Optimizing Energy-Latency Trade-off in Sensor Networks with Controlled Mobility

Optmzng Energy-Latency Trade-off n Sensor Networks wth Controlled Moblty Ryo Sughara Rajesh K. Gupta Computer Scence and Engneerng Department Unversty of Calforna, San Dego La Jolla, Calforna 9293 Emal: {ryo, rgupta}@ucsd.edu Abstract We consder the problem of plannng path and speed of a data mule n a sensor network. Ths problem s encountered n varous stuatons, such as modelng the moton of a data-collectng UAV n a feld of sensors for structural health montorng. Our specfc context here s use of a data mule as an alternatve or supplement to multhop forwardng n a sensor network. Whle a data mule can reduce the energy consumpton at each sensor node, t ncreases the latency from the tme the data s generated at a node to the tme the base staton receves t. In ths paper, we ntroduce the data mule schedulng or DMS framework that enables data mule moton plannng to mnmze the data delvery latency. The DMS framework s general; t can express many prevously proposed problem formulatons and problem settngs related to data mules. We desgn algorthms for DMS and extend to the more general case of combned data mule and multhop forwardng to enable a flexble trade-off between energy consumpton and data delvery latency. Usng DMS, we can calculate the optmal way for node-to-node forwardng and data mule moton plan. Our mplementaton and smulaton results usng ns2 show nearly monotonc decrease of data delvery latency for greater lmts on the energy consumpton, thus vastly ncreasng the flexblty n the energy-latency trade-off for sensor network communcatons. I. INTRODUCTION Controlled moblty presents an attractve alternatve to multhop forwardng for effcent data collecton n a sensor feld. In partcular, we consder collectng data from statonary sensor nodes usng a data mule va wreless communcaton. A data mule s a moble node wth rado and suffcent amount of storage to store the data from the sensors n the feld. Data mules have been used n recent sensor network applcatons, e.g., a robot n underwater envronmental montorng [1] and a UAV (unmanned aeral vehcle) n structural health montorng [2]. A data mule travels across the sensor feld and collects data from each sensor node when the dstance s short, and later deposts all the data to the base staton. In ths way, each sensor node can conserve energy, snce t only needs to send the data over a short dstance and has no need to forward other sensors data all the way to the base staton. Note that energy ssue s crtcal for sensor nodes as opposed to the data mule that returns to the base staton after the travel. However, one dsadvantage of ths approach s that t generally takes more tme to collect data, whch n turn ncurs larger data delvery latency. Thus optmzng the data delvery latency s vtal for the data mule approach to be useful n practce. In ths paper, we study the problem of optmzng the energy-latency trade-off when usng a data mule. We desgn a problem framework for optmzng the data mule s movement, whch we call the data mule schedulng (DMS) problem, and extend t to a general problem that combnes data mule and multhop forwardng. Compared to prevous studes, the DMS framework s comprehensve and general n the sense that t s capable of expressng many other formulatons. It s also flexble enough to adapt to dfferent problem settngs. In the DMS problem settng, we can control the movement of the data mule (path, speed) as well as ts communcaton (.e., from whch node t collects data at certan tme duraton). There s some smlarty to classcal schedulng problems. For nstance, the communcaton between the data mule and each node can be represented as a job that has both tme and locaton constrants. We analyze and desgn algorthms for the case that each sensor node generates data perodcally. Ths apples to many sensor network applcaton scenaros that montors the feld n the long term and thus enlarges the applcablty of the DMS framework. Then we consder the combned approach of data mule and multhop forwardng. In the pure data mule approach, the energy consumpton at each node s mnmum and the data delvery latency s relatvely large. On the other hand, multhop forwardng requres greater energy due to ncreased data transfer at each node but the latency s expected to be much shorter. Our work combnes these two approaches n such a way that the desgners of sensor networks can balance the energy consumpton and the data delvery latency accordng to applcaton needs. We formulate the problem by extendng the DMS problem and desgn centralzed and dstrbuted algorthms. Then we mplement the combned approach on the ns2 network smulator [3] to expermentally evaluate the effectveness of the formulaton and algorthms. Our contrbutons are: Formulate the DMS problem, a problem framework for optmal control of data mule for mnmzng the data delvery latency; Analyze the DMS problem for the perodc data generaton case; Extend the DMS problem for the combned approach of data mule and multhop forwardng for a flexble control of the energy-latency trade-off, and desgn centralzed and

