Specrum-Aware Daa Replicaion in Inermienly Conneced Cogniive Radio Neworks Absrac The opening of under-uilized specrum creaes an opporuniy for unlicensed users o achieve subsanial performance improvemen hrough cogniive radio echniques. In cogniive radio ad-hoc neworks, wih node mobiliy and low node densiy, he nework opology is highly dynamic and end-oend connecion is hard o mainain. We propose daa replicaion echniques o address hese problems and improve daa access performance in such inermienly conneced cogniive radio nework. Alhough daa replicaion has been exensively sudied in radiional disrupion oleran neworks, exising echniques canno be direcly applied here since hey do no consider he effecs of primary user appearance on daa replicaion. In his paper, we formulae specrum-aware daa replicaion as an opimizaion problem which ries o maximize he average daa rerieval probabiliy, subec o sorage and ime consrains. Since he problem is hard o solve based on mixed ineger programming, we furher design a disribued replicaion scheme based on he meric of replicaion benefi. Exensive simulaions based on synheic and realisic races show ha our scheme ouperforms exising schemes in erms of daa rerieval probabiliy in various scenarios. I. INTRODUCTION The pas few years have winessed he proliferaion of wireless devices (e.g., cell phones, ables, and lapops), accompanied by he explosion of wireless applicaions such as locaion-based services, mobile healhcare, remoe educaion, home enerainmen sysems, ec. Mos of hese devices are unlicensed and have o operae in he public ISM bands which are becoming increasingly congesed. Meanwhile, some oher licensed specrum bands (e.g., TV bands) are exremely underuilized. To address his problem, FCC approved unlicensed use of licensed specrum hrough cogniive radio echniques [], which enable dynamic configuraion of he operaing specrum. Depending on he nework archiecure, cogniive radio neworks can be eiher infrasrucure-based or ad-hoc based, where cogniive radio ad-hoc neworks [2], [3], [4], [5] do no require any infrasrucure suppor. They allow unlicensed users o deec available licensed channels and hen esablish connecions by hemselves. In some cases, users are only inermienly conneced when hey move ino he communicaion range of each oher (called conac). Such inermienly conneced cogniive radio nework can be viewed as a special case of Disrupion Toleran Nework (DTN) [6], which has This work was suppored in par by he US Naional Science Foundaion (NSF) under gran number CNS-32278 and by Nework Science CTA under gran W9NF-9-2-53. Jing Zhao and Guohong Cao Deparmen of Compuer Science and Engineering The Pennsylvania Sae Universiy E-mail: {uz39,gcao}@cse.psu.edu applicaions in balefield, disaser recovery, environmenal monioring, habia monioring, ransporaion, 3G offloading, ec. Due o mobiliy and limied range of he wireless communicaion, he conac duraion is usually shor. Thus, i is hard o ransmi large amoun of daa such as video, especially considering ha mos mobile devices use unlicensed ISM bands for peer-o-peer communicaion. Wih cogniive radio echniques, he licensed specrum can be opporunisically exploied o increase he daa ransmission capaciy among hese mobile devices. However, daa access will be more complex, since we no only need o consider he probabiliy of nodes reaching he desinaion, bu also consider he daa ransmission capaciy which is affeced by he primary user appearance. We propose daa replicaion echniques o improve he performance of daa access, in erms of daa access delay and daa availabiliy, in inermienly conneced cogniive radio neworks. Here, he key problem is where o replicae he daa o minimize he daa access delay and increase he daa availabiliy. Alhough daa replicaion has been exensively sudied in radiional disrupion oleran neworks [7], [8], [9], [], exising echniques canno be direcly applied since hey do no consider he effecs of primary user appearance on daa replicaion. In inermienly