Time-Sensitive Utility-Based Routing in Duty-Cycle Wireless Sensor Networks with Unreliable Links

Transcription

1 Time-Senitive Utility-Bae Routing in Duty-Cycle Wirele Senor Network with Unreliable Link Mingjun Xiao, Jie Wu, an Liuheng Huang School of Computer Science an Technology, Univerity of Science an Technology of China, Hefei, P. R. China Department of Computer Information an Science, Temple Univerity, Philaelphia, PA 9, USA Suzhou Intitute for Avance Stuy, Univerity of Science an Technology of China, Hefei, P. R. China {xiaomj, Abtract Utility-bae routing i a pecial routing approach, which take the reliability an tranmiion cot into account at the ame time. However, the exiting utility-bae routing algorithm have not yet coniere the elivery elay. Thu, they cannot work well in uty-cycle wirele enor network (WSN) ince elay i an important factor in uch WSN. In thi paper, we propoe a novel utility moel time-enitive utility moel. Unlike previou work, the utility of a meage elivery in our moel i not only affecte by the reliability an tranmiion cot but alo by the elivery elay. Uner the time-enitive utility moel, we erive an iterative formula to compute the time-varying utility of each meage elivery. Bae on the formula, we propoe an optimal time-enitive utility-bae routing algorithm, which i alo extene to the cae where retranmiion i allowe. The theoretical analyi an imulation reult how that our propoe algorithm can maximize the average utility of meage eliverie, which make a goo traeoff among reliability, elay, an cot. Inex Term Ditribute algorithm, uty-cycle wirele enor network, reliability, routing, time-enitive utility. I. INTRODUCTION Utility-bae routing in wirele network i a pecial routing approach bae on a compoite utility metric [], []. The utility i in term of the benefit (i.e., a rewar for the routing ource elivering a meage to the etination) minu the expecte cot incurre by meage elivery. Unlike wire connection, wirele connection are unreliable ue to interference an coverage iue. With utility-bae routing, the more valuable meage will be elivere through a more reliable route at the expene of a higher energy cot in tranmiion [], which remain a common phenomenon in wirele communication. Thi phenomenon reflect a traeoff between a highly reliable route (which i uually more cotly) an a le reliable route (which i uually le cotly) bae on the value of the meage. A imple analogy that relate to utility-bae routing i the potal ervice: a highvalue package (e.g., one that contain a paport for a via application) uually ue regitere mail for reliability at a higher premium cot. An orinary package i uually maile through a regular ervice. In thi paper, we focu on utility-bae routing in uty-cycle wirele enor network (WSN), in which enor perioically cheule themelve to be active for work an then tay ormant at other time to reuce the energy conumption [3] [7]. Compare with traitional WSN, meage elivery in uty-cycle WSN ha a non-negligible elay ince it ha to.8,5,.5,5, 4,,.8,5,.5,5, 4 benefit 5-t -t - 3.t path Fig.. An example of time-enitive utility-bae routing on a weighte graph. The ege weight of the graph i reliability, elay, cot. There are three meage with a linearly ecreae benefit over time t. Utility-bae routing trie to achieve the maximum utility, i.e., benefit minu cot. A a reult, it woul let the three meage be elivere along ifferent path. Their utility value are calculate in Section III-A an are lite in Fig. 5. wait for a certain amount of time until the meage receiver become active [6]. The elivery elay i thu an important factor for the routing eign. However, it ha not been aopte into the current utility-bae routing metric. In orer to take the elivery elay into account, we introuce time into the utility moel an propoe a Time-enitive Utility-bae Routing () algorithm for uty-cycle WSN. The benefit of a meage in thi algorithm linearly ecreae with the elivery time. The utility i till efine a the benefit minu the expecte cot. Since the benefit i time-relate, the elivery elay i inirectly ae into the utility moel. A a reult, the algorithm make a trae-off among reliability, elay, an cot. It allow reliability-concerne meage, elay-concerne meage, an cot-concerne meage to be elivere along ifferent path a hown in the example of Fig.. More pecifically, our major contribution inclue: ) We exten the utility moel into uty-cycle WSN an propoe a time-enitive utility moel. Compare with the exiting utility moel, the time-enitive utility imultaneouly take reliability, elay, an cot into account. A a reult, utility-bae routing in thi moel can make a trae-off among the three factor. ) We propoe an optimal time-enitive utility-bae routing algorithm. In thi algorithm, we firt preent a pecial iterative formula to compute the expecte utility of a given meage elivery. From the iterative formula, we eign a backwar erivation algorithm to etermine the optimal elivery path. The algorithm i a ingle-copy algorithm without retranmiion at each hop. To the bet of our knowlege, it i the firt utilitybae routing algorithm that conier the elivery elay.

