Global Optimization of File Availability Through Replication for Efficient File Sharing in MANETs

Transcription

1 Global Optimizatio of File Availability Through Replicatio for Efficiet File Sharig i MANETs Kag Che ad Haiyig She Departmet of Electrical ad Computer Egieerig Clemso Uiversity Clemso, South Carolia {kagc, sheh}@clemso.edu Abstract File sharig applicatios i mobile ad hoc etworks (MANETs) have attracted more ad more attetio i recet years. The efficiecy of file queryig suffers from the distictive properties of MANETs icludig ode mobility ad limited commuicatio rage ad resource. A ituitive method to alleviate this problem is to create file replicas i the etwork. However, despite the efforts o file replicatio, o research has focused o the global optimal replica sharig with miimum average queryig delay. Specifically, curret file replicatio protocols i MANETs have two shortcomigs. First, they lack a rule to allocate limited resource to differet files i order to miimize the average queryig delay. Secod, they simply cosider storage as resource for replicas, but eglect the fact that the file holders frequecy of meetig other odes also plays a importat role i determiig file availability. A ode havig a higher meetig frequecy with others provides higher availability to its files. I this paper, we itroduce a ew cocept of resource for file replicatio, which cosiders both ode storage ad meetig frequecy. We theoretically study the ifluece of resource allocatio o the average queryig delay ad derive a resource allocatio rule to miimize the average queryig delay. We further propose a distributed file replicatio protocol that follows the rule. The trace-drive experimets o both the real-world GENI testbed ad NS-2 show that our protocol ca achieve shorter average queryig delay at lower cost tha curret replicatio protocols, which justifies the correctess of our theoretical aalysis ad the effectiveess of the proposed protocol. I. INTRODUCTION File sharig applicatios, like Qik [1] ad Flixwago [2], i mobile ad hoc etworks (MANETs) have attracted more ad more attetio i recet years. Amog may feasible techiques, peer-to-peer (P2P) file sharig betwee odes i MANETs is promisig sice it avoids the problem of overloadig servers (i.e., base statios) i curret cliet-server based file sharig i the ifrastructure wireless etworks. Without the depedecy o cetral servers, odes ca freely ad uobtrusively access ad share files. For example, tourists ca share their travel experieces with other tourists or covey emergecy iformatio through their digital devices directly eve whe o base statio is available i remote areas. However, the distictive properties of MANETs, icludig ode mobility, limited commuicatio rage ad resource, have redered may difficulties i realizig such a P2P file sharig system. For example, file searchig turs out to be o-trivial ad time cosumig sice odes i MANETs move aroud freely ad ca exchage iformatio with others oly whe they are withi the commuicatio rage. Broadcastig ca quickly discover files, but it geerates the broadcast storm problem [3] with high eergy cosumptio. Probabilistic routig ad file discovery protocols [4] [6] avoid broadcastig by forwardig a query to a ode with higher probability of meetig the destiatio. But the opportuistic ecouterig of odes i MANETs may lead to large file discovery delay. File replicatio is a effective way to ehace file availability ad reduce the file queryig delay. It creates replicas for a file to improve its probability of beig ecoutered by requests. Ufortuately, it is impractical ad iefficiet to eable every ode to hold the replicas of all files i the system cosiderig limited ode resource. Also, file queryig delay is always a mai cocer i a file sharig system. Users ofte desire to receive their requested files quickly o matter the files are popular or upopular. Thus, a critical issue is raised for further ivestigatio: how to allocate the limited resource i the etwork to differet files for replicatio so that the overall average file queryig delay is miimized? Recetly, a umber of file replicatio protocols have bee proposed for MANETs [7] [11]. I these protocols, each idividual ode replicates files it frequetly queries [7] [9], or a group of odes create oe replica for each file they frequetly query [9] [11]. I the former, eighborig odes easily create redudat replicas i the system ad waste resource. Though group based file replicatio solves the problems by sharig replicas to be shared amog eighbors, eighborig odes may separate from each other due to ode mobility. I spite of the efforts, curret file replicatio protocols lack a rule to allocate limited resource to differet files for replica creatio i order to achieve the miimum global average queryig delay, i.e., global search efficiecy optimizatio uder limited resource. Moreover, they simply cosider storage as resource for replicas, but eglect that a ode s ability (i.e., frequecy) to meet other odes (meetig ability i short) also iflueces the availability of its files. Files i a ode with a higher meetig ability have higher file availability. I this paper, we itroduce a ew cocept of resource for file replicatio, which cosiders both ode storage ad ode meetig ability. The meetig ability of a ode is measured by the average umber odes it ca meet i a uit time. We theoretically study the ifluece of resource allocatio o the average queryig delay ad derive a optimal file replicatio rule that decides the amout of resource for each file based o its popularity ad size. To the best of our kowledge, this

2 work is the first attempt to theoretically ivestigate the problem of resource allocatio for replica creatio to achieve global file searchig optimizatio i MANETs. We further propose a file replicatio protocol that ca approximately realize the rule ad achieve the miimum global queryig delay i a fully distributed maer. Our experimet ad simulatio results show the superior performace of the proposed protocol i compariso with other represetative replicatio protocols. II. RELATED WORK The topic of file replicatio for efficiet file sharig applicatios i MANETs has bee studied recetly. I the proposed file replicatio protocols [9] [11], idividual or a group of odes decide the list of files to replicate accordig to file visitig frequecy. Hara [9] proposed three file replicatio protocols: Static Access Frequecy (), Dyamic Access Frequecy ad Neighborhood (DAFN) ad Dyamic Coectivity based Groupig (). I, each ode replicates its frequetly queried files util its available storage is used up. may lead to may duplicate replicas amog eighborig odes