conneced cogniive radio neworks, unlicensed users a differen regions are generally affeced by he primary users a ha area during he daa ransmission ime. Such spaial and emporal varying specrum availabiliy affecs he daa access delay and he daa rerieval probabiliy, and hence affecs he daa replicaion sraegy. For example, suppose node A frequenly conacs oher nodes compared o node B. If specrum availabiliy is no considered, replicaing daa a A is beer since he replicaed daa (a A) can be easily accessed by oher nodes and hence he daa access delay will be shorer. However, he informaion of specrum availabiliy may change he decision on where o replicae he daa. Suppose he conacs beween A and ohers ofen occur wihin he aciviy regions of he primary users. Then, less amoun of daa can be ransmied upon conac, and he replicaed daa a A has less chances o be rerieved by oher nodes. In conras, suppose he conacs beween B and ohers ofen occur ouside he aciviy regions of he primary users. Then, he replicaed daa a B has beer chances o be rerieved by ohers during he conac. Thus, we should oinly consider node conac paern and primary user appearance in deermining where o replicae daa, which brings more
challenges in designing appropriae daa replicaion sraegies. We propose a specrum-aware daa replicaion scheme o address he aforemenioned challenge. Due o high node mobiliy and limied channel capaciy, he amoun of daa ha can be ransmied during a conac is limied. As a resul, we no only have o deermine where o replicae, bu also how much o replicae a a node. The decision will be based on he node conac frequency, he primary user appearance, and he node mobiliy paern. The conribuions of he paper are hree-fold: To he bes of our knowledge, his is he firs paper o sudy specrum-aware daa replicaion in inermienly conneced cogniive radio neworks. We formulae he specrum-aware daa replicaion problem o deermine he opimal replicaion locaion, which maximizes he average daa rerieval probabiliy, subec o sorage and ime consrains. We calculae he daa ransmission capaciy and he daa rerieval probabiliy by using discree-ime Markov chains o model node mobiliy and primary user appearance. We furher propose a disribued packe-level replicaion scheme, whose effeciveness is validaed hrough exensive simulaions. The remainder of he paper is organized as follows. Secion II reviews relaed work. In Secion III, we provide an overview of our work. Secion IV formulaes and analyzes he specrum-aware daa replicaion problem. Secion V presens he proposed specrum-aware replicaion scheme in deail. We show evaluaion resuls in Secion VI, and conclude he paper in Secion VII. II. RELATED WORK Mos exising soluions on daa access in cogniive radio neworks assume he exisence of an end-o-end pah beween he daa source and daa requesers. They focus on designing efficien rouing proocols o minimize he rouing delay or maximize he hroughpu. For example, an on-demand proocol [] has been proposed o minimize he end-o-end delay hrough oin roue selecion and specrum assignmen. In [2], Pefkianakis e al. proposed a rouing proocol o selec he roue wih he highes available specrum. However, neiher of hem considers node mobiliy. In [3], Chowdhurya e al. proposed a geographic forwarding based specrum aware rouing proocol for cogniive radio ad-hoc neworks ha can adap o dynamic specrum availabiliy and node mobiliy. However, heir proocol is based on AODV [4] which has o esablish a roue o he desinaion, and hence no suiable for inermienly conneced neworks. Daa replicaion has been widely used o improve he performance of daa access in mobile ad-hoc neworks [5], [6], [7] and DTNs [7], [8], [9], []. In [5], he problem of finding he opimal replicaion locaion is formalized as a special case of he NP-hard conneced faciliy locaion problem [8], and hen solved by using a greedy algorihm which is wihin a facor of 6 of he opimal soluion. If here are muliple daa iems, muliple nodes may share and coordinae heir replicaed daa [6], [7]. Daa replicaion is also sudied in cogniive radio neworks o mee he delay consrains [9]. However, hese works do no consider mobiliy. For DTNs, disribued daa replicaion schemes have been proposed in [7], [8] by assuming a complee daa iem can be ransmied when wo nodes conac each oher. In realiy, he conac duraion is usually shor (due o mobiliy and limied range of peer-opeer wireless communicaion), so a complee daa iem may no be ransmied upon conac. Zhuo e al. [] addressed his problem hrough erasure coding and packe-level replicaion. However, in inermienly conneced cogniive radio neworks, he daa ransmission capaciy is also affeced by primary user appearance, which has no been considered in hese works. III. OVERVIEW We consider an inermienly conneced cogniive radio nework consising of mobile unlicensed users (nodes) whose communicaions may be affeced by he primary users. Each daa iem is generaed by he daa source, and requesed by oher nodes wih some query rae. To help daa requesers rerieve daa wihin a ime consrain, each node provides some sorage space for replicaing he daa iems. Due o node mobiliy and he appearance of primary users, here is no persisen nework connecion. As a resul, a node can only forward daa o anoher node if hey are wihin he communicaion range and have available communicaion channels. The daa ransmission capaciy (i.e., he amoun of daa ha can be ransmied upon conac) depends on he amoun of available specrum. The daa ransmission capaciy will be reduced due o primary user appearance, and a large daa iem (e.g., large video) may no be ransmied compleely upon conac, especially when he conac duraion is shor. If he daa is simply fragmened and only a par of i is ransmied during each conac, he well-known coupon collecor problem [2] will appear, where he node may keep looking for he las fragmen of he daa which is hard o find. To miigae his problem, we adop he erasure coding echnique [2] o encode daa ino a large se of coded packes, and hen any sufficienly large subse of coded packes can be used o reconsruc he daa. Thus, daa replicaion is performed a he coded packe level. Our goal is o decide which daa iems and how many packes should be replicaed by each node, in order o maximize he average daa rerieval probabiliy. We can formulae i as a specrum-aware daa replicaion problem, which is hard o solve based on mixed ineger programming. In our heurisic based approach, each node greedily replicaes he packe ha brings he maximum replicaion benefi unil he sorage space is fully uilized. The replicaion benefi depends on he daa rerieval probabiliy, which is affeced by boh node movemen and primary user appearance. In he nex wo secions, we firs calculae he daa rerieval probabiliy by using discreeime Markov chains o model node movemen and primary user appearance, and hen describe our disribued packe-level replicaion scheme in deail.
IV. PROBLEM FORMULATION AND ANALYSIS In his secion, we formally define he specrum-aware daa replicaion problem and propose a soluion o efficienly calculae he daa rerieval probabiliy. Finally, we discuss a cenralized soluion based on mixed ineger programming. A. Sysem Models Following exising works [22], [23], he movemen of a node v is modeled by a discree-ime Markov chain Xv, whose saes are represened by he locaions (he enire area can be divided ino a se of grids and each grid defines a locaion). The se of locaions is denoed by L = {,...,L}. Weusep i, v o denoe he probabiliy of node v o ransiion from locaion i o locaion. Each locaion is affeced by a number of primary users on each channel. Le Y denoe he availabiliy of channel c a locaion l a ime. Tha is, Y is if channel c is available for unlicensed users a locaion l a ime (no accessed by primary users); oherwise, Y is. Based on exising works [24], [25], [26], we assume Y follows a discree-ime Markov chain wih wo saes,, and use q i, o denoe he probabiliy of Y o ransiion from sae i o sae. Noe ha an unlicensed channel can also be modeled