Message Cab (MCab): Partition Restoration in MANETs Using Flexible Helping Hosts

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1 Wreless Sensor Network, 2010, 2, do: /wsn Publshed Onlne December 2010 ( Message Cab (MCab): Partton Restoraton n MANEs Usng Flexble Helpng Hosts Abstract ng Wang, Chor Png Low School of Electrcal and Electronc Engneerng,Nanyang echnologcal Unversty, Sngapore Emal: wang0235@e.ntu.edu.sg, cplow@e.ntu.edu.sg Receved September 18, 2010; revsed September 26, 2010; accepted October 12, 2010 Helpng hosts are ntensvely used n varous schemes to restore parttoned Moble Ad Hoc Networks (MANEs). Most of the exstng schemes offers only determnstc deployment and fxed routes for the helpng hosts, and are thus not able to deal wth fluctuatng network traffc, whch s a practcal condton n many MANE applcatons. In ths paper, we argue that flexble helpng hosts (referred to as Message Cabs (MCabs)), wth deployment and routes that response to the changes n the traffc demand of the network, may overcome ths drawback and reduce the message delay n the networks. o demonstrate the effectveness of ths observaton, we propose a new helpng host scheme namely the Message Cab (MCab) scheme for partton restoraton n MANEs, and valdate the performance through smulatons. Keywords: Moble Ad Hoc Networks (MANEs), Helpng Host, Message Cab, Adaptve Route Desgn, Dynamc Deployment 1. Introducton A Moble Ad Hoc Network (MANE), as descrbed n [1], s a knd of moble wreless networks whch s comprsed of a collecton of moble hosts connected through wreless channels. he drect connectons between the hosts are referred to as lnks. A host n a MANE exchanges messages wth other nodes as a termnal and forwards the messages as an ntermedate router at the same tme. he routng paths of a message n a MANE are formed by a seres of moble hosts. Messages are forwarded hop-by-hop. Whle the moblty of hosts enables the network to span over a large area, t also causes a hghly dynamc topology, whch s a major challenge to the applcatons of MANEs. When a host moves out of another s communcaton range, the lnk between them breaks, and the entre message routng path may be destroyed by ths broken lnk. hs possblty of lnk breakage may splt hosts nto dfferent parts between whch there s no possble path. hs n turn may result n packets not beng able to reach ther destnatons. We refer to ths phenomenon as network parttonng. Each solated part of a network s referred to as a partton of the network. he parttonng problem makes a crtcal strke on ad hoc routng because most protocols typcally assume that the network s always connected. o enhance the relablty and conserve energy, parttonng should be restored n MANEs. Varous approaches have been proposed for MANEs survvablty and restoraton. In partcular, helpng hosts are deployed to reconnect the network parttons, and we refer to such acton as partton restoraton. he helpng hosts are able to reconnect the network connectvty by movng from one partton to another n a MANE despte the fact that the normal hosts (.e. nonhelpng hosts) may be parttoned. hs dea s also extensvely dscussed n Delay olerant Networks (DN) and Wreless Sensor Networks () n order to collect data from dsconnected parts of the networks. he helpng hosts are addressed by dfferent names n varous schemes. In [2-7], they are referred to as ferres, whle n [8-10], they are called helpng nodes or forwardng nodes. Data MULEs n [11-13] are also known as a knd of helpng hosts, and n the DakNet project [14] buses are used as helpng nodes to connect broadband network to rural vllages. One of the most mportant and commonly dscussed objectves of these schemes s to enhance the connectvty and mze the communcaton delay n the network. On contrary, helpng hosts movement consumes conerable amount of energy and tme, and may cause Copyrght 2010 ScRes.

2 892. WANG E AL. long message delay n the network. o effcently utlze them, the deployment and route desgn of helpng hosts are crucal. In ths paper, we propose a new helpng host scheme for partton restoraton n MANEs, namely the Message Cab (MCab) scheme. he helpng hosts are lke cabs, n the sense that they are more flexble and adaptve to traffc than buses or ferres. he MCab scheme conssts of two essental parts, namely the Dynamc Cab Deployment (DCD) algorthm and the Adaptve Cab Route (ACR) algorthm for the purposes of selectng message cabs and mprovng the message cab route, respectvely. Both algorthms are able to deal wth fluctuatng traffc n the network, whch s a practcal scenaro n real lfe, but s not usually dscussed n the exstng works. herefore we say that the message cabs are flexble helpng hosts. We wll demonstrate that the MCab scheme overcomes the drawbacks of exstng schemes by ncurrng lower average message delay and the results are valdated through smulatons. In the followng parts of ths paper, we ntroduce the backgrounds of our work n Secton 2, and the model together wth our objectves n Secton 3. he two parts of the Message Cab (MCab) scheme, namely the Dynamc Cab Deployment (DCD) algorthm and the Adaptve Cab Route (ACR) algorthm are presented n Secton 4 and 5, respectvely. Smulaton and results are dscussed n Secton 6, whle Secton 7 concludes ths paper. 2. Background Before we present our proposed Message Cab (MCab) scheme, we need to explan two mportant concepts, namely the deployment and route desgn of the helpng hosts (or cabs n our scheme), together wth some exstng solutons. In addton, our assumptons and notatons are dscussed n ths secton Deployment Deployment s a procedure for selectng helpng hosts. In most of the exstng works, such as [2,10,13,14], the helpng hosts are a group of specally desgned hosts that have larger storage, more energy and/or hgher movng speed. hey are dfferent from the normal hosts and are assgned as helpng hosts pror to the commencement of network operatons. he deployment s thus statc, or determnstc. Such deployment mechansms allows helpng hosts to have hgher capablty n delverng messages across parttons but s less flexble. Snce the number of helpng hosts s fxed, t may turns out that there s too many, or too few helpng hosts to meet the traffc demand n the network. hus statc deployment may not be adaptve to network traffc demand. o overcome ths drawback, dynamc deployment s used n [8], where normal hosts wth sutable movng drecton and speed are chosen as helpng hosts (a.k.a helpng nodes). However, t s a centralzed scheme and thus not scalable wth network sze. More mportantly, under the assumpton that the network s parttoned, t s nfeasble to make all the hosts movement nformaton avalable to a central server to perform