whe they have the same iterested files. DAFN elimiates duplicate replicas amog eighbors. further reduces duplicate replicas i a group of odes with frequet coectios. It sums the access frequecies of all odes i a group ad creates replicas for files i the descedig order. Though DAFN ad eable replicas to be shared amog eighbors, eighborig odes may separate from each other due to ode mobility. Also, they icur high traffic load i idetifyig duplicates or maagig groups. Zhag et al [10] proposed to let each ode collect access statistics from eighbors to decide the creatio or reliquishmet of a replica. Duog ad Demeure [11] proposed to group odes with stable coectios ad let each ode checks its group members potetial possibility of requestig a file ad their storage status to decide replicate the file or ot. Also, each ode otifies all other odes i the system about its ewly created files by broadcastig. Yi ad Cao [8] proposed to cache popular files o the itersectio odes of file retrieval paths. Though it is effective for popular files, it fails to utilize all storage space i odes other tha the itersectio odes. Giauzzi [12] ivestigated the probability of acquirig a file, which has replicas i the etwork, from the potetially partitioed etwork. He also studied the file retrieval performace whe erasure codig [13] is employed to segmet files. Che [14] discussed how to decide the miimal umber of mobile servers eeded to satisfy the requiremet that every data item ca be obtaied withi at most k (k 1) hops by ay ode i the system. Kha et al. [15] exploited game theory ad derived a paymet scheme to solve the egative effects brought about by selfish mobile servers. Moussaoui et al. [7] proposed two steps of file replicatio, primary replicatio ad dyamic replicatio, to dissemiate replicas i the etwork i order to meet user eeds ad prevet data loss i the case of etwork partitio. I the primary replicatio step, ewly created files are distributed evely amog odes that are three hops away from each other through replicatio. Later, whe the etwork topology chages, dyamic replicatio is coducted, i which each ode checks its visitig frequecy to a file or the desity of a file (i.e., the umber of hops a request for the file has traveled) to make the replicatio decisio. III. THEORETICAL ANALYSIS OF GLOBALLY OPTIMAL FILE REPLICATION A. Node Movemet Model We defie the meetig ability of a ode i MANETs as the average umber of odes it ca meet i a uit time. Differet odes have differet meetig abilities due to various reasos (e.g., velocity ad active level). Node movemet patter also iflueces the ode meetig ability. We cosider a MANET sceario i which the ode movemet patter follows the modified radom waypoit model (RWP) [16], which has bee used i several MANET replicatio protocol [9], [10], [12]. I RWP, odes repeatedly select a radomly destiatio ad move to it at a radom speed straightly. So the each ode has roughly similar meetig ability. We let each ode has a fixed speed, which is radomly obtaied from a rage, i the RWP model. So from the perspectively of oe ode, it has the same probability of meetig ay other ode, which meas o local gatherig exists i the system. Although odes move radomly i the modified RWP model, they may have differet meetig abilities due to differet velocities. For example, odes with faster speed ca meet other odes more frequetly (i.e., with short average separatio period). We regard our work based o the modified RWP as a fudametal work ad will briefly itroduce how to adapt our fudametal aalysis to other ode movemet models i the ed of this sectio. B. Theoretical Aalysis TABLE I: Notatios i aalysis. Notatio Meaig q j The probability of queryig file j i the system m i The probability that the ext ecoutered ode is ode i p j The probability of obtaiig file j i the ext ecoutered ode N Total umber of odes V i Node i s meetig ability (i.e., frequecy of meetig odes) S i Storage space of ode i V Average meetig ability of all odes i the system F Total umber of files i the system b j Size of file j X ij Whether ode i cotais file j or ot V jk Meetig ability of the k th ode that holds file j j The umber of replicas for file j A j Allocated resource for file j for replicatio T j Average umber of time itervals eeded to meet file j T Average umber of time itervals eeded to meet a file (average T j) R Total amout of resource i the system P j Priority Value of file j, P j = q j /b j We first theoretically aalyze the ifluece of the file replica distributio o the overall query efficiecy. We assume there is o update o files i the system. Please refer to Table I for the meaigs of otatios used i our aalysis. If a ode is able to meet more odes durig a time period uit, it meas the ode has higher probability of beig ecoutered by other odes later o. We use m i to deote the probability that the ext ode a request holder meets is ode i. The, m i is proportioal to ode i s ability to meet odes (i.e., V i ). The

3 m i = (1) V N where N deotes the total umber of odes ad V deotes the average meetig ability of all odes i the system. We use vector (V j0, V j1,..., V jk,... ) to deote the meetig abilities of a group of odes holdig file j or its replica. The, the probability that a ode obtais its requested file j from its ecouterig ode is the sum of the probabilities of ecouterig odes that hold file j or its replica. That is, N N V i j p j = m ix ij = V N Xij = V jk (2) V N i=1 i=1 Vi where X ij is a zero-oe variable that deotes whether ode i cotais file j or its replica ad j is the umber of file j (icludig replicas) i the system. As stated above, a ode s probability of beig ecoutered by other odes is proportioal to the meetig ability of the ode. This idicates that files residig i odes with higher meetig ability have higher availability tha files i odes with lower meetig ability. So we take ito accout both ode s meetig ability ad storage i measurig a ode s resource. Whe a replica is created i a ode, ts probability of beig met by others is decided by the ode s meetig ability. So we regard it cosumes both storage resource ad meetig ability resource of the ode. Therefore, we deote the resource o a ode by S i V i, i which S i deotes ode i s storage space ad V i deotes its meetig ability. The, the total amout of resource i the system (R) is: N R = S iv i (3) i=1 Thus, the total resource allocated to file j is: j R j = b j V jk (4) where b j is the size of file j. Based o Equatio (4), Equatio (2) ca be represeted as j b j V jk p j = b jv N = Rj (5) b jv N Thus, the probability of ecouterig file j after k (k = 1, 2, 3, ) itervals is (1 p j ) k 1 p j ad the