here. If q, = q, =and q, = q, =, channel c can be viewed as an unlicensed channel which is never accessed by primary users. ) The Nework Model: We consider a nework of N unlicensed users (nodes) moving around L locaions. There are C channels, which may be someimes accessed by primary users. The se of nodes is denoed by N = {,...,N}, and he se of channels is denoed by C = {,...,C}. If wo nodes are a locaion l a he same ime, he oal amoun of daa ha can be ransmied beween hem a ime is β( c C Y ). Here β denoes he channel bandwidh, i.e., he oal amoun of daa ha can be ransmied per channel. We assume all channels have equal bandwidh, and a node can use muliple channels for ransmission a he same ime. In pracice, such flexibiliy in using muliple specrum bands can be achieved by k-agile sofware-defined radios [27]. 2) Daa Query: There are M daa iems of he same size G in he nework. The se of daa iems is denoed by M = {,...,M}. If he rae of erasure coding process is R, he daa iem of size G is coded ino GR/g uniformly sized packes of size g. Then any S =(+ɛ)g/g coded packes can be used o reconsruc he original daa iem, where ɛ is a parameer used in he erasure coding algorihm. Each daa iem is generaed by some node in he nework and requesed by ohers. The query rae for daa iem d by node v is denoed as λ. Suppose node v generaes a query for daa iem d a ime. The query succeeds if and only if node v can reconsruc daa iem d from he received coded packes wihin ime consrain T. To simplify presenaion, we assume uniform daa size and uniform ime consrain in his paper. Noe ha our approach can be easily exended o cases where daa iems have differen sizes and ime consrains as follows. Suppose daa iem d of size G d can be reconsruced by any S d coded packes, and is ime consrain is T d. To calculae he daa rerieval probabiliy of daa iem d, he proposed mehods can sill be applied afer replacing G (S, T ) wih G d (S d, T d ). B. Problem Definiion Definiion : Specrum-Aware Daa Replicaion Problem We use a N M marix z o represen he daa replicaion soluion, where each elemen z denoes he number of coded packes of daa iem d ha are replicaed by node v. Le A (z) denoe he oal number of coded packes of daa d ha node v can rerieve from ohers wihin he ime consrain T, wih daa replicaion soluion z. Le ρ v denoe he maximum number of packes ha can be replicaed by node v. The problem is o maximize he average daa rerieval probabiliy, subec o ime and sorage consrains. maximize λ P (A (z) S z ) () v N d M subec o z {,...,S}, v N, d M (2) z ρ v, v N (3) d M The obecive funcion () is he average daa rerieval probabiliy which is o be maximized. Consrain (2) ensures ha each node replicaes a mos S coded packes for each daa iem since a daa iem can be reconsruced by any S packes of i. Consrain (3) ensures ha he oal number of packes replicaed by each node does no exceed he sorage space of ha node. C. Calculaing he Daa Rerieval Probabiliy In his subsecion, we calculae he daa rerieval probabiliy P (A (z) S z ). We illusrae he calculaion seps in Figure (wih he noaions summarized in Table I) and describe he deails as follows. PA ( ( z) S z ) vd, vd, PX ( = l) v f ( ) A vd, ( z) a f ( w a ), ( ) A vd z f f U vw, U vw, ( a) ( a) f C l lc, ( a) PY ( = a) q lc, p v i, q lc, i, p v Seps for calculaing he daa rerieval probabiliy and evaluaing he Fig.. replicaion benefi (in Secion V-B) f K vw, ( a)