the selecton. Smlar problem can also be observed n [9]. herefore, we propose a localzed algorthm, namely the Dynamc Cab Deployment (DCD) algorthm to deploy helpng hosts (.e. message cabs) n the MCab scheme. he DCD algorthm allows the number of helpng hosts to change dynamcally wth the traffc volume, and thereby reduces the weghted average delay of messages n the network, and enhances the scalablty of the deployment process Route Desgn he route of a helpng host s the path t follows, whch usually connects dfferent parttons or hosts n the network. In [8,12,14], the route s not planned by any algorthm. he hosts random movement s utlzed to delver messages. However, t has been shown n many other works that the message delay can be sgnfcantly reduced f we coner the problem of route desgn as an optmzaton problem. For example, n [2], Zhao et al. have formulated the Massage Ferry Route (MFR) problem to fnd the optmal route for helpng hosts (.e. message ferres). In [4-7], solutons from the well studed ravelng Salesman Problem (SP) and ts varants are adopted as routes for helpnghosts. In these schemes, the route does not change after beng constructed, and s thus a fxed route. It s only sutable when the network traffc among the parttons s constant, whch s an dealzed assumpton. In most of the practcal cases, the traffc between any two parttons wll be a temporal varable, and the route should be able to adapt to the changes. Hence fxed routes are unlkely to be optmal n general. herefore, an adaptve route s more desrable. Ou et al. proposed a centralzed scheme n [10] to let the helpng hosts (a.k.a helpng nodes) move adaptvely to the packets destnatons. However, as we have dscussed n the prevous secton, centralzed schemes may perform poorly when the network s parttoned. In ths paper we propose a dstrbuted algorthm, namely the Adaptve Cab Route (ACR) algorthm, to construct cab routes by adoptng the Shortest Process me Frst (SPF) rule from the Job Sequencng Problem (JSP). Smulaton proves that our proposed scheme s able to effectvely reduce the message delay n the network. Copyrght 2010 ScRes.

3 . WANG E AL Assumptons and Notatons Whle many exstng schemes (e.g. [2,7,11] ) focus on statonary hosts wth known locatons and predctable network traffc, we try to deal wth a more practcal scenaro, where: the hosts are moble; the traffc n the network s randomly varant and s thus not predctable. As dscussed n [15], movements of hosts n MANEs can be conered as Levy Flghts, n whch the hosts tend to stay n a certan area for a long tme and occasonally make long dstance flghts to places far away. We could thus assume that a host stays n the same cluster for a certan perod of tme and wll also sometmes decdes to move to another cluster. Practcally, ths could be due to the assgent of tasks to the host, such as n a wreless sensor network, a sensor may need to reallocate tself to new postons to collect new data. Let s assume that the MANE of our nterest has n h moble hosts. We assume the network s parttoned to n c components, each of whch forms a cluster wth a chosen cluster head. he hosts n the same cluster are always connected. In order to smplfy the problem, we restrct the movement of a cluster head to be ne a crcular area, whch s referred to as the head zone. he radus of head zone s equal to the communcaton range of the cluster head, denoted as r, as shown n Fgure 1. he center of head zone of cluster s s denoted as pont 1 s n c. We use to denote the tme taken by a host to travel from C s to C d,1 s, d nc. We note that s a postve real number. We say cluster d s a neghbor of cluster s f a host s able to move drectly to cluster d from cluster s n one hop. Usng proper clusterng schemes, such as [16], the cluster head wll always be aware of the changes n ts cluster members, such as the movements, arrvals of new members and departures of exstng members. It also knows the locatons of other clusters, so when a host decdes to move to a new place, the cluster head knows whch s the next cluster the host s gong to jon. In add- Fgure 1. Network topology. ton, the cluster head works as a proxy between other normal hosts n the cluster and the helpng host as well. If a helpng host stops at C s, t s able to communcate wth the head of cluster s and delver the messages to other hosts n cluster s va the cluster head. he route of a helpng host, denoted as R, wll be a sequence of head zone centers ( C s 's ). Each of these head zone centers s lke a waypont (as llustrated n Fgure 1), whch s a temporary destnaton for the helpng host. Upon arrvng a waypont, the helpng host stays for a perod of tme to delver and receve the messages to/from the cluster head, before movng on towards the next waypont. he route segment between two consecutve wayponts s referred to as a leg (shown n Fgure 1). 3. System Model and Objectves o demonstrate our methodology of the MCab scheme, we descrbe an analogy between the MANE and a smple transportaton system whch serves several small towns. It wll also explan the reason why we name our helpng hosts as cabs and how they are dfferent from ferres. he towns represent the clusters, each of whch s dstant away from the others. he cars are lke the hosts they usually move wthn a town, and when t s necessary, they are also able to move from one town to another. he passengers are akn to messages, whch by themselves cannot move from town to town. Buses are provded as an exstng soluton to the nter-town transportaton problem. hey are smlar to the other statcally deployed helpng hosts (such as message ferres) that we have dscussed n the prevous secton. he statc deployment and fxed route desgn of buses perform poorly wth varyng volume of passengers. Hence, t would be preferable f we have a flexble soluton. Bees takng buses, the passengers could coner hrng a cab to travel to another town. he route of a cab wll depend on the passengers demands, and s thus more flexble than the bus routes. Practcally, t s also more convenent n terms of savng tme to hre a cab. he number of cabs s determned by how many passengers there are. When there are more passengers, more cabs can be recruted from the prvate cars (normal hosts) avalable; when the number of passengers drops, some cabs could retre and become prvate cars agan. Moreover, snce t s possble that some cars wll move to another town by ther drvers own decsons, a passenger may also take a rde from a prvate car whch s also movng to the hs/her destnaton town. hs wll utlze the moblty of prvate cars n the transportaton system to serve the passengers needs and save ther travelng tme. A car offerng rde to passengers s lke a Copyrght 2010 ScRes.