2 3) We alo exten the algorithm to cover the cae where retranmiion i allowe. We conier two cae: the retranmiion occur within the ame uty-cycle or at ifferent uty-cycle. For both cae, we preent the optimal olution. 4) We have conucte extenive imulation to evaluate the algorithm. The reult prove that the algorithm can achieve the better expecte utility compare to other algorithm. Meanwhile, the reult alo how that the propoe cheme can make a goo balance among reliability, elay, an cot. The remainer of the paper i organize a follow. We introuce the uty-cycle WSN, the time-enitive utility moel, an the problem of utility-bae routing in Section II. The algorithm i propoe in Section III an i extene in Section IV. In Section V, we evaluate the performance of our algorithm through extenive imulation. After reviewing relate work in Section VI, we conclue the paper in Section VII. All proof are preente in the Appenix. A. Network Moel II. NETWORK MODEL & PROBLEM We focu on the tatic uty-cycle WSN. Each enor only ha two poible working tate: the active tate, in which the enor can perform all the function of ening, litening, tranmitting, an receiving; an the ormant tate, in which the enor turn off all the functional moule except for a wake-up timer. Specifically, when a ormant enor wake up, it either witche to the active tate, or tranmit packet an then witche back to the ormant tate. In other wor, a enor can tranmit a packet at any time but can receive a packet only when it i active. Before the concrete network moel, we firt preent everal baic aumption: ) Time i ivie into equal-length time lot, an the whole network i looely ynchronize. The ynchronization can be achieve through exiting approache, e.g., FTSP [8]. In general, the time ynchronization error can be ignore compare with a time lot [6]. ) Each enor cheule it working tate cyclically. For implicity, we aume that all enor hare a common utycycle an each enor tay active at only one fixe time lot uring each uty-cycle, which i name by the active time lot of the enor. Thi aumption i reaonable. If enor have ifferent uty-cycle, the common uty-cycle can be et a their leat common multiple. If a enor ha multiple active time lot within a uty-cycle, we can replace thi noe by everal virtual noe, each of which only ha one active time lot in a uty-cycle. 3) The wirele communication link are unreliable, an the CSMA/CA mechanim i aopte to cope with the exitence of colliion. Previou reearch how that the link quality change very lowly over time [9]. Therefore, the average ucceful tranmiion probability erive from hitory recor i aopte to evaluate the link reliability. Bae on the above aumption, we conier a uty-cycle WSN that i compoe of a et of enor noe, enote by p =.5 c= i j T=3 i T=6 j (a) the initial WSN i,3,,3, i.5,4,.5,, i p =.5 c= p = t i, j j c= c= T=6 i p =.5.5,,.5,5, (b) the implifie WSN (c) the weighte graph (ege weight: p, t, c ) Fig.. Example: uty-cycle WSN moeling. V. The common uty-cycle i T. For each pair of neighboring enor, i an j (i, j V ), there i a ucceful tranmiion probability p i,j. Their active time lot are a i an a j (a i, a j [, T ]), repectively. Note that noe i get a meage only at the time lot a i. If it want to en the meage to noe j, it mut leep until noe j become active at the time lot a j. The tranmiion elay can be ignore ince it i much le than the elay incurre by the leep. Thu, the meage elivery elay from noe i to noe j i t i,j =(a j a i ) mo T. Beie, the tranmiion cot from noe i to noe j i enote by c i,j. Then, we can moel the uty-cycle WSN a a irect weighte graph G= V, W, where W ={ p i,j, t i,j, c i,j i, j V }. Fig. how an example of uty-cycle WSN moeling. Fig. (a) i an initial uty-cycle WSN compoe of two enor i an j, whoe uty-cycle are 3 an 6 time lot, an whoe active time lot are an 5, repectively. In Fig. (b), we utilize two virtual enor, i an i, to replace enor i. Then, the initial network i implifie to be a uty-cycle network, in which there i only one common uty-cycle, an each noe only ha one active time lot. After computing the elivery elay of neighboring noe accoring to their active time lot, we contruct the correponing irect weighte graph, a hown Fig. (c). In fact, any uty-cycle WSN can be converte to a irect weighte graph in thi way. B. Problem In thi paper, we only tuy ingle-copy non-ack routing an propoe a time-enitive utility moel. Unlike the previou utility moel, the time-enitive utility moel aign a timeenitive benefit an a utility to a meage elivery from an arbitrary ource to a etination. Thi utility metric take elivery elay, elivery cot, an reliability into account. Coniering a meage elivery from a ource to a etination, we preent the baic concept of benefit an utility a follow. Definition : The benefit of a meage, enote a b(t), refer to a linearly ecreaing rewar over time t if it i uccefully elivere to it etination; otherwie, zero rewar i returne. Let the initial benefit be β, an let the ecreae benefit in each time lot be name by benefit ecay coefficient j