average umber of time itervals eeded for a ode to meet a ode cotaiig file j is T j = k(1 p j) k 1 p j = 1 p j = bjv N R j (6) We use q j to deote the probability of origiatig a request for file j. The, the average umber of itervals eeded to satisfy a request is T = q jt j = q j b jv N R j = V N q jb j R j (7) We aim to miimize the global file queryig delay (i.e., T ) by file replicatio. Accordig to Equatio (7), T is decided by q j, b j ad R j, ad the values of q j ad b j are decided by the system. Thus, the problem of optimal resource allocatio is the coverted to fidig the optimal amout of resource (R j ) for each file j uder the restrictio of total available resource i order to achieve the miimum average queryig delay. Suppose B j = q j b j, with Equatios (3) ad (7), the problem of optimal resource allocatio is expressed by subject to: mi(t ) = mi{ q jb j R j R j R. } = mi{ B j R j } (8) Equatio (7) also idicates that each R j should be as large as possible i order to miimize T. Therefore, we let the sum of all R j equals R. R j = R (9) By applyig Formula (9), Formula (8) is chaged to mi(t ) = mi{ B 1 + B 2 B F + + R 1 R 2 R (R 1 + R R F 1 ) } (10) Next, we try to fid the value of R j (1 j F 1) that satisfies Formula (10). Specifically, we differetiate T o each R j (1 j F 1) respectively, ad fid the value of R j that makes the differetiated formula equal 0. The resultat formulas after differetiatio are B 1 B F R1 2 {R (R 1 + R R = 0 (11) F 1)} 2 B F 1 B F RF 2 1 {R (R 1 + R R = 0 (12) F 1)} 2 Combie all of the above F 1 equatios, we get B 1 = B2 = B3 BF 1 = = = BF (13) R1 2 R2 2 R3 2 RF 2 1 RF 2 Accordig to Equatio (9) ad Equatio (13), we ca see that the optimal allocatio is R j = Bj R (j = 1, 2, 3,, F ) (14) Bk This meas that the optimal resource allocatio is achieved through the square root policy, i.e., the portio of resource for file j is i direct proportio of the square root of B j : j R j B j b j V jk b jq j (15) That is j V jk qj b j j V jk P j (16) We call q j /b j the Priority Value (P ) of file j as it represets the relative priority i acquirig resource i order to realize the global optimizatio o queryig delay. By covertig Formula (15) to Formula (16), we covert the double-factor cosideratio (i.e., both storage ad meetig

4 ability) i the resource allocatio to the sigle-factor cosideratio (i.e., meetig ability). This is reasoable sice oce a replica is created, it aturally takes the storage resource ad meetig ability resource at the same time. Based o Formula (16), we derive the Optimal File Replicatio Rule (OFRR) that gives the directio for the optimal resource allocatio for each file that leads to the miimum average file queryig delay. OFRR. I order to achieve miimum overall file queryig delay, the sum of the meetig ability of replica odes of file j should be proportioal to P j = q j /b j. It is iterestig to fid that OFRR matches the square root assigmet rule derived by Kleirock [17] for the lik capacity assigmet i wireless commuicatio to maximize the etwork efficiecy. It also matches the fidigs i [18] that whe file servers may become uavailable due to ode dyamism, the wired P2P cotet distributio systems ca achieve the maximum file hit rate whe available storage is allocated i proportioal to a costat value plus l(q j /b j ) for each file. C. Extesio to Other Node Movemet Models Although above results are obtaied based o the modified RWP model i which odes move radomly ad idepedetly, the aalysis process ca be geeralized ad adapted to other ode movemet models. I ay kid of ode movemet model, we first eed to figure out the probability that the ewly met ode is ode i (i.e., m i i Formula (1)), which reflects the meetig ability resource of ode i. The, followig similar procedures from Formula (2) to Formula (6), the average umber of time itervals eeded to meet a specific file, say file j, ca be represeted as: T j = 1 p j = 1 (17) N m i Xij where p j ad m i represet p j ad m i uder the ew movemet model. The, similar to Formula (7), the average umber of itervals eeded to satisfy a request is T = q jt j = i=1 F q j, (18) N m i Xij where T represets T uder the ew movemet model. With Formula (18), we ca formulate the global optimizatio problem as miimizig T uder limited resource ad deduce the optimal resource allocatio rule. However, the calculatio of m i may be complex ad makes the miimizatio problem o-trivial i complex mobility models. For example, i the recetly proposed commuity based mobility model [19], odes gather together accordig to their social relatioships. Therefore, odes i the same commuity meet with each other more ofte tha with others. The, a ode s probability of meetig ode i i the ext ecouterig (m i ) differs from ode to ode sice we eed to cosider whether the ode ad ode i belog to the same i=1 social commuity. Further exploratio of the optimal resource allocatio rule uder other models is beyod the scope of this paper, ad we leave it as our future work. IV. DISTRIBUTED FILE REPLICATION PROTOCOL A. Challeges to Achieve the Optimal File Replicatio Rule Challege 1: resource allocatio without a cetral server. OFRR ad Formula (15) show that i order to realize the globally optimal queryig delay, each ode eeds to kow the popularity (q j ) ad size (b j ) of all files ad the total available resource to decide the portio of resource for each of its files for replica creatio. Specifically, suppose there are F files i the system with b 1 q 1 b F q F ad total resource R, the resource allocated to file j (R j ) is R j = R b jq j/ bk q k (19) So, a ituitive way to attai this goal is to setup a cetral server to collect ad distribute required iformatio. However, the ature of the distributed etwork, ode mobility ad trasmissio rage costrait become obstacles of buildig such a cetral service. Sice odes are costatly movig ad have limited commuicatio rages, it is impossible for each ode to update its iformatio to or receive iformatio from the server i a timely fashio. Thus, a severe challege is how to eable a ode to distributively figure out the proper portio of resource for each of its files without a cetral server. Eve though each ode kows b F jq j/ bk q k of each of its files, because of the time-varyig available total resource i the system (R) due to ode jois ad departures ad the total umber of files (F ) due to file deletios ad creatios, it is difficult for a ode to calculate the portio of resource of each of its file (R j ). For example, suppose there are oly two files i the system, say f 1 ad f 2, ad the ratio of their allocated resources is 4:1. If the total amout of resource R = 