4 894. WANG E AL. one-tme temporary cab that only works for a sngle trp to a partcular town. We refer to such cars as temp-cabs. o dstngush from them, we refer to those cabs that works for multple trps n a longer perod of tme as professonal cabs, or pro-cabs. We mtate the method of hrng pro-cabs and takng rdes from temp-cabs n the MANEs and propose the Message Cab (MCab) scheme. As shown n Fgure 2, the state of a prvate car (normal host), whch s not a cab nor a cluster head, can transform to a pro-cab or a tempcab under the control of the Dynamc Cab Deployment (DCD) algorthm: Pro-Cab Its movement s passvely determned by the Adaptve Cab Route (ACR) algorthm, n whch the route s adaptvely desgned based on the network traffc. It s recruted from a normal host, and contnues movng among the clusters for a certan predetermned perod of tme before retrng to be a normal host. emp-cab Its movement s pro-actvely determned by the host tself. It s a one-tme helpng host that only leaves ts orgnal cluster to ts destnaton cluster. It becomes a normal host agan after t arrves and has delvered the nter-cluster messages to the destnaton cluster. he key dfference between message cabs and the other types of helpng hosts n the exstng works (such as ferres, helpng nodes etc.) s that they are not selected before the network starts. herefore the number of cabs and cab routes can dynamcally change wth the traffc. Although ths knd of deployment does not allow the helpng hosts to have hgher capablty n movng speed or storage space (snce message cabs are just selected normal hosts), we found that t can stll effectvely reduce the message delay n the network. Snce hosts n the same cluster are connected, we can use exstng MANE routng protocols such as AODV or DSR for the communcaton between a cluster head and ts members. We note that the delay ncurred by the message transmsson wthn a cluster (ntra-cluster communcaton) s much smaller than the delvery between dfferent clusters (nter-cluster communcaton), and s less relevant to the cab deployment and route desgn. As a consequence, ntra-cluster communcaton wll be omtted n our followng dscusson. We should note that before a message s collected by a cab, t needs to wat at some cluster head for a certan tme duraton. We refer to ths amount of tme spent on watng as the watng delay of the message. After t s collected by a cab, the cab wll travel from ts source cluster to ts destnaton cluster, and thus ncurs a travelng delay for the message. herefore, the overall delay of a message s. Assume wthn tme duraton (0, t], there are n m messages that have been transmtted by the message cabs. he sze of message 1 s. he watng, travelng and overall delay of message are denoted as and, and.respectvely. Smlar to the objectves n [2-4], we are nterested n reducng the weghted average overall delay of the messages: where the weghted average watng delay ( ) s gven by 1, 1 and the weghted average travelng delay ( ) of all the messages can be taken as 1 1, We can see that f there are more cabs n the network, each cluster could be vsted more frequently, and the watng delay of messages reduces. It shows that the watng delay s closely related to the cab deployment plan. On the other hand, optmzaton of cab routes results n a shorter travelng delay. In the MCab scheme, we bound from above by usng the Dynamc Cab Deployment (DCD) algorthm to control the number of cabs, and s reduced by adoptng optmzaton technques n the Adaptve Cab Route (ACR) algorthm, whch desgns the routes of the cabs. (1) (2) (3) 4. Deployment of Message Cabs Fgure 2. States of a host In the deal scenaro, once a nter-cluster message s receved by the cluster head, there s always a cab ready to Copyrght 2010 ScRes.

5 . WANG E AL. 895 carry t towards ts destnaton, and wll be 0. However, n practce, wth unpredctable and fluctuatng traffc, t s mpossble to have a cab ready for message delvery as soon as a message arrves at the cluster head. It would also be neffcent f a cab carres only one message and does not fully utlze ts storage space. o solve ths problem, we try to make use of the normal hosts moblty as a temp-cab to gve a rde to the messages as well as to recrut pro-cabs from normal hosts n the DCD algorthm. We show that by dong so, we are able to bound the weghted watng delay of messages from above by a predetermned value, denoted as seconds. Snce the change of cluster membershp s handled by the cluster head, a host (say host a ) needs to report to the head of ts current cluster, say cluster s (as source) before t leaves for a new locaton. he cluster head of clusters then knows the new cluster (say cluster d, as destnaton) host a s gong to jon. It becomes possble that the head of cluster s lets host a to carry some messages whch have cluster d as ther destnatons. Host a a wll then delver these messages to the cluster head d when t arrves there and regsters tself as a new cluster member. herefore, when a host s leavng a cluster, ts state changes from normal host to temp-cab, and t s used to delver as many messages as possble across the parttoned clusters. Upon ts arrval, t delvers the messages to the head of the new cluster and ts state changes back to that of a normal host. hs procedure of deployng a temp-cab s depcted n Fgure 3(a). On the other hand, a tmer s used to control the tme when a pro-cab should be selected. Assumng there are n ' m nter-cluster messages stored n cluster head s, of each the sze s. he current watng delay of a message s the length of the tme duraton snce the message s receved by the cluster