3 b b = u ( ) b b = b expecte value i b i c i j t ucceful Fig. 3. u u t j c faile An example of time-enitive utility moel. an enote by δ, then the benefit atifie: { β t δ, ucceful elivery; b(t)=, faile elivery. Here, time t i the living time of the meage. A new generate meage (t = ) ha it maximum benefit value. Along with the meage elivery, the benefit woul linearly ecreae ue to the elape time. If the meage elivery fail, the benefit woul become zero. Thu, the concept of benefit take into account both the elivery elay an the ucceful elivery probability. Definition : The utility of a meage elivery, enote by u, i the benefit minu the total tranmiion cot of the meage elivery, which mean the gain of the meage elivery. Let the total tranmiion cot be c, then the utility atifie: u=b(t) c. () If the meage i uccefully elivere to the etination with the elay t,, the utility woul be b(t, ) c; otherwie if it fail, the utility woul be c. The utility value i affecte by the elivery elay, the path reliability, an the tranmiion cot. For example, for the elivery from to of the firt meage in Fig., the benefit i 5 t, = 45 an the utility i 45 for the ucceful elivery. The benefit i an the utility i for the faile elivery. The expecte value of utilitie for the two elivery cae i.8(45 )+.( ) = 6. The above concept b, u, an c are relate to the meage elivery from to. In aition, for implicity of ecription, we alo efine two notion for each noe: the remaining benefit of a noe an the expecte utility of a noe. Conier an arbitrary noe i in the elivery path from to, the remaining benefit an expecte utility of noe i are efine a follow. Definition 3: The remaining benefit of noe i, enote by b i, refer to the remaining benefit value when the meage arrive at noe i. That i: i () b i =β δ t,i. (3) Definition 4: The expecte utility of noe i, enote by u i (b), i the expecte utility for a meage elivery from noe i to the etination, in which the remaining benefit of the meage i b when it arrive at (or i generate by) noe i. Note that b i an u i (b) are the value from the point of view of noe i, i.e., the cae when noe i i the current meage forwarer. Moreover, u i (b) i an expecte value. Thi i becaue the meage elivery from noe i to the etination i uncertain. It might uccee or fail at ifferent hop. There are multiple poible reult. For each reult, there i a probability an a final utility value. u i (b) i the expecte value of thee final utility value. Note that u i (b) i a function of b. Thi mean that u i (b) can be erive only when b i given in avance. Fig. 3 how an example for the concept, in which the benefit linearly ecreae along time or become zero ue to a faile elivery. b i i the remaining benefit of noe i. c i the tranmiion cot. There i a utility u for each meage elivery no matter if it uccee or fail. The expecte utility of ource noe u (β) i the expecte value of u. With the baic efinition of benefit an utility, we can preent our problem of utility-bae routing a follow: given a uty-cycle network G= V, W, a ecribe in Section II-A, a ource noe, a etination noe, an initial benefit β, an a benefit ecay coefficient δ, then our objective i to maximize the expecte value of utility u for the meage elivery from to. Since thi expecte value i exactly equal to the expecte utility u (β), our objective become to maximize u (β). III. SOLUTION: THE ALGORITHM In thi ection, we conier the utility-bae routing problem for a non-retranmiion meage elivery from an arbitrary ource noe to a etination noe with an initial benefit β an a benefit ecay coefficient δ. We propoe an optimal Time-enitive Utility-bae Routing () algorithm, where the maximum expecte utility u (β) can be achieve. The key part of the algorithm i to fin an optimal elivery path in the initial phae. We firt preent an iterative formula, by which each noe can compute it own optimal expecte utility value when it know the optimal expecte utility value of the neighboring noe. Then, we eign a backwar erivation algorithm to calculate the optimal expecte utility value of each noe. Accoringly, the optimal elivery path i alo etermine. The routing phae of the algorithm jut let meage be elivere along their optimal path. Since the routing phae i traightforwar, we only focu on the proce of computing the expecte utility value of noe an fining the optimal elivery path in the following part. A. The Baic Formula We firt conier an arbitrary elivery path from noe to noe an erive a formula to compute the expecte utility value. Without the lo of generality, we let the path be = =n. Then, the expecte utility of the meage elivery from to i u (β)=u (β). Aume that all ege weight in the path, incluing the ucceful tranmiion probability, the elivery elay, an the tranmiion cot, are known. By computing the probability an utility value for each poible elivery cae, we can the get the formula. More pecifically, we have the following theorem. Theorem : The expecte utility value for the meage elivery with an initial benefit β an a benefit ecay coefficient δ along a given path = =n atifie: u (β)= p i,i+ (β δ t i,i+ ) c i,i+ i p j,j+. (4) j=