Symbols A (z) A w (z) U v,w U v,w C l Xv Y p i, v q i, p v q K v,w TABLE I TABLE OF NOTATIONS Meaning oal number of packes of daa iem d ha node v can rerieve from ohers wihin he ime consrain, given daa replicaion soluion z oal number of packes of daa iem d ha node v can rerieve from node w wihin he ime consrain, given daa replicaion soluion z oal amoun of daa ha can be ransmied from node w o node v wihin he ime consrain oal amoun of daa ha can be ransmied from node w o node v a ime number of available channels ha can be used a locaion l a ime locaion of node v a ime availabiliy of channel c a locaion l a ime probabiliy of node v o ransiion from locaion i o probabiliy of Y o ransiion from sae i o saionary probabiliy of node v o be a locaion saionary probabiliy of channel c o be a sae a locaion l maximum number of packes ha can be ransmied from node w o node v wihin he ime consrain ) Calculaion of P (A (z) S z ): In Definiion, here remains a problem of how o derive he closed form expression of P (A (z) S z ). Noe ha P (A (z) S z )= f A (z)(a) (4) a=s z where f A (z)(a) is he probabiliy mass funcion of A (z). Now he problem becomes how o calculae f A (z)(a). Le A w (z) be he oal number of coded packes of daa d ha node v can rerieve from node w wihin he ime consrain T, given daa replicaion soluion z. Since A (z) = w v Aw (z), we know from [2] ha f A (z)(a) = f A w (z) (a) (5) w v where f A w (z) (a) is he probabiliy mass funcion of A w (z). Equaion (5) indicaes ha f A (z)(a) is a discree convoluion of f A w (z) (a) (for w v). Le U v,w be he oal amoun of daa ha can be ransmied from node w o node v wihin he ime consrain. Then we have f A w (z) (a) = g(a+) ga f Uv,w (u)du a z w,d f gz Uv,w (u)du w,d a = z w,d oherwise where f Uv,w (a) is he probabiliy mass funcion of U v,w. The meaning of equaion (6) is as follows. If a z w,d,in order for node v o receive a coded packes of daa iem d from node w, he oal amoun of daa ha can be ransmied (U v,w ) has o be wihin he range of [ga, g(a +)) (g is he packe size). If node v receives z w,d coded packes from node w, U v,w has o be a leas gz w,d. I is impossible for he number of packes received from node w o exceed z w,d (which is he number of packes replicaed by node w). (6) Le Uv,w be he oal amoun of daa ha can be ransmied from node w o node v a ime. Since U v,w = T = U v,w, we have f Uv,w (a) = f U v,w (a) (7) {,...,T } where f U v,w (a) is he probabiliy mass funcion of Uv,w. Le Cl be he number of available channels ha can be used a locaion l a ime. Then we have f U v,w (βa) = f C (a)p (Xv = l)p (Xw = l) (8) l l L where f C (a) is he probabiliy mass funcion of C l l. P (X v = l) can be calculaed as follows. Suppose each node has equal probabiliy o be a all locaions a ime. Tha is, P (Xv = l) =/L for v N, l L. Since Xv follows a discree-ime Markov chain, P (Xv = l) can be calculaed from P (Xv ) using he following recurrence: P (Xv = ) = i L p i, v P (Xv = i), {,...,T} (9) Since Cl = c C Y f C (a) = l f Y (a) () c C where f Y (a) is he probabiliy mass funcion of Y. Suppose all channels are available a each locaion a ime. Tha is, P (Y =)=and P (Y Since Y a) (a.k.a., f Y following recurrence: P (Y = ) = =)=for l L, c C. follows a discree-ime Markov chain, P (Y (a)) can be calculaed from P (Y i {,} = ) using he q i, P (Y = i), {,...,T} () To summarize, he closed form expression of P (A (z) S z ) can be derived from a series of subsiuions using Equaions (4)-(). However, he calculaion of P (A (z) S z ) is sill oo complicaed. We reduce is compuaional complexiy hrough he following approximaion echniques. 2) Approximae Calculaions: We simplify he calculaion of P (A (z) S z ) hrough approximae calculaion of U v,w. Specifically, U v,w is approximaely calculaed based on he saionary probabiliies relaed o node movemen and primary user appearance. In general, lim n P (Xv +n = Xv = i) (lim n P (Y +n = Y = i)) exiss and is independen of i. Define p v = lim P (Xv +n = ), L n (2) q = lim P (Y +n = ), {, } n (3) where p v ( q ) can be solved by { p v = i L pi, v p i v, L L p v = (4)