head, and s denoted as '. he tmer s set to t n' m ', 1 n' m 1 so that f a pro-cab s recruted rght before the tmer expres, the average weghted delay of the messages stored n cluster head s wll be less than, whch s the requred upper bound. We note that the value of t needs to be updated every tme there s a change n the number of nter-cluster messages whch are stored n cluster head s, such as when a new nter-cluster message s receved and stored, or when some messages have been uploaded to a cab (ether temp or pro) by cluster head s. We let the tme duraton between the recrutment and retrement of a cab be denoted as. After havng served for seconds as a pro-cab, t retres. Upon ts re trement, a pro-cab does not stop mmedately. It contnues movng among the clusters to delver the remanng messages t has already collected, but wthout collectng new messages. When all the messages are delvered, t moves back to the cluster where t has been recruted, and regster wth the head as a normal host agan. Fgure 3 depcts the flowcharts for the DCD algorthm. o avod gong nto too much detals, we make some smplfcatons to the algorthm: he pro-cabs are randomly selected from the normal hosts n the cluster; If a cab does not have enough space to store all the messages for nter-cluster delvery, t delvers those messages wth larger weghted watng delay ' frst; When the memory of a cluster head overflows, those messages wth larger weghted watng delay ' wll also be dropped frst (.e. the hot-potato rule 1 ); he value of (.e. the length of tme duraton between the recrutment and retrement of the cabs) s a constant. Wth these smplfcatons, the DCD algorthm s a fully dstrbuted scheme whch does not requre any global nformaton. Lemma 1. he worst case complexty of the DCD algorthm s On m, where s the number of messages that have been generated durng the perod of network operaton. Proof: Based on the algorthm depcted n Fgure 3, we can observe the fact that the complexty of the procedures s ndependent of the number of clusters and the number of hosts. o update the tmer (refer to step 5 n Fgure 3(a) and step 3 n Fgure 3(b)), the cluster head needs to go through the messages that have been stored n ts memory space ( n ' m messages). In the worst case, all the messages are stored, and t thus requres On m tme. On the other hand, to upload the messages to the cab (step 4 n Fgure 3(a) and step 2 n Fgure 3(b)), and to delver the messages to another cluster head (step 7 n n Fgure 3(a), step 5 and step 8 n Fgure 3(b)), t requres O n m tme as well. We note that the plannng of routes (step 6 n n Fgure 3(a), step 4 and step 7 n Fgure 3(b)) wll be handled by the ACR algorthm, and s not part of cab deployment process handled by the DCD algorthm; thus ts complexty wll not be counted here. In addton, step 1 n Fgure 3(a) s handled by the clusterng scheme, and the pro-cab selecton (step 1 n Fgure 3(b)) s random accordng to our assumptons. herefore they do not ncur addtonal com- 1 We deal wth the elements that have heavest mpact to the system by ether processng them or droppng them frst. By droppng those messages wth heaver weghted delay, the average weghted delay of the success-fully delvered messages can be reduced. Copyrght 2010 ScRes.

6 896. WANG E AL. Cab Route (MCR) problem as a generalzaton of the exstng Massage Ferry Route (MFR) problem, and propose the Adaptve Cab Route (ACR) algorthm as a soluton. Snce only the pro-cabs route wll be desgned by our algorthm, we refer to them as cabs for the sake of convenence n ths secton he Message Cab Route (MCR) Problem In [2], Zhao et al. have formulated the Massage Ferry Route (MFR) problem to fnd the optmal route for helpng hosts (.e. message ferres), and ts objectve s to mze the average delay of the traffc: R R 1 s, dnb c = (4) b 1, nc where b s the average traffc per unt tme from s to d and R s the tme spent by the ferry to travel from (a)emp-cab (b) Pro-Cab Fgure 3. Flowcharts of the dynamc cab deployment (DCD) algorthm. plexty to the DCD algorthm. In addton, the f clauses (steps 2, 3 n Fgure 3(a) and step 6, 9 n Fgure 3(b) does not ncur addtonal complexty to the algorthm. As a result, the overall complexty of the DCD algorthm s O n m 5. Message CAB Route Desgn o mprove the route of cabs, we defne the Message s to d on the statc route R. But n our case, b could not be determned beforehand because we have assumed that the traffc s unpredctable. Moreover, when R s not fxed (.e. beng adaptve nstead), the travelng delay from one cluster to another s not a constant. herefore the solutons for the MFR problem may not perform well for the problem that we are addressng. Hence we defne a generalzed verson of the MFR problem whch s able to adapt to both statc and dynamc traffc demand and routes. We refer to ths problem as the Message Cab Route (MCR) problem: Defnton 1. (he Message Cab Route (MCR) problem) For a gven group of clusters, fnd the optmal vstng sequence for a cab, so that the weghted average travelng delay to delver n m messages, whch s expressed by 1 1 where s the travelng delay of message, can be mzed. We could make the followng observatons from the MCR problem: he MCR problem s a generalzaton of the MFR problem. In the MFR problem, there are two addtonal assumptons made as compared to the MCR problem, namely the traffc rate b between two clusters s constant, and the dstance R from cluster s to d on the gven route R s also a fxed value. hat s, for any message sent from cluster s to cluster d, ts travelng delay wll be. Let s say the network R operates (5) Copyrght 2010 ScRes.

