ) h 13 for all u Adj( ) 14 Send(NEW-HEIGH, h ( ))to u 15 PuhLiftOut(,,) 16 }//if Fig1 PuhLiftOut //when receie(push-reques, Δ )fromw RePR(, Δ, w ) 1 if w Adj( ) h ( w ) > h( ) if ty( ) Sink 3 PuhLiftIn(,w, Δ ) 4 ele 5 c( w) c( w ) Δ 6 ex( ) ex( ) Δ 7 }//ele 8 }ele if w Adj( ) h ( w ) > h( ) 9 PuhLiftOut(,w, Δ ) 1 ele 11 Send(PUSH-DENY, Δ )to w Fig11 RePR //when receie(push-deny, Δ )fromw RePD(, Δ, w ) 1 if w Adj( ) c( w) c( w ) Δ 3 ex( ) ex( ) Δ 4 PuhLiftIn(,,) 5 }ele 6 c ( w) c ( w ) Δ 7 ex( ) ex( ) Δ 8 PuhLiftOut(,,) 9 }//ele Fig1 RePD he time complexity of DA i OV ( ) he meage complexity of DA i OV ( A) 5 Concluion In thi paper, we formulate the lifetime imization problem of enor network a a flow problem on a tranportation network with power on ertice arc With BS algorithm, we can achiee imum lifetime routing of a enor network in any preciion if only we can find the flow on uch a tranportation network After propoe a centralized algorithm with time complexity 3 of OV ( ), we propoe an aynchronouly ditributed algorithm with time complexity of OV ( ) meage complexity of DA i OV ( A) Reference [1] M Bhardwaj, A Chrakaan, Garnett, Upper Bound on the Lifetime of Senor Network, IEEE International Conference on Communication, Helinki, Finl, June 1 [] M Bhardwaj, A Chrakaan, Bounding the Lifetime of Senor Network Via Optimal Role Aignment, IEEE INFOCOM [3] E J Duarte-Melo, M Liu, A Mira, A Modeling Framework for Computing Lifetime Information Capacity in Wirele Senor Network, Modeling Optimization in Mobile, Ad Hoc Wirele Network, Cambridge, UK, March 4 [4] Viek Rai, Rabi N Mahapatra, Lifetime Modeling of a Senor Network, Deign, Automation et in Europe, Munich, Germany, March 5 [5] J H Chang, L aiula, Energy conering routing in wirele ad-hoc network, IEEE INFOCOM [6] K Dagupta, K Kalpaki, P Namjohi, Efficient Algorithm for Maximum Lifetime Data Gathering Aggregation in Wirele Senor Network, Computer Network, ol 4, 3 [7] Sankar, Z Liu, Maximum Lifetime Routing in Wirele Ad-hoc Network, INFOCOM 4 [8] R Madan, S Lall, Ditributed Algorithm for Maximum Lifetime Routing in Wirele Senor Net-work, Global elecommunication Conference, IEEE, olume, No 4 [9] Andrew V Goldberg Robert E arjan, A New Approach to the Maximum Flow Problem, Journal of ACM, 35(4):91-94, 1988 [1] L Pham, M Bui, I Laallae, S H Do, A Ditributed Preflow-Puh for the Maximum Flow Problem, Innoatie Internet Community Sytem, 5th International Workhop, IICS 5, Pari, France, June, 5