2 dstrbuted algorthms for the extended DMS problem; Demonstrate the effectveness of formulaton and algorthms by experments on ns2 network smulator. The rest of ths paper s organzed as follows. In Secton II we ntroduce related work. Secton III gves an overvew of the DMS problem. In Secton IV we desgn algorthms for perodc data generaton case n the DMS problem. Secton V dscusses the combned approach of data mule and multhop forwardng for the extended DMS problem. The centralzed algorthm based on lnear program formulaton s also presented. Secton VI descrbes the dstrbuted algorthm for the forwardng problem. Secton VII shows the results of the smulaton experments on ns2 network smulator and Secton VIII concludes the paper. II. RELATED WORK Use of moble nodes for data collecton have been explored n sensor networks. Somasundara et al. [4], [5] studed the problem of choosng the path of a data mule that traverses at a constant speed through a sensor feld wth sensors generatng data at a gven rate. Ther formulaton also requres the data mule to vst the exact locaton of each sensor to collect data. They desgned heurstc algorthms(based on EDF schedulng) to fnd a path that mnmzes the buffer overflow at each sensor node. In the Message Ferryng project, Zhao and Ammar [6] examned the problem of path and speed optmzaton of a data mule n a feld of statonary nodes. The project has extended the work on controllably moble nodes case [7], multple data mules case [8], and arbtrarly moble nodes case [9]. Whle these formulatons are smlar n sprt to ours, we also generalze the problem to nclude a precse moblty model wth acceleraton constrants and stronger guarantees on the optmalty, as demonstrated n our prevous study [1]. There are also studes on combned data mule and multhop forwardng approach. Ho and Fall [11] dscussed such approach n the context of Delay Tolerant Networkng (DTN) archtecture. Burns et al. [12] expermentally showed that controlled moblty can mprove performance of routng n a network of randomly moble nodes. Also relevant to ths paper s work by Kansal et al. [13], who studed the case n whch a data mule perodcally travels across the sensor feld along a fxed path. In ther model, they can only change the speed of data mule. They used drected dffuson [14] for collectng data from the nodes outsde of the drect communcaton range of the data mule. Ther focus s on desgnng a robust communcaton nfrastructure that works even n uncertan envronments. Our work bulds upon ths work and seeks to buld a formal understandng of the problem wth stronger guarantees on the results. Ma and Yang [15], [16] desgned a heurstc algorthm for path selecton of a data mule. They formulate the multhop forwardng problem as a max-flow problem, assumng there s a lmt on energy consumpton at each node. Ther formulaton s smlar to ours n some ways, but one of the lmtatons s that ther path selecton algorthm can be appled only for certan types of confguratons. Specfcally, they assume that a data mule starts from the left edge of the deployment area, moves toward the rght edge, and comes back to the left edge agan. The algorthm also works only for connected networks. Xng et al. [17] also desgned path selecton algorthms when each node can forward data toward the base staton along a routng tree constructed n advance. Ther formulaton s smlar to the travelng salesman problem (TSP). They also assume the exstence of a dfferent type of nodes that do not generate data by themselves, n order to make the network connected and enable the constructon of routng tree rooted at the base staton. Although these assumptons allow the falover mechansm that mproves the data delvery rate, they also lmt the applcablty of the technque. Our problem framework can express not only ther settngs, but also more general settngs ncludng dsconnected networks. III. PROBLEM FRAMEWORK FOR OPTIMAL CONTROL OF DATA MULE To control a data mule for data collecton, one needs to determne the path and speed of the data mule and the schedule (.e., when to collect data from a node). However, smultaneously optmzng them s an NP-hard problem, whch s mpled by the NP-hardness of the smplfed path selecton problem [1]. Consequently, n prevous studes, the problem has been smplfed n varous ways by employng assumptons that restrct the capabltes of sensor nodes and data mule. Some examples are: data collecton s only possble at the exact locaton of each node, and the data mule can move only at a constant speed. These assumptons are sometmes approprate, but often make the formulaton only applcable to a specfc applcaton and settng. Our goal for desgnng the DMS problem s to provde a comprehensve and flexble problem framework n whch we can fully explot the networkng and moblty capabltes. For ths purpose, we frst decompose the problem nto followng three subproblems (see Fgure 1(b)(c)(d)): 1) Path selecton: determnes the trajectory of the data mule so that t travels wthn each sensor node s communcaton range at least once. 2) Speed control: determnes how the data mule changes the speed along the path, so that t spends enough tme wthn each node s communcaton range to collect all the data from t. 3) Job schedulng: determnes the schedule of data collecton from each node. The last two subproblems are solved jontly as a schedulng problem wth both locaton and tme constrants, whch we call the 1-D DMS problem. As for the path selecton subproblem, we have formulated t as an ndependent problem n [1], whch we brefly descrbe later. The DMS problem stated above s general and can be used to express several earler problems n the area. For nstance, the assumpton of no wreless communcaton (as n [4] [5]) s easly expressed by settng the communcaton range to zero n the path selecton subproblem. The constant speed assumpton

3 node B node C Locaton job A B C Executon tme e(a) e(b) e(c) Locaton Job A B C Executon tme e(a) e(b) e(c) Tme Data mule Communcaton range node A Speed Tme A B C Tme (a) Forwardng (b) Path selecton (c) Speed control (d) Job schedulng 1-D DMS Data Mule Schedulng (DMS) Fg. 1. Subproblems of the DMS problem: Forwardng problem (dscussed n Secton V) formulates the combned approach of data mule and multhop forwardng. (as n [15] [17]) and varable speed assumpton (as n [6], [13]) are handled n the speed control subproblem. In the followng three sectons, we dscuss detals of the DMS problem and how we extend t to broaden the coverage for more general cases. Frst, n Secton IV, we analyze the general case of the 1-D DMS problem n whch each sensor node generates data perodcally. Then, n Secton V, we consder the hybrd case that combnes data mule wth multhop forwardng. We realze ths by addng the forwardng