{ q = i {,} qi, qi, {, } {,} q = (5) If is large enough, P (Xv = ) (P (Y = )) will be very close o he saionary probabiliy p v ( q ). In disrupion oleran neworks, he ime consrain is usually loose (i.e., is usually large), so we can use p v ( q ) o approximae P (Xv = ) (P (Y = )). Then he expeced amoun of daa ha can be ransmied from node w o node v a ime (i.e., E(Uv,w)) is equal o β l L c C pl v p l w q. Le U denoe E(Uv,w), and P denoe l L pl v p l w. We assume ha nodes v and w conac each oher wih probabiliy P, and ha upon conac a ime, he oal amoun of daa ha can be ransmied from node w o node v is equal o U. Under his model, i is impossible for he amoun of daa ha can ransmied from node w o node v wihin he ime consrain o exceed UT. Thus, f Uv,w (a) =if a>ut. Now suppose a ηt. When a ((n )U,nU] (n ), he oal number of conacs beween nodes v and w is n, and he probabiliy for making his number of conacs is ( T n) P n ( P) T n. To summarize, he probabiliy mass funcion f Uv,w (a) can be approximaed by he following funcion: ( T ) f Uv,w (a) ={ U P a U a U ( P) T U a a UT (6) oherwise Furhermore, le K v,w be he maximum number of packes ha can be ransmied from node w o node v wihin he ime consrain T. K v,w can be calculaed as: { U v,w U v,w <S K v,w = g g (7) S oherwise By subsiuing Equaion (7) ino Equaion (6), P (K v,w = γ a) is equal o v,w(a), where γ S v,w(a) is defined as γ v,w(k) k= follows: (i) UT gs (we can obain S packes wihin he ime consrain T ): ( T ) ga ga P U U ga T ( P) U a<s γ v,w (a) = T ( T ) k= gs/u k P k ( P) T k a = S (8) oherwise (ii) UT <gs(we canno obain S packes wihin he ime consrain T ): { ( T ) ga γ v,w (a) = ga P U U ga T ( P) U a UT/g (9) oherwise D. Mixed Ineger Programming Formulaion The specrum-aware daa replicaion problem has he following mixed ineger programming formulaion. Le X represen he se of all possible paerns of node movemen. Each elemen X X is denoed by an N T vecor (Xv) N T, where Xv denoes he locaion a which node v is locaed a ime as aforemenioned in Secion IV-A. Le Y represen he se of all possible paerns of primary user appearance. Each elemen Y Y is denoed by an L C T vecor (Y ) L C T, where Y denoes he availabiliy of channel c a locaion l a ime as aforemenioned in Secion IV-A. Le R X,Y (z) denoe wheher node v can rerieve enough coded packes (a leas S packes) o reconsruc daa iem d wihin he ime consrain, given node movemen paern X, primary user appearance paern Y, and replicaion soluion z. R X,Y (z) can be calculaed as follows: { R X,Y (z) = min(z w N w,d, U X,Y g v,w ) S (2) oherwise where Uv,w X,Y is he amoun of daa ha can be ransmied from node w o node v wihin he ime consrain, given node movemen paern X and primary user appearance paern Y. Noe ha he number of packes of daa iem d ha can be ransmied from node w o node v should be bounded by z w,d (he number of packes of daa iem d ha are replicaed by node w). Uv,w X,Y is equal o β T = l L c C Y I Xv,,X w where Y denoes he availabiliy of channel c a locaion l a ime as aforemenioned in Secion IV-A, and I X v,xw is an indicaor funcion. If Xv = Xw, I X v,xw =; oherwise, I X v,xw =. Le P X denoe he probabiliy ha he node movemen follows paern X, and Q Y denoe he probabiliy ha he primary user appearance follows paern Y. Here we assume he availabiliy of differen channels a each locaion is independen, and he channel availabiliy a differen locaions is T,X = px v independen. Then, P X is equal o v v N v, and Q Y is equal o T,Y l L c C = qy. The specrum-aware daa replicaion problem can be redefined as follows: maximize λ P X Q Y R X,Y (z) (2) v N d M X X Y Y subec o z {,...,S}, v N, d M (22) z ρ v, v N (23) d M X X, Y Y, v N, d M: R X,Y (z) {, } (24) min(z w,d, g U v,w X,Y ) SR X,Y (z) (25) w N Consrains (24) and (25) ensure ha R X,Y (z) = if w N min(z w,d, g U v,w X,Y ) S is unsaisfied. Oherwise, R X,Y mus be equal o in order o maximize he obecive funcion. However, he min funcion makes Consrain (25) nonlinear, so we inroduce auxiliary variables h X,Y v,w,d (z) and replace Consrain (25) wih he following consrains. (z) SRX,Y (z) (26) w N h X,Y v,w,d h X,Y v,w,d (z) z w,d, w N (27) h X,Y v,w,d (z) g U X,Y v,w, w N (28)