4 .8,5,.8,5, benefit =5, = irectly computation u =.8 b =5, b =45, b = iteratively u (b ) = b = computation u (b ) =p, u (b ) c, =.8 u (b ) =p u (b ) c, =.8, Fig. 4. An example of the expecte utility computation. The ege weight of the graph i reliability, elay, cot. The irect computation an the iterative computation achieve the ame reult. Now we erive an iterative formula which can be ue to locally compute the expecte utility value. Conier two arbitrary ajacent noe i an j = i + ( i n ) in the elivery path = n = n. Note that their expecte utilitie u i (b) an u j (b) actually are two function about the remaining benefit b. For mot of the function value, e.g., u i (β) an u j (β), there i not a local iterative relationhip between them. Even if the value of u j (β) an the link information between i an j are known, there i no formula that we can ue to erive the value u i (β). Fortunately, we fin that for a pairwie pecial remaining benefit b i an b j, there i a local relationhip between u i (b i ) an u j (b i ), a hown in the following theorem. Theorem : The expecte utilitie of two neighboring noe i an j atify: u i (b i )=p i,j u j (b j ) c i,j. (5) Eq. 5 i an iterative formula, by which each noe i can erive it own expecte utility from the expecte utility value of it next-hop neighbor noe. Thu, once we know the value of u (b ), we can ue Eq. 5 to iteratively erive the value of u (β) = u (b ), which woul achieve the ame reult a the irect computation accoring to Eq. 4. Fig. 4 how a imple example to compute the expecte utility of the elivery path in Fig. through the two metho. Thee reult emontrate that the irect computation an the iterative computation achieve the ame reult. We alo compute the expecte utility value of all elivery path in Fig. an lit them in Fig. 5. Thee reult prove that the meage with variou benefit woul have ifferent optimal elivery path. Moreover, we have u i (b i )<u j (b j ) accoring to Eq. 5. Thi mean that the expecte utility value of noe woul increae along with a meage elivery path. The etination noe ha the maximum expecte utility value in the elivery path. B. The Baic Iea Once we have the iterative formula about the expecte utility, we can erive the expecte utility value of noe by applying a backwar erivation algorithm. The expecte utility of the etination noe i firt calculate. Thi expecte utility i ue a a ee to iteratively compute the expecte utility value of it neighbor through Eq. 5. Then, the expecte utility of next noe i calculate in the ame way, an o on, benefit path 5-t -t 3-.t Fig. 5. The expecte utility value of each elivery path in Fig.. until the expecte utility value of all noe are etermine. Accoringly, the relate optimal elivery path woul be foun uring thi iterative computation proce. However, there i a problem with thi metho. That i, the ee of the iterative computation proce, i.e., the expecte utility of etination u (b ), cannot be irectly etermine. Accoring to our efinition, the expecte utility u (b ) i not a imple value but a function of the remaining benefit b. It can be calculate only when b i known. The remaining benefit b can be compute only when the elivery elay i etermine. However, the elivery elay cannot be calculate ince we o not know the meage elivery path. A imilar problem alo exit in the mile of the computation proce. For example, when we want to compute an expecte utility u i (b i ) through Eq. 5, we nee to know the remaining benefit b i. However, b i can be etermine only when the optimal elivery path from ource to noe i i known. To overcome the above problem, we exten the iterative computation of a ingle-point expecte utility to the computation of the whole expecte utility function for each noe. Thi i feaible becaue the expecte utility function i icrete an the range of the function parameter (i.e., the poible value of the remaining benefit) i limite. Note that the maximum remaining benefit value in the whole network i the initial benefit β. The minimum an the maximum elivery elay between pairwie neighboring noe are one time lot an T time lot, repectively. The ifference of remaining benefit value of pairwie neighboring noe thu only might be {δ, δ,, (T )δ}. Moreover, each meage elivery path ha at mot ( V ) hop. Therefore, the remaining benefit value of each noe only might be {β ( V )(T )δ,, β δ, β}, enote by Φ. Here we point out that the ize of the remaining benefit et Φ i not a large value ince the uty-cycle T in a uty-cycle WSN i generally much le than the number of noe V in orer to provie a vali ervice. Bae on thi iea, our olution i preente a follow. At the beginning, the etination noe calculate the expecte utility value u (b) for each poible remaining benefit b Φ. Then, it tart the Φ parallele backwar erivation computation procee by taking thee expecte utility value a the ee. Each noe ue Eq. 5 to etermine it maximum expecte utility value an puhe the backwar computation proce until the ource noe get the expecte utility value. Accoringly, the optimal elivery path alo woul be recore. Note that the Φ parallele backwar erivation computation procee are not inepenent of each other. The backwar erivation computation with a large-b ee will require the computation reult with a low-b ee.