subproblem n front of the path selecton subproblem, as shown n Fgure 1(a). Fnally n Secton VI, we desgn a dstrbuted algorthm for the forwardng subproblem. IV. PERIODIC 1-D DMS PROBLEM Once we choose a path of the data mule, or the data mule moves along a predetermned path, by consderng the path as a locaton axs, we obtan the 1-D DMS problem. The problem conssts of two subproblems: speed control and job schedulng. The nput to the speed control subproblem s a set of locaton jobs representng data collecton tasks. A locaton job has an executon tme and s assocated wth (possbly multple) locaton ntervals that correspond to the ntersectons of the node s communcaton range and the data mule s path. A soluton for the 1-D DMS problem s twofold. One s tme-speed profle, whch determnes the speed changes of the data mule. Wth a tme-speed profle, each pont on the locaton axs can be mapped onto a pont on the tme axs. Then we obtan a schedulng problem havng a set of jobs, each of whch has an executon tme and feasble ntervals. For ths problem, we need to determne job schedule that defnes when the data mule communcates wth each node. The objectve of the 1-D DMS problem s to fnd a speed control plan and a feasble job schedule so that the total travel tme of the data mule s mnmzed. In the perodc case of the 1-D DMS problem, each sensor node generates data at a gven rate and a data mule travels across the sensor feld perodcally. Ths models a common type of sensor network applcatons that contnuously montors the feld n the long term, and has a larger coverage than nonperodc case, whch has been analyzed n our prevous work [18]. The objectve s to mnmze the perod,.e., the tme the data mule takes for each travel, snce t largely affects the data delvery latency. In the speed control subproblem, we consder three dfferent constrants on the dynamcs of the data mule. The frst s constant speed, where the data mule cannot change the speed after t starts to move. The second s varable speed, where the data mule can nstantaneously change the speed wthn a speed range [v mn,v max ]. The thrd s varable speed wth acceleraton constrant, whch we call the generalzed model, snce t ncludes prevous two models as specal cases. In the generalzed model, the data mule can change the speed, but the rate of change s wthn the maxmum absolute acceleraton a max. Ths model s most approprate when we cannot gnore the nerta, for example n case that a helcopter s used as a data mule as n [2]. We now present the algorthms for the 1-D DMS problem under dfferent dynamcs constrants. A. Termnology, defntons, and assumptons Forthejobschedulngsubproblem,ajob τ hasanexecuton tme e and a set I of feasble ntervals. A feasble nterval I I s a tme nterval [r(i),d(i)], where r(i) s a release tme and d(i) s a deadlne. A job can be executed only wthn ts feasble ntervals. A smple job s a job wth one feasble nterval, whereas a general job can have multple feasble ntervals.fornstance,nfgure1(d),jobb andc aresmple jobs and job A s a general job. Smlarly for the speed control subproblem, a locaton job τ has an executon tme e and a set I of feasble locaton ntervals. A feasble locaton nterval I I s a locaton nterval [r(i), d(i)], where r(i) s a release locaton and d(i) s a deadlne locaton. A locaton job can be executed only wthn ts feasble locaton ntervals. A smple locaton job s a locaton job wth one feasble locaton nterval, whereas a general locaton job can have multple feasble locaton ntervals. In Fgure 1(c), locaton job B and C are smple locaton jobs and locaton job A s a general locaton job. For an nterval I = [r,d] (also for a locaton nterval), I denotes the length d r. We also defne contanment as

4 follows: I I f and only f r r and d d where I = [r,d ]. Let T t denote the travel tme of one perod. The data mule needs to stay at the base staton for constant tme T b to depost the data to the base staton and refuel etc. Thus the length of one perod s T t + T b. For the system to be stable, n each perod of travel, the data mule needs to collect the data generated n one perod. Each sensor node s statonary. Communcaton range and data generaton rate are known. Communcaton s always successful n the communcaton range and bandwdth s a known constant. All locaton jobs are preemptble wthout any cost ncurred and can be executed over multple feasble locaton ntervals. There s no dependency among the locaton jobs. There s only one data mule. Data mule can communcate wth one node at a tme. Dependng on the dynamcs constrant, data mule may have constrants on the maxmum speed and maxmum acceleraton. B. Algorthms 1) Processor demand analyss: Frst we present an algorthm based on processor demand analyss. Ths algorthm apples to the constant speed model wth smple locaton jobs,.e., each locaton job has only one feasble locaton nterval. Let e denote the executon tme of -th locaton job for one perod. It s defned as follows: e λ R (T t + T b ), (1) where λ s the data generaton rate of -th node and R s the bandwdth, both of whch are known constants. Processor demand g(i) for locaton nterval I for one perod s g(i) I I e, where I s the feasble locaton nterval of the -th locaton job. Let g (I) denote the processor demand for I for unt tme, whch s defned as follows: g (I) g(i) T t + T b = I I λ R. (2) The set of locaton jobs s feasble f and only f the speed v of data mule satsfes v I mn I I g(i) = 1 I mn T t + T b I I g (I), (3) where I s the total travel nterval. When T b >, we obtan the followng constrant usng T t = I /v: v ( mn I I ) I 1 g (I) I. (4) T b For a feasble soluton to exst, the followng must be satsfed: I I < mn I I g (I). (5) When ths s satsfed, the maxmum speed s the rght hand sde of (4). When ths s not satsfed, t s not possble to collect data wthout loss. When T b =, we obtan the followng from (3): I I mn I I g (I). (6) Note that (6) contans nether v nor T t. What t mples s, when ths s satsfed, the speed of data mule can be arbtrary. Ths valdates the expermental observaton n [13] that the speed of data mule does not matter f the data mule travels the sensor feld perodcally. To determne the job schedule, we map each locaton job to a job usng the obtaned maxmum speed, and use the EDF algorthm. It s always possble because we determne the speed such that the feasblty s preserved and also because the EDF algorthm s optmal. 