40, the amout of resource allocated to f 1 is 32. If R = 60, the amout for f 1 should be adjusted to 48. If f 2 is deleted, the amout for f 1 the should be 60. Further, the time-varyig file popularity ad subsequet chage of b j q j make the problem eve more formidable. Therefore, OFRR caot be simply realized by lettig each ode distribute replicas of a file util a absolute amout of resource is used for the replicas. Solutio to Challege 1: resource competitio. Formula (16) shows that the sum of the meetig ability of replica F odes of each file, V F k, is proportioal to the file s priority value P. This also meas that the ratio of each file s P to its F V F k has the same value. Therefore, OFRR fially achieves 1 2 F P 1/ V 1k = P 2/ V 2k = P F / V F k (20) where j (j [1, 2,, F ]) represets the umber of replica odes of file j. The we ca let each file, say file j, periodically compete for the resource with its curret P j j/ V jk. I oe competitio, the file with the highest P j / j V jk wis ad receives resource for oe replica. After a file creates a replica, its P j j/ V jk decreases. The competitio stops

5 whe all available resource is allocated ad o oe ca wi a competitio. Thus, files with larger P j j/ V jk wi more competitios ad receive more resource ad files with smaller P j j/ V jk oly wi few competitios ad receive less resource. Hece, the competitio gradually lets each file receive its deserved portio of resource based o OFRR. Therefore, by eablig file owers to distributively compete for resource for their files, we ca realize OFRR without a cetral server. Challege 2: competitio for distributed resource. I MANETs, all available resource is scattered amog differet odes movig aroud i the etwork. This poses three problems. First, file owers have limited probability to gather to coduct the resource competitio. Secod, after a file is replicated to a umber of odes, it is difficult for its ower to collect the popularity of the replicas to update the P of the file. Third, sice the umber of odes met by a file ower ad a ode s capability are both limited, a sigle file ower caot distribute replicas efficietly ad quickly. We propose a optimized way to solve these problems by regardig a file ad its ewly created replica as two differet files, which participate i further competitio idepedetly. However, this brigs aother challege: how ca the replicas esure that the Vjk is proportioal to its P i the resource competitio? Solutio to Challege 2: distributive competitio o selective resources. As metioed, eablig replica odes to replicate files makes it difficult to keep P proportioal to Vjk. We idirectly resolve this problem by keepig the average V of the replica odes of a file close to V via selectively choosig replica odes. Formula (16) ca the be re-expressed as qj qj j V j j P j (21) b j b j I such a case, whe the umber of replicas of each file is proportioal to its P = q j /b j, OFRR is also satisfied. Accordigly, we deliberately select odes to create replicas so that the average meetig ability of replica odes equals to V. Thus, each ode competes for resource for its file j oly with its P. To allow odes to replicate files i a distributed maer, upo wiig a competitio for a file, a ode splits the file s P evely betwee the file ad the replica file. Each file keeps replicatig util it fails a competitio. Thus, for a file with k replicas, each of its replica s P geerally equals P j /k. The sum of these replicas P s equals P j (P j is the P of the origial file j). I other words, the umber of splits each file j has experieced (i.e., the umber of replicas of each file) is proportioal to its P j, causig the umber of replicas of each file is proportioal to the sum of meetig ability of its replica odes. As a result, Formula (16) is satisfied. B. Desig of the File Replicatio Protocol Accordig to the aalysis above, we propose the Priority Competitio ad Split file replicatio protocol (). We first itroduce how a ode retrieves the parameters eeded i followed by a detailed descriptio of. Each ode eeds to kow the average meetig ability of all odes (V ). As odes move radomly ad idepedetly i the etwork, we ca assume that the set of odes ecoutered by File Try at most K times Select oe eighbor by the OFRR RULE Failure Priority competitio Success Fig. 1: Replica distributio process. Replica creatio & priority split each ode is radomly chose from the set of all odes i the etwork. The, the average meetig ability of all ecoutered odes of a ode ca geerally represet the average meetig ability of all odes i the etwork. As a ode meets more ad more odes i the system, its calculated V coverges to the real value. I, each ode i periodically calculates its meetig ability (V i ) measured by the frequecy it meets other odes, ad exchages its V i with its eighbors by piggybackig the iformatio ito beaco messages. Each ode also periodically calculates the popularity of each of its files (q j ) measured by the umber of its received requests for the file i a uit of time period, ad calculates the file s P j = q j /b j. With above iformatio, a ode ca order all of its files i descedig order of their P s ad creates replicas for the files i the top-dow maer. I the Solutio to Challege 2, odes replicate files i a distributed maer, ad each replicatig ode tries to esure that the average meetig ability of replica odes of a file equals to V. That is, V j V, where j deotes the total umber of replicas of file j created by a ode ad V j deotes the average meetig ability of the replica odes. Therefore, each ode eeds to keep track of j ad V of j each of its file. After creatig a replica, the replicatig ode icreases j by 1 ad also updates V usig the V of the j ew replica ode. Sice the computatio oly ivolves simple operatios ad oly oe value eeds piggybackig, is suitable to the eergy-costraied MANETs. Figure 1 demostrates the process of the replicatio of a file i. For example, suppose ode i eeds to replicate file j. It keeps tryig to replicate file j o odes it ecouters util oe replica is successfully created or K attempts have bee made. To choose a eighbor to replicate file j, ode i first checks the meetig abilities of its eighbors. Recall that a replicatig ode should keep the average meetig ability of the replica odes for each of its files at V. Node i fids the eighbor that does ot cotai file j ad has V k that makes ( j V + V k)/( j j + 1) the closest to V. If the eighbor s available storage space is larger tha the size of file j (S j ), it creates a replica for file j. Otherwise, a competitio is lauched amog file j s replica ad other replicas already residig i the eighbor based o their P s. The priority value of the ew replica is set to half of the origial file s P. The competitio is coducted as a drawig to select oe or more replicas to be deleted. Accordig to OFRR, each replica has a probability of beig selected to remove, which is iversely proportioal to its P. Assume there are d replicas i competitio. Each replica is resposible for a rage i [0, d 1/P k] ad the legth of the rage equals its 1/P. The eighbor radomly chooses a umber i [0, d 1/P k], ad the replica whose rage ows the umber is chose. If the size of the chose replica is less tha S j, the eighbor repeats