5 Algorithm The Centralize Algorithm Require: G= V, W={ p i,j, t i,j, c i,j i, j V }, ( V ), Φ, δ. Enure: u i (b), path i (b) (i V, b Φ). : for each b Φ (in the acening orer) o : u (b)=b, u i( ) (b)=, Q= ; 3: while V Q o 4: Fin the noe i with the larget u i (b) from V Q; 5: if u i (b)= then 6: Break; 7: Q=Q {i}; 8: for each neighbor j of noe i o 9: Compute the new utility u j (b) uing Eq. 5; : if u j (b) < u j (b) then : u j (b)=u j (b), path j(b)=i ; Algorithm The Ditribute Algorithm Require: G= V, W={ p i,j, t i,j, c i,j i, j V }, ( V ), Φ, δ. Enure: u i (b), path i (b) (i V, b Φ). : for each noe i o : Initialize: u i(=) (b) = b, u i( ) (b) = ( b Φ); 3: for each time lot in T o 4: if noe i i active then 5: Receive new expecte utilitie from neighbor; 6: Compute new u i (b) ( b Φ) uing Eq. 5; 7: if u i (b) < u i (b) ( b Φ) then 8: u i (b)=u i (b); 9: Determine path i (b) accoring to u i (b); : if neighbor j i active then : Sen new expecte utility to noe j; C. The Detaile Algorithm With regar to our olution, we firt preent a centralize algorithm (Algorithm ), an then we alo give a itribute verion of thi algorithm (Algorithm ). The centralize algorithm (Algorithm ) aume that the ource noe ha collecte the reliability, elivery elay, an tranmiion cot of the whole network an ha contructe a weighte irecte graph. Bae on thi graph, the centralize algorithm firt compute the expecte utility value of all the noe for the minimum remaining benefit in Φ. Then, it increae the remaining benefit an compute the expecte utility value for the new remaining benefit in Φ tep-bytep, a hown in Step. For each remaining benefit b, the correponing expecte utility value can be calculate ince they only epen on the expecte utility value which have been compute before. Step - give the baic proce of the backwar erivation computation. Step make an initialization. Step 4-7 exten the et of noe whoe optimal expecte utility value have been etermine. Step 9- etermine the optimal expecte utility value. In Step 5, if u i (b)=, we top the current computation ince the meage elivery cannot achieve a poitive utility. Beie, each noe i recor it optimal next hop in path i (b) for each remaining benefit b. The correctne of thi algorithm i traightforwar. The backwar iterative computation cheme an Eq. 5 can enure the optimality of our algorithm. Moreover, the computational overhea i only O( Φ V )=O(T V 3 ). Algorithm i a itribute olution. Each noe in thi algorithm initialize in Step, an then continuouly upate it expecte utility value when it become active (Step 4-9) until the algorithm converge. More pecifically, the noe firt receive the new expecte utility value from it neighboring noe in Step 5. Then, it compute it own new expecte utility value accoring to Eq. 5 in Step 6-9, an it meanwhile etermine the optimal elivery path. When it neighboring noe become active, it alo woul notify them of it new optimal expecte utility value (Step -). Compare to the centralize algorithm, the itribute algo- rithm aopt a imilar proce to compute the expecte utility value of each noe, but remove the cheuling orer of thee expecte utility value being calculate. Note that the expecte utility value of noe woul trictly increae along with a meage elivery path. Moreover, each expecte utility can be compute only when the expecte utility relate to a maller remaining benefit i compute before. Thee woul enure that the whole computation woul not lea to a loop. All of the expecte utility value woul be automatically calculate in equence ue to their epenent relationhip. Thi enure the correctne an convergence of the algorithm. Moreover, in each roun of computation, i.e., a uty-cycle T, at leat one optimal expecte utility value can be etermine. For each remaining benefit b, the maximum expecte utility value i firt etermine. Then, the econ maximum expecte utility value i etermine in the next roun of computation, an o on. The whole algorithm will converge by at mot O( Φ V )=O(T V ) roun of computation. In each roun of computation, each noe woul receive at mot Φ( V ) expecte utility value from it neighboring noe. Thu, the computational overhea i O( Φ V )=O(T V ). In both algorithm, we have actually calculate all poible expecte utility value. In fact, many of them are uele. Thu, we can remove thee uele computation to reuce the overhea. Thi can be realize by a flooing operation. When the ource noe publihe an initial benefit value β to the network, each noe i erive an recor it remaining benefit b i that might be ue. After thi proce, we only nee to compute the expecte utility relate to thee recore remaining benefit value when we ue the algorithm. A a reult, many uele expecte utility value woul not be calculate. Fig. 6 how the proce of computing the expecte utility of noe in Fig. through Algorithm. In Fig. 6(a), the ource publihe the initial benefit value β, an each noe recor the remaining benefit that might be ue in the following tep. In Fig. 6(b)-6(f), we compute the expecte utility value of all noe by increaing the remaining benefit tep-by-tep. The expecte utility for the remaining benefit b=3 i firt calculate, which i ue to compute the expecte utility for b=35. If there are multiple expecte utility

6 meage =5 = u(5)=?.8,5,.5,5,4 u(35)=? u(45)=?,,.8,5, u(35)=? u(45)=?.5,5,4 u(3)=? u()=? u(5)=? u(35)=? u(45)=? u(35)=? u(45)=? u(3)=3 u()=? u(5)=? u(35)= p, u(3) -c, u(35)=4 u(45)=? u(35)= u(45)=? u(35)= p, u(3) -c, u(3)=3 u()=? (a) publih β, δ (b) compute u(b=3) (c) compute u(b=35) u(35)=4 u(45)=? u(35)=4 u(45)= u(45)= p, u() -c, > u(45)= p, u(35) -c, u(35)=4 u(45)= u(5)=? u(35)= u(45)=? u(3)=3 u()= u(5)=? u(45)= p, u(35) -c, < u(45)= p, u() -c, u(35)= u(45)=6 u(3)=3 u()= u(5)=7.6 u(5)= p, u(45) -c, > u(5)= p, u(45) -c, u(35)= u(45)=6 u(3)=3 u()= () compute u(b=) (e) compute u(b=45) (f) compute u(b=5) Fig. 6. Example: computing the expecte utility of noe in Fig. for the meage elivery with benefit 5 t. value incurre by multiple path, the larget one i electe, a hown in Fig. 6(e) an 6(f). The example, which only contain five roun of computation, how that our algorithm i efficient. IV. EXTENSIONS In