2) LP formulaton: For the constant speed model wth general locaton jobs, and also for the varable speed model, we can use a lnear program formulaton. We splt the total travel nterval I nto (2m + 2) locaton ntervals [l,l 1 ], [l 1,l 2 ],..., [l 2m+1,l 2m+2 ], where m s the number of feasble locaton ntervals of all locaton jobs, l P r P d, l l +1, and P r,p d are the lst of release locaton and deadlne locatons, respectvely 1. Then we have the followng lnear program: Varables For each locaton nterval [l,l +1 ], z : Tme that the data mule stays n ths nterval p j : Tme allocated to locaton job j n ths nterval Objectve Mnmze the total travel tme 2m+1 = z. Constrants (Speed) For the varable speed model, l +1 l v max z. (7) For the constant speed model, we requre the speed for all the locaton ntervals to be dentcal. Instead of (7), for the locaton ntervals satsfyng l +1 l >, we have z z k =, (8) l +1 l l k+1 l k where k s any value satsfyng l k+1 l k >. (Feasble nterval) p j f I I j,[l,l +1 ] I, where I j s the set of feasble locaton ntervals of locaton job j. Otherwse p j =. (Job completon) For locaton job j, ( 2m+1 p j = λ 2m+1 ) j z + T b, (9) R = = where R s the bandwdth of communcaton from each node to the data mule. The rght hand sde s the amount of tme to transmt the data generated n one perod. (Processor demand) j p j z. The LP problem may be ether nfeasble or unbounded 2. When t s nfeasble, t s mpossble to collect all data. When t s unbounded, the speed s arbtrary. 1 A locaton nterval degenerates to a pont when l = l +1, but t does not affect the valdty of the formulaton. 2 It may be unbounded only n the constant speed model.

5 For the obtaned soluton, we can make a job schedule n the followng way. Locaton nterval [l,l +1 ] s mapped to the tme nterval [ 1 k= z k, k= z k]. For each tme nterval, we allocate p 1 for job 1 from the start of the nterval, p 2 for job 2 after that, and contnue ths for all jobs. 3) Iteratve method: For the generalzed model, we have desgned a heurstc algorthm for the non-perodc case n [18]. The algorthm assumes a speed control n whch the data mule frst accelerates at a max, then keeps the top speed, and decelerates at a max, and fnds the maxmum top speed that preserves the feasblty. Then t apples recursvely to the locaton ntervals that admt further ncrease of the speed. We can use ths algorthm for perodc case as well. Specfcally, we can estmate T t teratvely n the followng manner: Run the LP-based algorthm assumng no acceleraton constrant (.e., the varable speed model). Set the result to the ntal value of ˆT t, the estmate of T t. Repeat Run the heurstc algorthm wth the executon tme e = λ ( ˆT t + T b )/R. Denote the travel tme as T t. If T t ˆT t < ǫ, break the loop. Otherwse, update ˆT t by T t and repeat. V. COMBINING DMS WITH MULTIHOP FORWARDING Usng the DMS problem, we are able to determne data mule s speed and schedule for sensor data collecton so that the travel tme s mnmzed. We now consder a combned approach of data mule and multhop forwardng. In our framework, we realze ths by defnng a new forwardng problem that s placed n front of the DMS problem as shown n Fgure 1. The forwardng problem s to determne how much data each node forwards to other nodes and to the data mule whle satsfyng a predetermned energy consumpton constrant. Frst we consder the path selecton problem. Then we dscuss the forwardng problem and present a centralzed algorthm based on lnear program formulaton. A. Overvew of path selecton problem For the nodes to send ther data to the data mule, a path needs to ntersect wth ther communcaton ranges, as shown n Fgure 2(a). The objectve s to fnd a path such that the shortest travel tme of the data mule n the 1-D DMS problem nduced by that path s mnmzed. However, fndng a smooth path as shown n the fgure s computatonally expensve. In addton, maneuverng the data mule along such a smooth path s often dffcult n practce. From these reasons, we have desgned and analyzed a smplfed problem n [1]. As shown n Fgure 2(b), we consder a complete graph havng vertces at sensor nodes locatons and assume the data mule moves between vertces along a straght lne. Each edge s assocated wth a cost and a set of labels, where the latter represents the set of nodes whose communcaton ranges ntersect wth ths edge. In ths way, whle travelng along an edge, the data mule can collect data from the nodes n the 1 2 3 s (Base staton) (a) 4 5 Fg. 2. Path selecton problem: (a) Orgnal problem wth an example path. (b) Smplfed problem, n whch the objectve s to fnd the shortest labelcoverng tour n the graph. labels assocated wth t. The objectve s to fnd a labelcoverng tour that mnmzes the total cost of the edges n the tour, where label-coverng means that, for any label, there exsts at least one edge n the tour that contans the label. We use Eucldean dstance as the cost metrc, snce we have observed n the experments that t has a strong postve correlaton wth the shortest travel tme n the nduced 1-D DMS problem. The smplfed problem s stll NP-hard and we have desgned an approxmaton algorthm. The algorthm frst fnds a TSPtourbyusnganyTSPsolverasanexternalmodule.Then, usng dynamc programmng, t fnds a short label-coverng tour that can be constructed by shortcuttng the TSP tour, whch s also a label-coverng tour by tself. The algorthm runs n C TSP + O(n 3 ) tme, where C TSP s the computaton tme of the TSP solver. An approxmate label-coverng tour T APP found by ths algorthm satsfes