7 . WANG E AL. 897 from tme 0 to t. he total sze of all the messages that have been generated durng ths perod can be expressed as 1 s, dntb c. On the other hand, usng our notaton, snce the number of these messages s n m, and the sze of each message s de- noted by and thus, the total sze s thus 1, n c 1 t b 1 s, dn c tb n m R 1 n m 1. herefore Equaton (5) becomes equvalent to Equaton 4 under the assumptons of the MFR problem. Hence t s easy to see that the MCR problem s a generalzed verson of the MFR problem. he MCR problem s MAX-SNP-hard, and thus polynomal tme approxmaton schemes are unlkely to exsts to ths problem. We coner a smpler specal case of the MCR problem. Coner a partcular nstance where a cab collects nc 1 messages, each for a dstnct destnaton cluster, from cluster s. Before t fnshes delverng these messages, other clusters do not upload any new message to the cab. he objectve functon, Equaton (5) therefore becomes nc 1 1 nc 1 1 hs s exactly the objectve functon of the Weghted Mum Latency Problem (WMLP) [17], where s referred to as the latency of the tour startng from s to the destnaton cluster of message, and s the weght. In the WMLP, we try to fnd the tour that vsts all the vertces n a graph that mzes the weghted latency, represented by the above equaton. Unfortunately, the WMLP s known to be a MAX-SNP-hard problem [18]. Generally, there s no polynomal tme approxmaton scheme for MAX-SNP-hard problems [19]. Even for a more smplfed scenaro, where s constant and the traffc s unform among the clusters, to mze n c 1 1., we stll need to solve the rav- elng Salesman Problem (SP), whch s also known to be NP-hard. herefore, t s nfeasble to completely generate an optmzed cab route. A statc route cannot be an optmal soluton. hs s because n the network, traffc cannot be constant and unform all the tme. If some cluster receves messages more frequently than others, t wll be a waste of tme to vst all the other clusters before returnng to, whch s what that wll take place wth a statc route. Moreover, due to the nature of some of the MANE tasks, such as area exploraton or survellance, the frequency and szes of messages may vary over tme. A statc route could not adapt tself to such changes. he key to fndng a sutable cab route s to determne the next leg. he cab stops to delver and collect messages to/from a cluster head after each leg. herefore, we do not need to plan the route beyond the next leg, as the future legs should be adaptvely determned accordng to the messages the ferry collects n the future and have not been unveled to the ferry yet. herefore, f a scheme can produce each leg optmally, t offers a good soluton to the MCR problem. Based on the above observatons, we use a weghtng scheme to choose the best 2 cluster head among all the neghbors as the next waypont for a cab to move to and ths n turn wll eventually forms an adaptve route. he Shortest Process me Frst (SPF) rule from the Job Schedulng Problem (JSP) s adopted to compute the weght of the clusters, and we refer to our proposed approach as the Adaptve Cab Route (ACR) algorthm he Shortest Process me Frst (SPF) Rule In the Job Sequencng Problem (JSP) [20] of a sngle machne, we need to fnd the optmal sequence of a seres of jobs k wth weght 3 l k and processng tme p k to mze the average delay of these jobs whch s gven by: klkk jsp klk Smth proved n [21] that the optmal soluton to JSP can be produced by applyng the Shortest Process me Frst (SPF) rule to sequence the jobs: SPF Rule: Sequencng the jobs n order of nondecreasng rato pk l k produces an optmal schedule to mze jsp. Comparng Equaton (6) wth Equaton (3), we can observe that the objectve functons of JSP and MCR are smlar (detals wll be dscussed n the next Secton). Hence SPF would be a useful tool to construct adaptve ferry routes. In ths paper, to ensure that the equatons that we derve n the next Secton are well defned, we 2 As the most sutable waypont n a cab route to mze 3 Larger l k represents hgher mportance and vce versa. Copyrght 2010 ScRes.

8 898. WANG E AL. defne an nverse SPF (SPF) rule: SPF Rule: o optmally sequence the jobs n JSP, the job wth hghest lk p k value should be chosen frst. It s easy to see that SPF s logcally equvalent to SPF. hey are both able to solve JSP optmally he Adaptve Cab Route (ACR) Algorthm We may nterpret the event that the cab goes to a destnaton cluster d as job d. Assumng the cab s currently at cluster s, we could say that the requred processng tme of job d s the travelng tme from cluster s to cluster d, e.., whch s smlar to p k n JSP. In order to apply the SPF rule, we need to determne the weght l k of these jobs. We note n JSP, the weght of a job ndcates the how much each job contrbutes to the objectve functon jsp. Smlarly, job d contrbutes to n the MCR problem by delverng the messages wth destnatons n cluster d. Usng dest to denote the ndex of the destnaton cluster of message (.e. message s meant to be delvered to C dest ), the total sze of messages delvered by the cab n job d can be expressed as. d dest : We use ths value as the weght of job d (lke l k n JSP). hen we can choose the cluster wth maxmal rato of Md as the next waypont of the adaptve cab route accordng to the SPF rule. We also note that MCR and JSP are stll two dfferent problems. Because n MCR, vares when the cab s locaton (cluster s) changes, whle n JSP p k s constant. herefore SPF may not provde the exact optmal soluton to MCR. However, we beleve t stll provdes a good ndcaton of whch cluster head should be chosen to be the next waypont. Accordng to SPF, we could defne a weghtng functon W d as d (7) Wd ε A cluster wth the maxmal weght wll be chosen as the next waypont n the adaptve route. o break a te, we defne d as the tme of the most recent arrval of the cab at cluster d. Gven any two clusters C 1 and C 2, f 1 < 2, t means that the tme snce the last cab s arrval to cluster C 1 s longer than that to cluster C 2. If the two clustersboth have the maxmum weght W among all the clusters, C 1 wll be chosen as the next waypont. he algorthm shown n able 1 llustrates how the ACR algorthm determnes the cab s next waypont when t arrves cluster s at tme. Lemma 2. he complexty of the ACR algorthm s able 1. ACR algorthm. ACR(cluster s, tme ){ ntalze W 0 d and M 0 d for all d for each un-delvered message do %Loop 1% dest for each cluster d do %Loop 2% d Wd for all the clusters do %Loop 3% fnd d max of whch W s the maxmum dmax f there are multple that d ' s W W then d' dmax for all the d ' s do %Loop 4% fnd d ' max of whch d ' max s the mum the next waypont s C d else the next waypont s C set s } 'max dmax O nc. Proof: In Loop 1 of ACR, the algorthm goes through the cab s storage to calculate the accumulated sze of messages that wll be delvered to cluster dest. Snce the total number of messages s, Loop 1 takes On m tme n the worst case. o calculate the weght W d for each cluster n Loop 2, the algorthm goes through all the n c clusters and therefore On c tme s requred. Smlarly, n order to fnd the cluster wth maxmum weght, another On c tme s requred n Loop 3. o break the te, Loop 4 wll be executed for Onc tmes n the worst case. he overall complexty for algorthm ACR s thus Onc. We note the complexty of the ACR algorthm (Lemma 2) as well as the DCD algorthm (Lemma 1) s much lower than most of the exstng schemes wth helpng hosts. Moreover, beng a fully localzed scheme, MCab s extremely sutable for the MANEs where the resources are lmted. 6. Smulaton Results o valdate the effectveness of the MCab scheme, extensve smulatons are carred out. We randomly generate the network topology and traffc n C++ programs and compare the results wth exstng schemes. We model a MANE constructed n a 500 m by 500 m area. he number of hosts n each cluster s set to 20 at the begnnng of the smulatons. he communcaton range of the hosts s 5 m, and the storage sze s 10Mb. he hosts move at a speed of 10 m/s. he traffc n the MANE can be specfed by the number of messages per unt tme, but as the sze of messages also vares, t s more convenent to descrbe t as the sze of data transmtted per unt tme,.e. klobts Copyrght 2010 ScRes.