6 the same process util available storage is o less tha S j. If file j is amog the selected files, which meas file j fails the competitio, oly file j s replica is deleted. Otherwise, all selected files are removed. Also, if file j fails, ode i will lauch aother attempt for file j util the maximum umber of attempts (K) is reached. Each attempt starts with idetifyig the eighbor to replicate file. The settig of K attempts is to esure that each file ca compete with a subset of sufficiet replicas i the system. If ode i fails to create a replica for file j after K attempts, the replicas i ode i with smaller P s tha file j are ulikely to wi a competitio. Thus, at this momet, ode i stops replicatig files util the ext time period. Fially, all available resource i the system is allocated to replicas accordig to their P s ad OFRR is realized. Accordig to the Solutio to Challege 2, we regard a file j s replica as a differet file from file j i. Therefore, if ode i successfully creates a replica for file j, it splits the file s P evely betwee file j ad the ew replica. Thus, each file s priority is P/2. After the splittig, the two copies of file j ivolve i further resource competitio idepedetly. Without the splittig strategy, files with large P s will receive more ad more resource ad starve files with small P s. As the popularity of files, their P s ad available system resource chage as time goes o, each ode periodically executes. C. Aalysis of the Effectiveess of I this sectio, we prove the effectiveess of through aalysis. We refer to the process a ode tries to copy a file to its eighbors as oe roud of replicatio distributio. Whe a replica is created for a file with P, the two copies will replicate files with priority P/2 i the ext roud. After the secod roud, suppose there is o update of the priority value, the four copies of the file will further replicate files with priority P/4, ad so o. So, the sum of the Ps of the replicas of each origial file is P plus the icrease of its priority value, we ca regard the replicas of a file as a whole ad they compete available resource i the system with accumulated priority P i each roud. Therefore, i each roud of replica distributio, based o our desig of, the overall probability of creatig a replica for a origial file j, deoted by P s j, is proportioal to its overall P j. That is: P s j P j (22) The, suppose total M rouds of competitio are coducted, the expected umber of replicas, deoted by j, for file j is j = MP s j j P j (23) Therefore, we ca coclude that the ca realize Equatio (21), i which the umber of replicas of each file is proportioal to its P, thereby realizig OFRR. V. PERFORMANCE EVALUATION We coducted experimets o the GENI Orbit testbed [20], [21], which is a MANET testbed cosistig of 400 odes equipped with wireless cards, ad the NS-2 [22] simulator. We used a real-world MANET trace [23] to drive odes mobility i both experimets. The real trace [23] was obtaied through a outdoor project i Dartmouth Uiversity ad it provides positio records of 35 laptop odes movig radomly ad idepedetly across differet sectios of a ope field. I order to evaluate our protocol uder differet etwork sizes ad ode mobilities, we also coducted simulatio o the NS- 2 with differet etwork sizes ad ode mobilities sythesized by the modified RWP model as previously idicated. I order to validate the adaptivity of, we used two routig protocols i the experimets. We first used the Static Wait routig protocol [24], i which each query stays o the source ode util meetig the destiatio, i the GENI experimet. We the used the PROPHET probabilistic routig protocol [5], i which a ode routes requests to the eighbor with the highest meetig ability, i the simulatio. We set a larger TTL for Static Wait sice it eeds more time to fid a file holder tha PROPHET. We evaluated the performace of i compariso with [9], [9], [11] ad [8]. The details of these protocols ca be foud i Sectio II. We also icluded the performace of the cetralized protocol that replicates files accordig to OFRR, which is deoted as. shows the best possible performace of OFRR. Table II shows the parameters used i experimets, uless otherwise specified. The parameters are determied by referrig to the settigs i [8], [25] ad the real trace. Accordig to the works i [8], [26], we determied the file size ad storage space. As the work i [18], the popularity of files followed a Zipf distributio ad the Zipf parameter was set to. Iitially, files were evely distributed to each ode ad o replica existed i the system. I the sythesized mobility, the speed of a ode was radomly chose from the rage of [s/2, 3s/2], where s is the cofigured average ode movemet speed. Sice the real trace does ot idicate the commuicatio rage of each ode, we set the commuicatio rage to 100m i the simulatio ad set it to 60m i the GENI experimet i order to see the ifluece of differet trasmissio rages o the performace. We evaluated the performace of with K = 3. Each test was ru by 5 times ad the average value for each metric is preseted. We used the followig metrics i the experimets: Hit Rate. This refers to the percet of requests that are successfully resolved by either origial files or replicas. This metric shows the effectiveess of replicatio protocols i ehacig file availability. Average delay. This is the average delay time of all requests. To make the compariso fair, we icluded all requests i the calculatio. For uresolved requests, we set their delays as the TTL. This metric shows the efficiecy of replicatio protocols i terms of file queryig delay. Replicatio cost. This is the total umber of messages geerated i creatig replicates. This metric shows the overhead of replicatio protocols. Cumulative Distributio Fuctio (CDF) of the proportio of replicas. This is the CDF of the proportio of replicas of each file. This metric reflects the amout of resource allocated to each file for replicatio ad shows whether a replicatio protocol ca achieve OFRR i resource allocatio.