T APP α( T OPT + 2nr), where α s the approxmaton rato of the TSP solver, T OPT s the shortest label-coverng tour, n s the number of nodes, and r s the radus of communcaton range. Smulaton experments have demonstrated that our formulaton and algorthm effectvely explot broader communcaton range and yeld shorter travel tme than prevous studes such as [6], [15] [17]. B. Forwardng problem The objectve of the forwardng problem s to fnd a forwardng plan such that the nduced DMS problem has the shortest total travel tme. Dfferent from the pure data mule approach, n whch each node sends ts data only to the data mule, t can now forward ts data to other neghborng nodes as well. More mportantly, f a node decdes to forward all data to other nodes, the data mule does not need to collect data drectly from ths node. Then the data mule can possbly take a shorter path to reduce the travel tme. We present a centralzed algorthm based on lnear program formulaton. Snce fndng the optmal forwardng plan that mnmzes the travel tme n the nduced DMS problem s at least as hard as the DMS problem, we make t an ndependent problem by changng the objectve functon. We mnmze the average dstance of nodes from the base staton weghted by the amount of data at each node after 1 1, 2 2 1, 2 1 2,3 s 1,2,3 3 (b) 3 2,3,4 4 1,4 3,4 5 1, 5 3,4,5 2,4,5 4 4,5 5

6 forwardng. There are three reasons why ths s a reasonable choce as the objectve functon. Frst, ths functon s lkely to shorten the path of the data mule by forcng the nodes at the edge of network to prmarly use forwardng. Secondly, ths functon allows a smooth transton between the data mule approach and multhop forwardng. As the energy consumpton lmt grows, more data s forwarded closer to the base staton. In a connected network, all the data s eventually forwarded to the base staton wthout usng a data mule, whch s equvalent to pure multhop forwardng. Fnally, snce the functon s lnear, we can formulate the problem as a lnear program as descrbed below. We assume the locaton of sensor nodes and the connectvty between them are known. We also assume the followng parameters are gven: λ : Data generaton rate of node : Energy consumpton lmt at each node per unt tme E r,e s : Energy consumpton for recevng and sendng unt data R: Bandwdth,.e., maxmum data rate that each node can communcate wth other nodes and the data mule Then we have the followng lnear program: Varables x j : Amount of data sent from node to j per unt tme Objectve Mnmze d λ, where d s the dstance between node and the base staton, and λ s the data rate that node sends drectly to the data mule. λ s defned by the dfference of ncomng data rate and outgong data rate as follows: Constrants x =. λ = j x j + λ j x j. (1) (Connectvty) For j, x j f node j s n the communcaton range of node. Otherwse x j =. (Flow conservaton) λ. (Energy consumpton) For each node, E r x j + E s x j + λ, (11) j j where the frst term n the left hand sde s the amount of energy consumed by recevng data and the second term s that for sendng data. About the latter, node sends j x j to other nodes and λ to the data mule per unt tme, when averaged over tme. Usng Equaton (1), the sum of these two equals j x j + λ. (Bandwdth) Per unt tme, the amount of ncomng data s j x j and outgong data s j x j + λ. After some manpulatons, we obtan 2 j x j + λ R. (12) The formulaton above s also capable of expressng the case n whch each node communcates along the preconstructed routng tree as n [17]. Ths s possble by replacng the connectvty constrant wth the followng one: (Routng tree) For j, x j, f node j s node s parent n the routng tree. Otherwse x j =. VI. DISTRIBUTED ALGORITHM FOR FORWARDING The LP formulaton above yelds the optmal forwardng plan n the sense that t mnmzes the weghted dstance of data from the base staton. However n practce, t may be dffcult to tell each node about the lst of forwardng destnaton and the data rate for each. To cope wth ths ssue, we present a dstrbuted algorthm where each node determnes the forwardng destnaton and the data rate n a dstrbuted manner. In the algorthm, we consder the case that each node forwards the data along a routng tree. For connected networks, there s only one routng tree rooted at the base staton. For dsconnected networks, there are multple routng trees, one for each connected cluster. In each cluster, the node closest to the base staton s chosen as the root. We descrbe how to dentfy connected clusters, construct ntra-cluster routng trees, and plan the forwardng rate. A. Clusterng and constructng routng trees We can smultaneously fnd connected clusters and construct ntra-cluster routng trees by extendng DSDV [19], whch s a routng scheme based on the dstance vector algorthm. We extend DSDV so that each node exchanges ID and poston of the nterm root node. An nterm root node s the node that s reachable and closest to the base staton as far as the current node knows. The nformaton on root node s updated when the current node knows the one closer to the base staton, and s propagated to neghbors when t s updated. These communcatons can be pggybacked on the update packets of normal DSDV. When t reaches a convergence, each node has the correct nformaton on the root node and the next hop for reachng the root. To plan the forwardng rate, each node needs to learn the set of mmedate chld nodes as well as the parent. Ths s realzed by each node sendng a message to the parent node along the establshed routng tree. B. Plannng the forwardng rate Forwardng rate s calculated n the followng three phases. 1) Request: The request phase s ntated from the leaf nodes and proceeds toward the root. Each node tells the parent the cumulatve data rate, whch s the total data rate generated at the node and ts descendants. Let Λ denote cumulatve data rate of node, whch s defned as follows: Λ λ + j C Λ j, (13) where C s the set of mmedate chldren of node.