thi ection, we exten the algorithm from the cae of non-retranmiion to the cae with retranmiion. We conier two retranmiion cae. One involve the retranmiion occurring within the ame active time lot when a time lot i et to be large enough. Another i that the retranmiion occur at ifferent uty-cycle when a time lot i et to be a mall time interval. For both cae, we preent the optimal olution. If the retranmiion occur within the ame active time lot, it woul improve the ucceful elivery probability an alo increae the tranmiion cot, but it woul not reult in an increae elivery elay. Conier an arbitrary noe i an it next-hop noe j. After k-time retranmiion, the correponing ucceful elivery probability become ( p i,j ) k, an the tranmiion cot become kc i,j. Thu, the iterative formula about the expecte utility for the k-time retranmiion atifie: u i (b i ) k =[ ( p i,j ) k ]u j (b j ) kc i,j. (6) Accoring to Eq. 6, we can fin an optimal retranmiion time ˆk to maximize the expecte utility value u i (b i ). More pecifically, we have the following theorem. Theorem 3: The optimal retranmiion time ˆk for the meage elivery from noe i an it next-hop noe j atifie: ˆk = ln c i,j ln p i,j u j (b j ) ln( p i,j ) or ln c i,j ln p i,j u j (b j ). (7) ln( p i,j ) If the retranmiion occur at ifferent uty-cycle, it woul not only increae the ucceful elivery probability an the tranmiion cot, but alo woul reult in an increae elivery elay. An h-time retranmiion woul lea to a elivery elay ht. Accoringly, the remaining benefit of noe j woul be ecreae by δht. Thu, the iterative formula about the expecte utility for the h-time retranmiion become: u i (b i ) h =[ ( p i,j ) h ]u j (b j δht ) hc i,j. (8) Obviouly, the optimal retranmiion number ĥ for thi cae mut be le than ˆk ue to u j (b j δht ) < u j (b j ). Thu, we have ĥ [, ˆk]. Then, teting all poible h [, ˆk] to maximize u i (b i ) h by uing Eq. 8, we can obtain the optimal retranmiion number ĥ. Note that uner any circumtance, the optimal number of retranmiion can be etermine locally once the expecte utility value of the next hop noe i given. Therefore, it can be irectly embee into incluing both centralize an itribute algorithm. A a reult, the optimal number of retranmiion of all noe can be etermine. V. PERFORMANCE EVALUATION In thi ection, we conuct extenive imulation to evaluate the performance of our propoe algorithm, incluing an it extene verion with the concern of retranmiion, which i enote by -R. Beie an -R, we alo implement three other algorithm to compare with. The compare algorithm, the evaluation metho, etting, an reult are preente a follow. A. Algorithm in Comparion Since our propoe algorithm are the firt utility-bae routing algorithm eigne for uty-cycle WSN, to the bet of our knowlege, there are no exiting algorithm that we can compare with. Thu, accoring to the metric what we are concerne with, we carefully eign an implement three other algorithm:,, an. i a hortet-path-bae algorithm, in which each noe exploit the Dijktra algorithm to etermine the hortet path w.r.t. elay, an then it let meage be elivere along

7 5 3 -R 3 -R 3 -R 6 (a) Number of noe: V = 6 (b) Number of noe: V = 6 Fig. 7. Performance comparion of utility v. initial benefit. 6 -R 6 -R -R (a) Number of noe: V = (b) Number of noe: V = Fig. 8. Performance comparion of utility v. benefit ecay coefficient (a) Number of noe: V = (b) Number of noe: V = Fig. 9. The relationhip of utility v. initial benefit an benefit ecay coefficient. TABLE I EVALUATION SETTINGS. Parameter name Default value Range Deployment area S m m - Number of noe V - -6 Tranmiion raiu.5 S/ V m - Tranmiion probability Tranmiion cot - - Scheuling cycle - Initial benefit - Benefit ecay coefficient..-. Number of meage, - their hortet path. let meage be elivere along the path which have the larget ucceful elivery probabilitie. eliver meage along the path with the mallet expecte elivery cot. Both the path with the larget elivery ratio an the path with the minimum elivery cot are alo etermine by the Dijktra algorithm. B. Simulation Setting an Metric In the imulation, we eploy V enor noe in a m m quare area. More pecifically, we ivie the whole quare area into V equivalent mall quare lattice, an then let each noe be eploye at a ranom poition in a lattice. The tranmiion moel of enor noe i the traitional ik moel. That i, each pair of enor noe can communicate with each other only when their itance i le than a given tranmiion raiu. We let all enor noe hare a common tranmiion raiu an et the raiu to be.5 (> + ) time of the ie length of the mall quare lattice. A a reult, the enor noe in the neighboring lattice mut be within the tranmiion raiu an thu can communicate with each other. In thi way, the V enor noe are ranomly an uniformly eploye in the whole quare area while enuring that the whole network i fully connecte. Next, we let all of the enor noe hare a common utycycle an et the cycle to be time lot. Each noe become active only at one time lot in each cycle. The active time lot i ranomly electe while enuring that it i ifferent from the neighboring noe. Each pair of neighboring noe ha aociate with a ucceful tranmiion probability an cot, which are ranomly electe from [.3,.9] an [, ], repectively. In aition, the initial benefit an the benefit ecay coefficient are electe from [, ] an [.,.], repectively. All of the evaluation variable are hown in Table I. The major metric in our imulation i the average utility, which i the average value of utilitie of all meage eliverie. In orer to emontrate that our utility-bae algorithm make a goo traeoff among reliability, elay, an cot, we alo compare the average elivery elay, elivery ratio, an aver-