9 . WANG E AL. 899 per second (kb/s). We refer t as the volume of the traffc. he number of pro-cabs may vary n the smulaton. We defne the effectve number of pro-cabs as the average number of pro-cabs over tme to descrbe how many pro-cabs are deployed n the MANE Performance of the DCD Algorthm We start wth our study on the performance of the DCD algorthm. he man objectve of the DCD algorthm s to dynamcally recrut cabs n the MANE to delver nter-cluster messages. he algorthm s controlled by two parameters, namely (the upper bound of the weghted watng delay) and (the tme duraton that a host serves as a pro-cab). o deploy temp-cabs, the performance of the DCD algorthm s also closely related to the frequency n whch the hosts move from one cluster to another. A varable s defned as the average length of perod (n seconds) that a host stays n a cluster before t moves to another one. Fgure 4 dsplays how the number of recruted cabs changes wth the volume of nter-cluster traffc. he left vertcal axs corresponds to the traffc volume whle the number of pro-cabs are ndcated on the rght axs. o study the mpact of, and on the performance of the DCD algorthm, we choose two (hgh and low) values for each of these varables. Each of the fgures corresponds to a partcular combnaton of the values of and, and plots the two groups of results whch correspond to the two values of. As shown n able 2, the values of are 500 s and 100 s; the values of are 2000 s and 200s; the values of are 5000 s and 200s. he effectve number of pro-cabs are also shown n able 2. 1) he value of : he value of sgnfcantly changes the effectve number of pro-cabs. Wth a hgh value of ( = 5000 s), the hosts tend to stay n the same cluster for a long tme, and thus there are less chances that messages could be delvered by a temp-cab. herefore, more pro-cabs have to be recruted to keep the watng delay below. If the value of s low ( = 200 s), t mples that the hosts frequently move among the clusters. herefore a lot of nter-cluster messages could be delvered by temp-cabs, and there are fewer messages that are left on the cluster head. herefore, fewer pro-cabs need to be recruted. able 2. Effectve Number of Pro-Cabs. 200s 5000s 2000s 200s 200s 2000s 100s s We can observe ths phenomenon n Fgure 4(a) and Fgure 4(c) by comparng lne 1 ( 200 s, 100 s, 5000 s ) wth lne 5 ( 200 s, 100 s, = 200 s). For the same values of and, more procabs wll be recruted when 2000 s, as depcted by lne 1. When decreases to 200 s, more temp-cabs could be used, and thus fewer pro-cabs are needed to delver the messages, as shown by lne 5. Smlar fact can be observed by comparng lne 2 wth lne 6, lne 3 wth lne 7, and lne 4 wth lne 8 n Fgure 4. In able 2, we can also see the effectve number of pro-cabs s much smaller when s low ( 200 s ). 2) he value of : controls the duraton for whch a host serves as a pro-cab. It controls the frequency for trggerng the pro-cab recrutng procedure, and thus affects how fast the system could respond to the change n traffc volume. When the value of s hgh ( 2000 s ), the procabs have a long servce tme and a slow retrement. Comparng lne 1 wth lne 2 n Fgure 4(a) on the tme nterval [7000, 8000], we can see that the number of cabs stays as hgh as 6 when 2000 s (as depcted by lne 2) even though the traffc volume has already dropped to a lower level, where only about 3 pro-cabs wll be deployed f 200 s (as depcted by lne 1), meanng that several cabs may be unnecessary for the purpose of keepng the weghted watng delay low. Smlar phenomena can also be observed n the tme nterval [4000, 5000] n Fgure 4(a), [9000, 10000] n Fgure 4(b), and [8500, 10000] n Fgure 4(c), resultng n the effectve numbers of cabs beng much larger when = 2000 s (as shown n able 2). A low value of ( 200 s ) causes the pro-cabs to only serve for a short perod of tme, and change back to the state of normal host sooner. However, messages are stll beng generated and stored n the cluster heads, causng new pro-cabs to be recruted. he change n the cab number s thus more rapd and frequent than when 2000 s. Snce cabs are frequently recruted and retred and lnes 1, 3, 5 and 7 appear to be more spky than lnes 2, 4, 6 and 8 respectvely n Fgure 4. We should also note that frequent change n the number of cabs may also cause unwanted nterrupton to the other tasks of the hosts. For example, n order to collect relable data, a sensor may need to stay statonary at the same poston for some mum duraton. Hence low values of may affect the effcency of the network task, although t s able to help to reduce the number of pro-cabs. 3) he value of : Comparng Fgure 4(a) wth Fgure 4(b), or Fgure 4(c) wth Fgure 4(d), we can also observe the fact that the value of nfluences the number of cabs more drectly. Copyrght 2010 ScRes.