7 2) Allocate: The allocate phase proceeds downwards from the root. Parent node tells each mmedate chld the allocated data rate, whch s the maxmum data rate that the parent can receve from ths chld. Let y (n) denote the total data rate that node receves from needs to satsfy ts chldren. Then y (n) and thus E r y (n) + (λ + y (n) )E s, (14) y (n) λ E s E r + E s. (15) For each chld node, we dstrbute the maxmum data rate proportonally by the cumulatve data rate. Thus the maxmum data rate X j that chld node j can send to the parent s X j = Λ j E lmt λ E s. (16) k C Λ k E r + E s 3) Plan: The plan phase proceeds upwards from the leaf nodes. Node determnes the forwardng rate and tell t to the parent. For node, the total data rate y (out) to be sent to ether the parent or the data mule s y (out) = λ + y (n), (17) where y (n) = j C x j. We try to forward the data to parent node as much as possble and send the remanng data to the data mule. Therefore, f we let node j be the parent of, data rate x j s { } x j = mn y (out),x. (18) By settng x j n ths way, nequalty (15) s satsfed. Data rate λ to the data mule s λ = y (out) x j. (19) VII. SIMULATION EXPERIMENTS We expermentally evaluate the combned approach of data mule and multhop forwardng n the perodc data generaton case, specfcally on the effectveness of formulaton and algorthms n optmzng the energy-latency trade-off. A. Methods We have mplemented the centralzed and dstrbuted algorthms for the forwardng problem and the algorthms for the DMS problem n MATLAB wth YALMIP nterface [2] and SeDuM [21] for LP solver. The MATLAB program generates a Tcl scrpt for ns2 [3], whch smulates the movement of the data mule and the communcaton among the data mule and the nodes. To assess performance, we measure the delvery latency for each data packet from the tme t s generated to the tme the base staton receves t ether from neghborng nodes or va the data mule. For each test case, the smulaton on ns2 s repeated multple perods untl t reaches stablty. We consder t stable when the average delvery latency of the data receved n the current perod s wthn ±1% of that of the prevous g g (a) g 1.5g 1.5g Fg. 3. Network topology: (a) Connected network; (b) Dsconnected network. Whte crcle s the base staton. Lne between two crcles represents that they are wthn the communcaton range. Grd sze g s set to.8r, where r s the radus of communcaton range, and a unformly random dsturbance of [.25r,.25r] s added to the poston of each node. perod. If t s stable, we use the data for the next perod as the fnal results. Fgure 3 shows two network topologes we use for the experments. Both of them have sensor nodes, one base staton and one data mule, but one s a connected network and the other s a dsconnected network. The dsconnected network conssts of four connected networks of 25 nodes and the base staton s not drectly reachable from any nodes. For the data mule s movement, we use the varable speed model. The range of speed s v 1m/s, whch roughly smulates the movement of a UAV used n [2]. For ns2 smulator, we use FreeSpace propagaton model wth m communcaton range. We use 82.11 MAC (wth RTS/CTS) wth 2 Mbps raw bandwdth, whch s the default value for ns2. Packet sze s 4 Bytes. Other parameters are set as follows. Energy consumpton for sendng/recevng unt data s assumed to be equal,.e., E r = E s. The rate of data generaton at each node λ s Byte/sec. Let E denote the energy consumpton at each node for pure data mule case wthout any node-to-node forwardng. Then E s expressed as λ E s, and ths s the mnmum possble value of. We measured the latency for = E,...,5E. Effectve bandwdth R s set to 4 Kbps, consderng the overhead of RTS/CTS and packet header. B. Results Fgure 4 s an example of forwardng plan and calculated path. The small crcles represent the nodes and large crcles are ther communcaton ranges. Color of each crcle represents how much data the node sends drectly to the data mule. Whte crcles mean zero and colored crcles mean nonzero. As the forwardng algorthms try to gather data close to the base staton, whch s located n the center n ths example, the nodes at the edge of the network forward all data to the ones closer to the center. Nodes that have the base staton wthn ther communcaton range forward all the data drectly to the base staton. In ns2 smulaton, the delvery latency reached stablty n all tested cases. Average number of perods untl reachng stablty was 5.2 (centralzed) and 5.6 (dstrbuted) n the g (b) 1.5g 1.5g