7 TABLE II: Simulatio parameters. Real trace Sythesized mobility Eviromet Parameters GENI / NS-2 NS-2 Simulatio area 600m 300m 1000m 1000m Node Parameters Number of odes Commuicatio rage 60m / 100m 250m Average movemet speed - 6m/s The size of a file Number of files i each ode Storage space for replicas Query Parameters Iitializatio period 500s / 800s 200s Queryig period 1500s / 1200s 600s TTL of each request 1000s / 200s 200s Total time for each test 3000s / 3000s 1000s A. Performace i the Trace-Drive GENI experimets 1) Hit Rate ad Average Delay: Table III shows the results of each protocol i the trace-drive experimets o GENI. We see that the hit rates i differet replicatio protocols follow <<<<<. This is because i protocols with loger queryig delay, more requests are dropped due to TTL, leadig to lower hit rates. The result is supported by the fact that the results o average delay preset a reverse order, as show i the secod colum of the table. We see that ad lead to lower delays compared with others. This is attributed to the guidace of OFRR, which aims to miimize the average queryig delay. Although odes with high meetig ability may move at a log time scale, they ca meet more odes i a uit time ad thereby deliver queries to their destiatios more quickly o a average base. Therefore, by cosiderig both storage ad meetig ability as resource to ehace file availability, ad optimally allocate all available resource to differet files for replicatio to ehace global file availability ad overall file searchig efficiecy. O the cotrary, other protocols oly replicate files locally, cosumig resource with redudat replicas ad failig to achieve high file availability uder ode mobility. geerates aroud 20% higher average delay tha. This is because has the kowledge of all iformatio of each ode eeded i OFRR beforehad, while has to distribute replicas i a fully distributed maer. The closer performace of to tha others demostrates the effectiveess of i realizig OFRR i a distributed maer. TABLE III: Experimetal results of the trace-drive experimets o GENI. Protocol Hit rate Average / 1% / 99% delay (s) Replicatio cost / 1 / / 1 / / 1 / / 1 / / 1 / / 1 / We see that the average delays of other four protocols follow >>>. oly utilizes the storage o itersectio odes, which idicates that it fails to fully utilize storage space i all odes. Therefore, it caot create as may replicas as other protocols ad exhibits the highest delay. Other protocols ca fully utilize storage space. I, each ode replicates its frequetly queried files util its memory is filled up. Sice file popularity follows the Zipf distributio, almost all resource is allocated to popular files, leadig to large delay for requests queryig for upopular files. Therefore, caot achieve global optimizatio of all file queries. I, a ode replicates files iterested by its eighbors that have less storage resource tha itself, makig replicas be shared amog eighbors. However, as the sharig of replicas is ot i the whole group, oly reders a slightly lower delay tha. further improves ad by coductig the file replicatio o a group level. It elimiates duplicate replicas amog group members ad uses released memory for other replicas, thereby geeratig smaller average delay. We fid that the 1st percetiles of the delays of all protocols are 1. This is because some requests are immediately satisfied by direct eighbors, leadig to very short delay. The 99th percetiles of the delays of the protocols approximately follow the relatioship o average delay. Above results justify that ehaces the file searchig efficiecy by its global optimizatio of file availability. 2) Replicatio Cost: From the table, we fid that the replicatio costs of differet protocols follow > >>===0. shows the highest replicatio cost because it eeds to broadcast each ew file to all odes i the system. icurs moderate replicatio cost because group members eed to exchage iformatio to reduce duplicate replicas. has very low replicatio cost because each ode oly tries at most K times to create a ew replica for each file it holds., ad have o replicatio cost sice they do ot eed to exchage iformatio betwee odes for file replicatio. However, may geerate redudat replicas, ad fails to utilize all storage. 3) Replica Distributio: Figure 2 shows the CDF of the proportio of resource allocated to each file for replica creatio i differet protocols. From the figure, we fid that exhibits the closest similarity to while other protocols follow:, where meas closer similarity to. Combiig the results o average delay, we fid a iterestig pheomeo: except, a protocol with closer similarity to has less average delay. This proves the correctess of our theoretical aalysis ad the resultat OFRR rule expressed i Formula (16). has large average delay because it does ot utilize all storage space for replica creatio, though it exhibits similarity with. We also observe that the CDFs of the proportio of resource allocated to replicas of,, ad icreases to over quickly. This is because they allocate most resource to popular files, resultig i more replicas for these files. Though these protocols CDF of the proportio of replicas File sequece i decreasig order of popularity Fig. 2: CDF of the resource allocated to replicas i trace-drive GENI experimet. ca reduce the delay of queries for popular files but caot reduce the delay of queries for upopular files. is superior over these protocols because it averagely ca reduce the delay of queries for both popular ad upopular files.