10 900. WANG E AL. (a) = 100 s, = 5000 s When the value of s hgh ( 500 s ), the cluster heads are able to tolerate larger weghted watng delay before recrutng new pro-cabs, and less pro-cabs wll be hred n the MANEs. hs s the reason why n able 2, the effectve numbers of pro-cabs are much smaller when 500 s. On the other hand, f the value s low ( 100 s ), the cluster heads have to frequently hre new pro-cabs to keep the watng delay of the messages low. Comparng Fgure 4(a) wth Fgure 4(b), or Fgure 4(c) wth Fgure 4(d), t s easy to observe that the number of procabs sgnfcantly ncreases when the value of s low. In general, our smulaton results show that the DCD algorthm can effectvely adapts the number of cabs to the traffc volume of the network. We wll also show how t bounds the weghted watng delay below n Secton VI-C. Before that, the performance of the ACR algorthm wll be dscussed Performance of the ACR Algorthm (b) = 500 s, = 5000 s (c) = 100 s, = 200 s (d) = 500 s, = 200 s Fgure 4. Performance of the DCD algorthm. o evaluate the performance of the ACR algorthm, we assume that cabs are selected beforehand and are randomly deployed wthout the use of the DCD algorthm n ths secton. We compare the delay ncurred by the adaptve route constructed by the ACR algorthm wth the most commonly adopted soluton,.e. the SP route. It s well-known that SP s a NP-hard problem, where optmal soluton cannot be found wthn polynomal tme. We use brute force to fnd the optmal SP route n the smulaton. However t would only be feasble to use o address ths ssue, we also use the Improvng Search Algorthm [22] to fnd an approxmate soluton to SP as a feasble route. Both optmal and approxmate SP routes are statc and are used as benchmarks to compare wth the routes obtaned by the ACR algorthm. 10 clusters of hosts are conered for ths smulaton. he cabs are randomly allocated n dfferent clusters ntally, and move accordng to the routes generated by the ACR algorthm, optmal SP algorthm, or approxmate SP algorthm. he results are shown n Fgure 5. We can see that ncreasng the number of cabs reduces the average delay of the ACR routes, but no sgnfcant change can be observed for SP and approxmate SP routes. hs s because when the same statc route s used, the delay of a message only depends on the dstance between ts source and destnaton on the route, and s not affected by the number of cabs. herefore once the route s constructed, the delay of messages wll not be affected by the change n the number of cabs. On the other hand, when the ACR algorthm s used, each cab defnes ts own route based on the messages t Copyrght 2010 ScRes.

11 . WANG E AL. 901 Fgure 5. Performance of the ACR algorthm (travelng delay). s carryng. he delay of a message can be further shortened f there are fewer messages to be carred by a sngle cab. For example, f a cab only carres one message, t wll drectly move to the destnaton cluster of the message. A far amount of tme can be thus saved. As the number of cabs ncreases, fewer messages wll be carred by each of them, and the average delay s thus further decreased. Moreover, snce the ACR algorthm s fully dstrbuted, no collaboraton s needed among the cabs. Each of them can decde ts route locally. he ncrease n cab number does not affect the complexty of the scheme at all Overall Performance of the MCab Scheme In the MCab scheme, when both the DCD and ACR algorthms are appled for the cab deployment and route desgn, the average weghted delay s further reduced. We demonstrate ths result n Fgure 6 to Fgure 8 by showng how the MCab scheme perform when there are dfferent number of clusters n c. he three fgures dsplays the weghted average delay of the messages, the effectve number of pro-cabs and the percentage (n sze) of messages delvered by procabs, respectvely. In each fgure, two values of (5000 s and 200 s) are used n the smulaton. wo dfferent mplementatons of the DCD algorthm ( 100 s, 2000 s and 500 s, 200 s ) are demonstrated. he results for the other two cases ( 500 s, 2000 s and 100 s, 200 s ) exhbt smlar results, and are thus omtted n ths secton In Fgure 6 the smulaton results are shown as a group of columns. he upper part (above 0) of each column shows the duraton of average watng delay, and the lower part (below 0) shows the duraton of average travelng delay. As a result, the entre bar length shows the overall average delay of the correspondng scheme. We compare the results wth the case where a sngle helpng host s deployed n themf scheme, and moves on a SP route or an approxmate SP route. Moreover, we also plot the values of the average weghted delay when the ACR algorthm s appled to a sngle cab wthout the DCD algorthm n the fgure as a reference. It can be seen from Fgure 6 that the total delay s much lower wth the MCab scheme. Let s coner the case when there are 5 clusters. We can observe that for ths case the MF scheme wth approxmate SP ncurs the longest message delay. It s followed by the MF scheme wth optmal SP, because the optmal route of SP wll be shorter than an approxmate route. As we have shown n Secton VI-B, the ACR algorthm wll reduce the travelng delay by usng adaptve cab routes nstead of fxed ones. However, as the ACR algorthm calculates the weghts of the clusters based on the messages that have been stored n the cab, t does not guarantee a lower watng delay for those messages that have not yet been uploaded to the cabs. herefore, the watng delay s not sgnfcantly reduced by the ACR algorthm alone (wthout the DCD algorthm). Moreover, t can be observed n some partcular ncdences that t may ncur a slghtly hgher watng delay than the MF schemes (e.g s wth 15 clusters). When the DCD algorthm s also appled (.e. the MCab scheme), the watng delay s further reduced, because some of the messages can be carred by the temp-cabs and do not need to wat for the pro-cabs. he message delay reduces to the mum when the MCR scheme wth 100 s and 2000 s s adopted. hs s because when 100 s, more procabs are deployed than the case when 500 s as we dscussed n Secton VI-A. he same fact can also be observed from Fgure 7, where on average 4.5 pro-cabs are deployed to serve 5 clusters when 5000 s, 100 s as compare to 1.3 pro-cabs when 500 s. We note the other cluster szes n Fgure 6 also exhbt the same performance trend descrbed above. It should also be ponted out that when there are 5 clusters and 5000 s, the dfference between the results for MCab ( 500 s, 2000 s ) and ACR (wthout DCD) s not as sgnfcant as when there are more clusters, or when the value of s lower ( 200 s, n Fgure 6(b)). hs s because the watng delay n ths case s lower than 500 s even when there s only one cab. As a result, we note that the average number of cabs s also about 1 when the DCD algorthm s used, whch means t s not necessary to deploy more cabs to further reduce the average weghted watng delay n the MCab scheme. Moreover, snce the number of temp-cabs deployed n ths scenaro s also very few as s large, the performance s very smlar to the ACR (wthout DCD) case. Copyrght 2010 ScRes.