8 4 11 21 31 41 51 61 71 81 91 11 3 1 2 3 4 5 6 7 8 9 2 9 19 29 39 49 59 69 79 89 99 8 18 28 38 48 58 68 78 88 98 7 17 27 37 47 57 67 77 87 97 1 6 16 26 36 46 56 66 76 86 96 5 15 25 35 45 55 65 75 85 95 2 4 14 24 34 44 54 64 74 84 94 3 3 13 23 33 43 53 63 73 83 93 2 12 22 32 42 52 62 72 82 92 4 5 5 5 4 3 2 = E Data mule only Avg latency = 432.81 sec Avg latency (Base staton) Avg latency (Data mule) Avg latency (Total) Data mule s travel tme = 49E Multhop forwardng only Avg latency = 4.17 sec Fg. 4. Example of forwardng plan and calculated path: Connected network, = 1E, centralzed forwardng algorthm. Nodes n whte forward all data and the data mule does not collect data drectly from them. Path s shown n bold lne. connected network, and 4. (centralzed) and 4.1 (dstrbuted) n the dsconnected network. Fgure 5 shows the smulaton results for the connected network and dsconnected network when the centralzed algorthm s used for the forwardng problem. For both networks, = E corresponds to the pure data mule case. The average latency n ths case was 432.81 secs for the connected network and 513.7 secs for the dsconnected network. These are qute smlar to the total travel tme (44.73 secs and 511.68 secs, respectvely). For the connected network, t became pure multhop forwardng when = 49E, where all the data are sent to the base staton by multhop forwardng and the data mule s not used. The average latency n ths case was 4.17 secs. Fgure 6 shows the comparson of average data delvery latency between the two forwardng algorthms. In both of the connected and dsconnected networks, the centralzed scheme based on LP formulaton acheved shorter average latency than the dstrbuted algorthm n most of the cases. On average, the rato of average latency was 1.53 (mn:.93, max:2.5) for the connected network and 1.31 (mn:.95, max:1.8) for the dsconnected network. C. Dscussons For both of the connected and the dsconnected networks, the smulaton results showed the decrease of data delvery latency as the energy consumpton lmt ncreases. The decrease was almost monotonc, demonstratng fne-graned control of the trade-off between energy and latency. It was also shown that formulaton of the forwardng problem, especally the choce of objectve functon s approprate, due to the fact that the centralzed algorthm acheved a better trade-off than the dstrbuted one, whch yelds suboptmal forwardng plans. We can also observe that the travel tme of the data mule s nearly equal to the average latency for the data delvered by the data mule. It demonstrates that mnmzng the travel tme for the purpose of mnmzng the data delvery latency s a vald approach. In addton, ths mples that we can estmate the average delay solely by solvng the DMS problem. Fgure 7 shows the hstograms of data delvery latency for two dfferent energy consumpton lmts for each of the connected and dsconnected networks. As these fgures show, 1 2 3 4 5 Energy consumpton lmt ( E) 6 5 4 3 2 = E Data mule only Avg latency = 513.7 sec Avg latency (Total) Data mule s travel tme 1 2 3 4 5 Energy consumpton lmt ( E) Fg. 5. Data delvery latency for varyng energy consumpton lmt: (top) connected network, (bottom) dsconnected network. The centralzed forwardng algorthm s used. regardless of the dfferent network topology and the dfferent total travel tme, more than 98% of the data has delvery latency wthn double of the travel tme. Ths means we can estmate the maxmum delvery latency as well as the average. In practce, our problem formulaton and algorthms provde sensor network desgners a good estmate of the data delvery latency when there s an energy consumpton lmt, whch s mposed by ther applcaton scenaros. Conversely, snce the energy-latency curve s nearly monotonc and the problem s solved n relatvely short tme 3, by usng bnary search, we can also estmate the maxmum energy consumpton at each node when there s a constrant on the average or the maxmum of data delvery latency, as assumed n [17]. VIII. CONCLUSIONS AND FUTURE WORK Controlled moblty, as represented by the moton of a data mule, provdes an alternatve approach to multhop forwardng for collectng data from sensor networks. Whle t allows a sgnfcant reducton n energy consumpton, ncreased data delvery latency s a bg ssue. In ths paper, we have presented the data mule schedulng (DMS) problem as a problem framework for optmally controllng a data mule and have extended t to enable flexble energy-latency trade-off. We have presented a framework to capture and analyze communcaton 3 For nodes case, solvng the forwardng problem and the DMS problem takes around 1 secs on MATLAB runnng on a PC.