8 B. Performace i the Trace-Drive Simulatio 1) Hit Rate ad Average Delay: Table IV shows the results of each protocol i the trace-drive experimets o NS-2. We see the hit rates of the six protocols follow the same relatioship as i Table III due to the same reasos. We fid that the average delays of the six protocols are much less tha those i the GENI experimet. This is caused by two reasos. First, the trace-drive simulatio adopts the PROPHET for file searchig, which ca locate files more quickly tha the Static Wait searchig protocol used i the GENI experimet. Secod, the commuicatio rage of two odes (100m) i the simulatio is larger tha that i the GENI experimet (60m), leadig to shorter searchig delay sice a ode ca reach more eighbors. Also, the six protocols preset lower hit rates tha those i the GENI experimet. This is because the trace-drive simulatio used much smaller TTL. The relative performace betwee differet protocols i the simulatio matches that i the GENI experimet, which further proves the correctess of our aalysis ad the effectiveess of the proposed. TABLE IV: Simulatio results of the trace-drive experimets. Protocol Hit rate Average / 1% / 99% delay (s) Replicatio cost / / / / / / / / / / / / ) Replicatio Cost: From Table IV, we fid that the replicatio costs of differet protocols follow > >>===0. This matches the results i Table III ad the reasos are the same. 3) Replica Distributio: Figure 3 shows the CDF of the proportio of resource allocated to replicas of each file i the six protocols. From the figure, we fid similar tred as that i Figure 2. That is, except, a protocol with closer similarity to has less average delay. This further proves the correctess of our theoretical aalysis through trace-drive simulatio. CDF of the proportio of replicas C. Performace With Differet Network Sizes File sequece i decreasig order of popularity Fig. 3: CDF of the resource allocated to replicas i trace-drive simulatio. I this test, we examied the performace of ad other protocols whe the total umber of odes varied from 20 to 110 with a 10 icrease i each step. 1) Hit Rate: Figure 4(a) plots the hit rates of the six replicatio protocols. We see the same relatioship betwee differet protocols as foud i Table III ad Table IV with the same reasos. Similarly, the reasos are also supported by the fact that the average delays of the six protocols preset reverse order of the hit rate, as show i Figure 4(b). 2) Average Delay: Figure 4(b) shows the average query delays of the six protocols. We observe the same results as that foud i Table III ad Table IV. Specifically, at all etwork sizes, has 10%-15% less average delay tha,, ad, ad it shows aroud 15% - 20% higher average delay tha. has the largest average delay. Such results are cosistet with aforemetioed coclusios because of the same reasos. The results i Figure 4(a) ad Figure 4(b) cofirm the validity of our aalysis ad the effectiveess of i differet etwork sizes. More odes i the etwork eable a ode to have more eighbors ad hece more optios to forward queries to the file holder. It is iterestig to see that i the figures, the hit rate ad average delay of each protocol geerally remai stable as the umber of odes icreases. This is because odes move radomly ad idepedetly i the etwork. So, the probabilities that a query forwarder meets a file holder are approximately the same i etworks with differet sizes. Figure 4(c) plots the 1st ad 99th percetiles of the delays of the six protocols. We fid that the 1st percetiles of delays of all protocols are all 1s. The relatioship betwee the 99th percetiles of the delays of the six protocols is i lie with that of the average delays i Figure 4(b), ad that of the 99th percetiles i Table III ad Table IV because of the same reasos explaied previously. The result cofirms that is effective i reducig the average queryig delay i etworks with differet sizes. 3) Replicatio Cost: Figure 4(d) illustrates the replicatio cost of each protocol. The replicatio costs of, ad are ot show sice they equal 0. We fid that geerates high replicatio cost, shows moderate replicatio cost, ad produces low replicatio cost. The result is cosistet with those i Table III ad Table IV because of the same reasos. We also observe that the replicatio costs of, ad grow as the umber of odes i the system icreases. This is because as the umber of odes icreases, geerates more messages durig the broadcastig process for ewly geerated files, produces more exchage messages betwee group members, ad replicates more files to eighbors. 4) Replica Distributio: Figures 5(a) ad 5(b) show the CDF of the proportio of resource allocated to replicas i each protocol whe the umber of odes is 20 ad 110, respectively. From the figures, we fid that all protocols exhibit similar relatioship as Figures 2 ad 3. That is, except, shows the closest close similarity to ad others follow:. The results agai cofirm the correctess of our theoretical aalysis with results from differet etwork sizes. We fid that Figures 5(a) ad 5(b) show similar results, which demostrates the effectiveess of i differet etwork sizes. Combiig above results, we coclude that OFRR ca help shorte the average queryig delay ad ca realize it effectively i etworks with differet sizes. D. Performace With Differet Node Mobilities I this test, we examied the performace of the six protocols whe the average movemet speed of odes varied from 1.5 m/s to 9 m/s with 1.5 m/s icrease i each step. 1) Hit Rate: Figure 6(a) illustrates the hit rates of the six replicatio protocols. We observe the same relatioship betwee differet protocols as those foud i Table III, Table IV ad Figure 4(a) with the same reasos. We also fid that, for

9 Hit rate Number of odes (a) Hit rate. ay (s) rage del Aver Number of odes (b) Average delay. (c) The 1% & 99% delays. Fig. 4: Performace of the file replicatio protocols with differet etwork sizes. s) Delay (s 99% Delay (s) 1% D Number of odes ost catio co Replic 2.5E E E E+03 Number of odes (d) Replicatio cost. e Hit rate Average speed (m/s) (a) Hit rate. ay (s) rage del Aver Average speed (m/s) (b) Average delay. (c) The 1% & 99% delays. Fig. 6: Performace of the file replicatio protocols with differet ode mobilities. s) Delay (s 99% Delay (s) 1% D Average speed (m/s) cost icatio c Repli 5.0E E E Average speed (m/s) (d) Replicatio cost. CDF of the proportio of replicas File sequece i decreasig order of popularity (a) Network size = 20 odes. (b) Network size = 110 odes. Fig. 5: CDF of the resource allocated to replicas with differet etwork sizes. CDF of the proportio of replicas File sequece i decreasig order of popularity all protocols, the hit rate is low at slow movemet speed ad is satisfactory (i.e., >90%) whe the average movemet speed is higher tha 7.5 m/s. This is because a ode usually eeds log time to ecouter requested files whe it moves slowly, leadig to more dropped requests due to TTL expiratio. 