8 Average Delivery Delay 6 6 (a) Number of noe: V = -R Average Delivery Delay 6 (b) Number of noe: V = -R Average Delivery Delay 6 -R Fig.. Performance comparion of elivery elay v. initial benefit. Average Delivery Delay -R Average Delivery Delay -R Average Delivery Delay -R (a) Number of noe: V = (b) Number of noe: V = Fig.. Performance comparion of elivery elay v. benefit ecay coefficient R.6. -R.3.. -R. 6 (a) Number of noe: V =. 6 (b) Number of noe: V =. 6 Fig.. Performance comparion of elivery ratio v. initial benefit...8 -R R R. (a) Number of noe: V =. (b) Number of noe: V =. Fig. 3. Performance comparion of elivery ratio v. benefit ecay coefficient. age elivery cot of the five algorithm beie of the average utility. The average elivery elay an average elivery cot are the average value of elivery elay an the cot of all meage eliverie. The elivery ratio i the ratio of ucceful eliverie an all meage eliverie. C. Evaluation Reult We conuct nine group of imulation in total. In each imulation, we prouce, meage by ranomly electing the ource an etination. For each meage elivery, we recor it utility, total tranmiion cot, an the elivery elay if the meage elivery uccee. The concrete imulation an reult are preente a follow. We firt evaluate the performance on utility through three group of imulation. The number of noe are et to be V =,, 6. In the firt group of imulation, we fix the benefit ecay coefficient δ =. an change the initial benefit value from to, i.e., β =,,,, to compare the average utility of the five algorithm. The reult are hown in Fig. 7. Compare with,, an, increae the utility by 459.6%, 464.3%, an 637.3% on average, repectively. Compare with, the -R algorithm increae the utility by up to 4.3% (47.9% on average). In the econ group of imulation, we fix the initial benefit β = an change the benefit ecay coefficient from. to.. The comparion reult on the average utility are hown in Fig. 8. Compare with,, an, increae the utility by 35.%, 93.9%, an 49.9% on average, repectively. Compare with,

9 Average Delivery Cot 6 -R Average Delivery Cot 6 -R Average Delivery Cot 6 -R (a) Number of noe: V = (b) Number of noe: V = Fig. 4. Performance comparion of elivery cot v. initial benefit. Average Delivery Cot -R Average Delivery Cot -R Average Delivery Cot -R (a) Number of noe: V = (b) Number of noe: V = Fig. 5. Performance comparion of elivery cot v. benefit ecay coefficient. the -R algorithm increae the utility by up to 4.3% (87.3% on average). In the thir group of imulation, we change both the initial benefit an the benefit ecay coefficient at the ame time to recor the change of average utility of the algorithm, a hown in Fig. 9. Thee reult emontrate the optimal utility performance of our propoe algorithm. Moreover, the larger the initial benefit an the maller the benefit ecay coefficient are, the larger the average utility woul be. The reult alo how that retranmiion can achieve an ignificant increae in performance. Next, we evaluate the performance on the elivery ratio, elay, an cot through ix group of imulation. We firt et the number of noe to be V =,, 6, an then change the initial benefit an the benefit ecay coefficient to recor the average elivery elay, elivery ratio, an average elivery cot of the five algorithm, repectively. Since the elivery ratio of the five algorithm are ifferent, it i unfair to only compare the average elivery elay an average elivery cot of the ucceful eliverie. In orer to make the comparion fair, we alo recor the faile elivery with the maximum elay an cot. The reult are hown in Fig. -5. Compare with,, an, ecreae the elivery elay by 47.%, 46.%, an 46.% on average, increae the elivery ratio by 396.4%, 44.%, 84.7% on average, an reuce the elivery cot by 59.%, 58.4%, an 58.4% on average, repectively. Here even ha a much better performance with elay an cot than an ue to it goo elivery ratio. The reult how that the algorithm ha achieve goo performance with reliability, elay, an cot at the ame time. It make a goo traeoff among the three factor. VI. RELATED WORK The routing problem in WSN ha been tuie for many year, an a lot of algorithm have been propoe for traitional non-uty-cycle WSN []. Compare to the traitional WSN, the elivery elay i an important factor in uty-cycle WSN routing eign. Without a concern for elay, thee algorithm cannot work well in uty-cycle WSN. Thu, ome elay-concerne routing algorithm, incluing a unicat algorithm DSF [3], [7] an two flooing-bae algorithm [4], [6], were propoe recently. However, compare with our utilitybae algorithm, none of them, no matter the traitional algorithm or the elay-concerne routing algorithm, aopt the utility metric which take reliability, elay, an cot into account at the ame time. The concept of utility-bae routing wa firt propoe by M. Lu an J. Wu to balance the reliability an tranmiion cot of the meage elivery in a hoc network []. Then, the utility-bae routing algorithm i extene into the opportunitic tranmiion moel in [], []. The benefit in thee utility moel i unchange uring the meage