9 5 Centralzed 4 Dstrbuted 3 2 1 2 3 4 5 Energy consumpton lmt ( E ) 6 5 4 3 Centralzed Dstrbuted 2 1 2 3 4 5 Energy consumpton lmt ( E ) Sze (KByte) Sze (KByte) 15 5 (276.7) Cumulatve T t =234.8sec 2T t dst. (%) T t =31.69sec 2T t Connected network:.% 2 3 4 5 6 (313.3) T t =65.13sec 5 2T t 98.2% Connected network: = 5E 2 3 4 5 6 = 2E 8 6 4 2 Cumulatve dst. (%) 8 6 4 2 Sze (KByte) Sze (KByte) 15 5 15 5 2 3 4 5 6 Dsconnected network: T t =137.33sec 2T t 99.25% Dsconnected network: 99.98% = 5E 2 3 4 5 6 = 2E Cumulatve dst. (%) 8 6 4 2 Cumulatve dst. (%) 8 6 4 2 Fg. 6. Average data delvery latency for dfferent forwardng algorthms: (top) connected network, (bottom) dsconnected network Fg. 7. Hstogram of data delvery latency: For the connected network, gray bars are for the data delvered to the base staton from neghborng nodes, and black bars are for the data delvered va the data mule. The centralzed forwardng algorthm s used. strateges that use combnatons of data mule and multhop forwardng. To valdate our results, we have mplemented our algorthms and smulated them on ns2 network smulator. The results showed nearly monotonc decrease of the data delvery latency for larger energy consumpton lmt, demonstratng the effectveness of the formulaton and the algorthms n optmzng the energy-latency trade-off. Our future work ncludes makng the problem formulaton and the algorthms vald also n envronments wth ncreased uncertanty. For example, we are currently workng on relaxng the assumpton on communcaton regon. One dea s to employ a sem-onlne algorthm that ntally plans the moton offlne solely based on the knowledge about small regons around each node. Then, at runtme, t opportunstcally explots the addtonal communcaton regon that s not known beforehand to optmze the moton. REFERENCES [1] I. Vaslescu, K. Kotay, D. Rus, M. Dunbabn, and P. Corke, Data collecton, storage, and retreval wth an underwater sensor network, n SenSys, 25, pp. 154 165. [2] M. Todd, D. Mascarenas, E. Flynn, T. Rosng, B. Lee, D. Musan, S. Dasgupta, S. Kpotufe, D. Hsu, R. Gupta, G. Park, T. Overly, M. Nothnagel, and C. Farrar, A dfferent approach to sensor networkng for SHM: Remote powerng and nterrogaton wth unmanned aeral vehcles, n Proceedngs of the 6th Internatonal workshop on Structural Health Montorng, 27. [3] ns2 network smulator, http://www.s.edu/nsnam/ns/. [4] A. A. Somasundara, A. Ramamoorthy, and M. B. Srvastava, Moble element schedulng for effcent data collecton n wreless sensor networks wth dynamc deadlnes, n RTSS, 24, pp. 296 35. [5], Moble element schedulng wth dynamc deadlnes, IEEE Trans. Moble Computng, vol. 6, no. 4, pp. 395 41, 27. [6] W. Zhao and M. Ammar, Message ferryng: Proactve routng n hghlyparttoned wreless ad hoc networks, n FTDCS, 23, pp. 38 314. [7] W. Zhao, M. Ammar, and E. Zegura, A message ferryng approach for data delvery n sparse moble ad hoc networks, n MobHoc, 24, pp. 187 198. [8], Controllng the moblty of multple data transport ferres n a delay-tolerant network, n INFOCOM, 25, pp. 147 1418. [9] M. M. B. Tarq, M. Ammar, and E. Zegura, Message ferry route desgn for sparse ad hoc networks wth moble nodes, n MobHoc, 26, pp. 37 48. [1] R. Sughara and R. K. Gupta, Improvng the data delvery latency n sensor networks wth controlled moblty, n DCOSS, 28. [11] M. Ho and K. Fall, Poster: Delay tolerant networkng for sensor networks, n SECON, 24. [12] B. Burns, O. Brock, and B. N. Levne, MV routng and capacty buldng n dsrupton tolerant networks, n INFOCOM, 25, pp. 398 48. [13] A. Kansal, A. A. Somasundara, D. D. Jea, M. B. Srvastava, and D. Estrn, Intellgent flud nfrastructure for embedded networks, n MobSys, 24, pp. 111 124. [14] C. Intanagonwwat, R. Govndan, and D. Estrn, Drected dffuson: a scalable and robust communcaton paradgm for sensor networks, n MobCom, 2, pp. 56 67. [15] M. Ma and Y. Yang, SenCar: An energy effcent data gatherng mechansm for large scale multhop sensor networks. n DCOSS, 26, pp. 498 513. [16], SenCar: An energy effcent data gatherng mechansm for largescale multhop sensor networks, IEEE Trans. Parallel and Dstrbuted System, vol. 18, no. 1, pp. 1476 1488, 27. [17] G.Xng,T.Wang,Z.Xe,andW.Ja, Rendezvousplannngnmobltyasssted wreless sensor networks, n RTSS, 27, pp. 311 32. [18] R. Sughara and R. K. Gupta, Data mule schedulng n sensor networks: Schedulng under locaton and tme constrants, UCSD Tech. Rep., vol. CS27-911, 27. [19] C. E. Perkns and P. Bhagwat, Hghly dynamc destnaton-sequenced dstance-vector routng (DSDV) for moble computers, n SIGCOMM, 1994, pp. 234 244. [2] J. Löfberg, Yalmp : A toolbox for modelng and optmzaton n MATLAB, n Proceedngs of the CACSD Conference, Tape, Tawan, 24. [Onlne]. Avalable: http://control.ee.ethz.ch/ joloef/yalmp.php [21] J. F. Sturm, Usng SeDuM 1.2, a MATLAB toolbox for optmzaton over symmetrc cones, Optmzaton Methods and Software, vol. 11 12, pp. 625 653, 1999.