2) Average Delay: Figure 6(b) shows the average queryig delays of the six protocols. We observe that shows the closest result to, ad it reduces the average delay of,, ad by about 10%-15%. Agai, the result is cosistet with those i Table III, Table IV ad Figure 4(b) due to the same reasos. The result also shows that the chage of ode movemet speed does ot affect the relative performace amog differet protocols. This is because, as show i Equatio (21), the effectiveess of replicatio protocol with the same etwork size ad ode mobility distributio is oly determied by the resource allocatio for file replicas. These results cofirm the correctess of the OFRR ad the effectiveess of the with differet ode mobilities. We also observe that the average delays of all protocols decrease as ode movemet speed icreases. Whe odes move faster, the average time eeded for two odes to meet with each other is shorteed, leadig to less average delay. The result implies that the movemet speed of a ode affects the umber of odes it ca ecouter i a uit period ad hece the availability of its files, which justifies the ecessity of cosiderig ode meetig ability as resource i file replicatio. Figure 6(c) depicts the 1st ad 99th percetiles of the delays of the six replicatio protocols. Similar to the results i previous experimets, the 1st percetiles of delays of all protocols are early 0 ad the 99th percetiles of the delays of these protocols preset the same relatioship as i Table III ad Table IV for the same reasos. Whe the average speed is slow (i.e., 1.5 m/s ad 3 m/s), the 99th percetiles of the delays of all protocols equal the TTL (200s) sice we use the TTL as the delay of dropped requests. Whe odes move slowly, they averagely eed loger time to ecouter requested files. 3) Replicatio Cost: From Figure 6(d), we fid that PRDS presets the highest replicatio cost, has moderate replicatio cost, ad geerates low replicatio cost. We did ot plot the replicatio costs of other protocols i the figure sice the results are almost 0. The relatioship of the six protocols o replicatio cost remais the same as those i Table III, Table IV ad Figure 4(d) because of the same reasos. We also fid that the replicatio costs of PRDS, ad remai stable as the ode movemet speed icreases. The replicatio costs of ad PRDS are oly decided by the umber of odes i the system, sice the former exchages iformatio betwee group members for replicatio ad the latter broadcasts messages through the etwork for ewly created files. For, the umber of replica distributio attempts is urelated to ode mobility. So their replicatio costs remai stable whe the ode movemet speed icreases. 4) Replica Distributio: Figures 7(a) ad 7(b) show the CDF of the proportio of resource allocated to replicas of each file i each protocol whe the average movemet speed of odes is 1.5 m/s ad 9 m/s, respectively. We fid that all protocols geerate similar results as those i Figures 5(a) ad 5(b) because of the same reasos. The results agai verify the correctess of our theoretical aalysis ad the effectiveess of i followig OFRR i various ode mobilities. E. Performace With Differet Storage Sizes We also tested the performace of differet replicatio protocols whe the storage space for replicas i each ode

10 CDF of the proportio of replicas File sequece i decreasig order of popularity (a) Average speed = 1.5 m/s. (b) Average speed = 9 m/s. Fig. 7: CDF of the resource allocated to replicas with differet ode mobilities. e Hit rate Storage size CDF of the proportio of replicas File sequece i decreasig order of popularity (a) Hit rate. (b) Average delay. Fig. 8: Performace with differet storage sizes with real trace mobility. ay (s) rage del Aver Storage size rages from 20 to 110 with 10 icrease i each step o the NS- 2 simulator. Figure 8 ad Figure 9 show the hit rate ad average delay of the six protocols i the real trace ad sythesized ode mobility, respectively. We see that they show the same relatioship o their performaces with the real trace mobility ad with the sythesized mobility. Specifically, as the storage size icreases, the hit rates of all protocols icrease ad their average delays decrease. This is because the umber of replicas of each file icreases whe there is more storage space i the system, leadig to higher hit rate ad lower average delay. We also fid that the performace relatioship betwee the six protocols o the two metrics matches those i Table III ad Table IV due to the same reasos. Such results cofirm the correctess of OFRR ad the effectiveess of with differet degrees of storage resource costrait. VI. CONCLUSION I this paper, we ivestigated the problem of how to allocate limited resource i file replicatio for global file searchig efficiecy optimizatio i MANETs. We first theoretically aalyzed the ifluece of replica distributio o the average queryig delay uder costraied available resource, ad derived a optimal replicatio rule to allocate the limited resource to file replicas i order to miimize the average queryig delay. Ulike previous protocols that oly cosider storage space as resource, we also cosider file holder s ability to meet odes as available resource sice it also affects the average queryig delay. This ew cocept ehaces the correctess of the deduced rule ad the effectiveess of the accordigly developed protocol. Fially, we desiged the Priority Competitio ad Split replicatio protocol () that realizes the proposed optimal replicatio rule i a fully distributed maer. Experimets o both real-world GENI testbed ad NS-2 with real trace ad sythesized mobility cofirm both the correctess of our theoretical aalysis ad the effectiveess of. I our future work, we will study the effect of i a MANET with other ode movemet models. e Hit rate Storage size (a) Hit rate. (b) Average delay. Fig. 9: Performace with differet storage sizes with sythesized mobility. ay (s) rage del Aver ACKNOWLEDGEMENTS Storage size This research was supported i part by U.S. NSF grats OCI , CNS , CNS , CNS , CNS ad CNS , Microsoft Research Faculty Fellowship , ad Sadia Natioal Laboratories grat REFERENCES [1] Qik, [2] Flixwago, [3] Y. Tseg, S. Ni, ad E. Shih, Adaptive approaches to relievig broadcast storms i a wireless multihop mobile ad hoc etwork, i Proc. of ICDCS, 2001, pp [4] B. Chiara, C. Marco, J. Jacopo, ad P. Adrea, Hibop: A history based routig protocol for opportuistic etworks, i Proc. of WoWMoM, [5] A. Lidgre, A. Doria, ad O. Schele, Probabilistic routig i itermittetly coected etworks, MC2R, vol. 7, o. 3, pp , [6] F. Li ad J. Wu, Mops: Providig cotet-based service i disruptiotolerat etworks, i Proc. of ICDCS, 2009, pp [7] S. Moussaoui, M. Guerroumi, ad N. Badache, Data replicatio i mobile ad hoc etworks, i Proc. of MSN, 2006, pp [8] L. Yi ad G. 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