elivery. The utility moel o not take the elivery elay into account. Without coniering the elivery elay, they cannot work well in uty-cycle WSN. Unlike metric ue in thee earlier paper, the timeenitive utility i a compoite metric which take the elivery ratio, elay, an cot into account at the ame time. To the bet of our knowlege, the time-enitive utility moel an our propoe algorithm are the firt utility moel an utilitybae routing algorithm eigne for uty-cycle WSN. VII. CONCLUSION In thi paper, we propoe a time-enitive utility moel for uty-cycle WSN. Unlike the previou utility moel, the timeenitive utility moel take the elivery elay into account, which i an important metric in uty-cycle WSN. Uner thi moel, we preent an iterative formula to compute the utility value of each meage elivery. Bae on the iterative formula, we eign an optimal time-enitive utility-bae algorithm to eliver meage, an we exten the algorithm to the cae where retranmiion i allowe. Both of the algorithm can

10 maximize the average utility value of the meage eliverie, which can achieve a goo traeoff among reliability, elay, an cot. Simulation alo prove the ignificant performance of our propoe algorithm. ACKNOWLEDGMENT Thi work i upporte by the National Gran Funamental Reearch 973 Program of China (Grant No.CB395), the National Science an Technology Major Project (Grant No. ZX35-), the National Natural Science Founation of China (Grant No. 639), the Natural Science Founation of Jiangu Province in China(Grant No. BK95), an Chinee Univeritie Scientific Fun. REFERENCES [] M. Lu, F. Li, an J. Wu, Efficient opportunitic routing in utility-bae a hoc network, IEEE Tranaction on Reliability, vol. 58, no. 3, pp , 9. [] J. Wu, M. Lu, an F. Li, Utility-bae opportunitic routing in multihop wirele network, in IEEE ICDCS, 8. [3] Y. Gu an T. He, Dynamic witching-bae ata forwaring for lowuty-cycle wirele enor network, IEEE Tranaction on Mobile Computing, vol., no., pp ,. [4] S. Guo, S. M. Kim, T. Zhu, Y. Gu, an T. He, Correlate flooing in low-uty-cycle wirele enor network, in IEEE ICNP,. [5] Y. Gu, T. He, M. Lin, an J. Xu, Spatiotemporal elay control for low-uty-cycle enor network, in IEEE RTSS, 9. [6] S. Guo, Y. Gu, B. Jiang, an T. He, Opportunitic flooing in low-utycycle wirele enor network with unreliable link, in ACM MobiCom, 9. [7] Y. Gu an T. He, Data forwaring in extremely low uty-cycle enor network with unreliable communication link, in ACM SenSy, 7. [8] M. Maróti, B. Kuy, G. Simon, an Á. Léeczi, The flooing time ynchronization protocol, in ACM SenSy, 4. [9] S. Lin, J. Zhang, G. Zhou, L. Gu, T. He, an J. A. Stankovic, Atpc: Aaptive tranmiion power control for wirele enor network, in ACM SenSy, 6. [] J. N. Al-Karaki an A. E. Kamal, Routing technique in wirele enor network: A urvey, IEEE Wirele Communication, vol., no. 6, pp. 6 8, 4. [] M. Lu an J. Wu, Social welfare bae routing in a hoc network, in ICPP, 6. Appenix A. Proof of Theorem We can erive Eq. 4 by computing an umming the utility value of all poible elivery cae. If the meage elivery uccee, enote by, it mean that each-hop meage tranmiion in the path i ucceful. Then, the elivery elay i the um of each-hop t i,i+. Moreover, the ucceful elivery elay, i.e., probability P, benefit b, an total tranmiion cot c atify: P = p i,i+ ; b =β δ t i,i+ ; c = c i,i+. (9) If the meage elivery fail at the link k k+ ( k ), enote by k k+, the correponing benefit woul become zero, an the total cot only contain the tranmiion cot for the elivery from to h. That i: k k P k k+ =( p k,k+ ) p i,i+ ; b k k+ =; c k k+ = c i,i+. () The expecte utility u i the expecte value of the utilitie for the ucceful elivery an all poible faile eliverie. Thu, we have: u (β)=p (b c )+ P k k+ (b k k+ c k k+ ). () k= Further, after replacing the right ie of Eq. by Eq. 9- an by combining the relate item, we can get Eq. 4. B. Proof of Theorem We erive the iterative formula about the expecte utility value of two neighboring noe i an j a follow. Accoring to Eq. 4, we get the formula for u i (b i ) an u j (b j ): u i (b i )= p h,h+ (b i δ h=i u j (b j )= p h,h+ (b j δ h=j h=i h=j t h,h+ ) h=i t h,h+ ) h=j c h,h+ h p g,g+ ; () g= c h,h+ h p g,g+. (3) g= Comparing u i (b i ) an u j (b j ), we have: ( u i (b i )=p i,j u j (b j ) p h,h+ b i b j δ t i,j ) c i,j. (4) h=i Since noe i an j are ajacent in the elivery path, then accoring to Eq. 3, the remaining benefit of noe i an j atify: b i =b j +δ t i,j. (5) Therefore, by ubtituting Eq. 5 into Eq. 4, we can get: C. Proof of Theorem 3 u i (b i )=p i,j u j (b j ) c i,j. Bae on Eq. 6, we compute the expecte utility value u i (b i ) for the k-time retranmiion an the (k + )-time retranmiion: u i (b i ) k+ = [ ( p i,j ) k+ ]u j (b j ) (k+)c i,j ; (6) u i (b i ) k = [ ( p i,j ) k ]u j (b j ) kc i,j. (7) With Eq. 6 an Eq. 7, we have: u i (b i ) k+ u i (b i ) k =( p i,j ) k p i,j u j (b j ) c i,j. (8) Let k atify ( p i,j ) k p i,j u j (b j ) c i,j =, then we can get: k = ln c i,j ln p i,j u j (b j ). (9) ln( p i,j ) Accoring to Eq. 8, we have that u i (b i ) k <u i (b i ) k+ if an only if k < k. That i, when the number of retranmiion k increae, the expecte utility value u i (b i ) ecreae after increaing. Moreover, the maximum expecte utility value u i (b i ) can be achieve only when k =k. Since k i an integer, the optimal number of the retranmiion atifie: ˆk = k or ˆk = k.