12 902. WANG E AL. (a) = 5000 s Fgure 6. Delay of messages. (b) = 200 s (a) = 5000 s Fgure 7. Effectve number of pro-cabs. (b) = 200 s (a) = 5000 s (b) = 200 s Fgure 8. Percentage of messages delvered by pro-cabs. When the number of clusters ncreases, the weghted average watng delay wth the ACR algorthm (wthout DCD) ncreases as well. hs s due to the fact that the pro-cab needs to vst more clusters before delverng the message to ts destnaton. As a result, when the DCD algorthm s appled (.e. the MCab scheme), more procabs wll be recruted to lower the watng delay so that t does not exceeds the predetermned upper bound. Moreover, we can observe that under the control of the DCD algorthm, the weghted average watng delay of Copyrght 2010 ScRes.

13 . WANG E AL. 903 the messages are bounded by the values of, whch are ndcated by the respectve reference lnes (500 s and 100 s) n Fgure 6. he effectveness of deployng temp-cabs can also be demonstrated by comparng the heght of the columns representng MCab scheme ( 500 s, 200 s ) n Fgure 6(a) and Fgure 6(b), where the values of weghted average watng delay decrease wth the value of. As decreases from 5000 s to 200 s, more temp-cabs can be used for nter-cluster message delvery, thus less pro- cabs are recruted (as depcted n Fgure 7), and a lower percentage of messages wll be delvered by the pro-cabs (as depcted n Fgure 8). It thus reduces the watng delay of the messages, snce some of them are taken to ther respectve destnaton clusters by temp-cabs before the tmer expres. hs phenomenon cannot be observed when 100 s, 2000 s, and when there are 20 clusters for 500 s, 200 s, because n these cases addtonal pro-cabs are recruted n order to bound the watng delay below. Interestngly, the travelng delay s also slghtly reduced by usng more temp-cabs. hs s because the messages carred by a temp-cab are selected based on ther destnatons. he temp-cab takes them from the source cluster head and moves drectly to ther destnaton cluster, whle a pro-cab s shared by messages wth dfferent destnatons, and may have to vst several other clusters (as destnatons of other messages stored n the pro-cab) before eventually delver these messages. However, as we can see from Fgure 8, the majorty of messages are delvered by the procabs n most of the scenaros, and the weghted average travelng delay s stll domnated by the routes of pro-cabs,.e. the ACR algorthm. In concluson, smulaton valdates that both the DCD and ACR algorthms works as we expected, and the MCab scheme effectvely reduces the average weghted watng delay. 7. Conclusons In ths paper, we propose a scheme wth flexble helpng hosts, namely Message Cab (MCab) for message delvery n parttoned MANEs. It conssts of two algorthms, referred to as the Dynamc Cab Deployment (DCD) algorthm and the Adaptve Cab Route (ACR) algorthm. he DCD algorthm dynamcally selects hosts to become the helpng hosts (cabs) and move among the clusters to delver nter-cluster messages, and the ACR algorthm desgns the route of the cabs so that the delay of the messages can be reduced. Comparng wth the exstng schemes wth helpng hosts, we have shown that the MCab scheme effectvely shorten the delay of the messages wth the smulatons and s adaptve to the varyng traffc n the network, whch has not been dscussed n the exstng works. 8. References [1] S. Corson and J. Macker, Moble Ad Hoc Networkng (MANE): Routng Protocol Performance Issues and Evaluaton Coneratons, Unted States, [2] W. Zhao and M. Ammar, Message Ferryng: Proactve Routng n Hghly-Parttoned Wreless Ad Hoc Networks, Proceedngs of the 9th IEEE Workshop on Future rends of Dstrbuted Computng Systems (FDCS 03), Washngton, DC, 2003, pp [3] W. Zhao, M. Ammar and E. Zegura, A Message Ferryng Approach for Data Delvery n Sparse Moble Ad hoc Networks, Proceedngs of the 5th ACM Internatonal Symposum on Moble Ad Hoc Networkng and Computng (MobHoc 04), New York, 2004, pp [4] W. Zhao, M. Ammar and E. Zegura, Controllng the Moblty of Multple Data ransport Ferres n a Delay-olerant Network, Proceedngs of the 24th Annual Jont Conference of the IEEE Computer and Communcatons Socetes (INFOCOM 05), Mam, Vol. 2, 2005, pp [5] M. M. B. arq, M. Ammar and E. Zegura, Message Ferry Route Desgn for Sparse Ad Hoc Networks wth Moble Nodes, Proceedngs of the 7th ACM nternatonal symposum on Moble Ad Hoc Networkng and Computng (MobHoc 06), New York, NY, 2006, pp [6] M. Ye, X. ang and D. L. Lee, Far Delay olerant Moble Data Ferryng, Proceedngs of the 10th Internatonal Conference on Moble Data Management: Systems, Servces and Mddle-ware (MDM 09). Washngton, DC, 2009, pp [7] M. H. Ammar, D. Chakrabarty, A. D. Sarma, S. Kalyanasundaram and R. J. Lpton, Algorthms for Message Ferryng on Moble Ad Hoc Networks, Proceedngs of the IARCS Annual Conference on Foundatons of Software echnology and heoretcal Computer Scence (FSCS 09), II Kanpur, 2009, pp [8] Q. L and D. Rus, Communcaton n Dsconnected Ad Hoc Networks Usng Message Relay, Journal of Parallel and Dstrbuted Computng, Vol. 63, No. 1, 2003, pp [9] S.-H. Chung, K.-F. Ssu, C.-H. Chou, and H. C. Jau, Improvng Data ransmsson wth Helpng Nodes for Geographcal Ad Hoc Routng, Computer Networks, Vol. 51, 2007, pp [10] C.-H. Ou, K.-F. Ssu and H. C. Jau, Connectng Network Parttons wth Locaton-Asssted Forwardng Nodes n Moble Ad Hoc Envroents, Proceedngs of the 10th IEEE Pacfc Rm Internatonal Symposum on Dependable Computng (PRDC 04), Washngton, DC, 2004, pp [11] D. Borsett, C. Casett, C.-F. Chassern, M. Fore and J. M. Barcel o-ordnas, Vrtual Data Mules for Data Col- Copyrght 2010 ScRes.