Now he problem becomes a mixed ineger programming problem, which is NP-hard in general. This problem is more complicaed due o is exponenial number of variables (consrains). For example, since X and Y have L N T elemens and 2 L C T elemens respecively, he number of variables h X,Y v,w,d (z) is N 2 ML N T 2 L C T. Even for a small sized problem wih N =, M =, L =5, C =, T =5, he number is.5 5, which is oo big o be loaded ino general compuer memory by any opimizaion sofware (e.g., CPLEX). To address his challenge, we propose he following disribued replicaion scheme based on some heurisics. V. TRUM-AWARE REPLICATION SCHEME In his secion, we presen our disribued specrum-aware replicaion scheme. A. Main Idea Our daa replicaion scheme is a disribued algorihm ha runs locally a each node. Specifically, each node greedily replicaes he packe ha brings he maximum replicaion benefi unil he sorage is fully uilized. Here he key problem is how o evaluae he replicaion benefi accuraely. A sraigh-forward soluion is based on he increased daa rerieval probabiliy if he packe is replicaed a he node. However, he average daa rerieval probabiliy can only be calculaed using he knowledge of all nodes replicaion sraegies and mobiliy paerns, which is impossible in a disribued environmen. In our scheme, each node only uses a reasonable amoun of informaion o evaluae he replicaion benefi, which is based on he number of useful packes conribued by he replicaion. B. Replicaion Benefi We inroduce he concep of conribuion and conribuion gain, and hen give he definiion of replicaion benefi. The conribuion (conribuion gain) represens he capabiliy of a node o conribue all is replicaed packes (he newly replicaed packe) o anoher node. Definiion 2: Conribuion The conribuion provided by node v o node w in erms of daa iem d, denoed by B w (z ), is he expeced number of coded packes of d ha v can ransmi o w wihin he ime consrain. B(z w )=E(A v w,d(z )) z S = ap (K v,w = a)+ z P (K v,w = a) a= a=z (29) where P (K v,w = a) is derived in Secion IV-C2. Definiion 3: Conribuion Gain The conribuion gain provided by node v o w in erms of daa iem d, denoed by ΔB w (z ), is he incremen in B w by replicaing an exra coded packe of d a node v. ΔB w (z )=B w (z +) B w (z ) (3) Noe ha ΔB w (S) =, since S packes are enough o reconsruc he original daa iem. The conribuion gain provided by a node o iself is defined o be, since he node can always use he newly replicaed packe o reconsruc he original daa iem. The conribuion gain ΔB w (z ) is a non-increasing funcion, which indicaes he conribuion gain provided by a node decreases as more packes are replicaed a ha node. This can be explained as follows. For nodes v and w, he limied conac opporuniies resric he number of packes ha can be ransmied beween hem. Even if node v replicaes many packes of daa d, some of hem may never be ransmied o node w. As a resul, replicaing more packes is less efficien, so i leads o lower conribuion gain. Now we define he replicaion benefi based on he conribuion gain. Definiion 4: Replicaion Benefi The replicaion benefi provided by node v in erms of daa d, denoed by B (z ), is he weighed sum of he conribuion gain provided by node v o any node w in erms of each daa iem d. B (z )= λ w,d ΔB(z w ) (3) w N where λ w,d is he query rae of node v o daa iem d, and can be esimaed by λ w,d = n w,d /h. Here node w couns he number of requess in a period of h ime unis, and n w,d is he number of requess for daa iem d during h. As can be seen, he replicaion benefi can be calculaed wih a reasonable amoun of informaion. This is because he replicaion benefi B (z ) is based on K v,w (hrough a series of subsiuions using Equaions (29)-(3)), whose calculaion only depends on he conac paern beween node v and oher nodes in he nework and he paern of he primary user appearance (as shown in Secion IV-C2). These informaion can be colleced by he node iself, and he query raes of oher nodes can be exchanged upon conac. C. The Disribued Proocol When wo nodes conac, hey exchange packes replicaed in heir sorage. Wih sofware defined radio, full-duplex communicaions can be achieved such ha he packes can be sen o and received from anoher node a he same ime [28]. Therefore, we only need o focus on downloading packes upon conac. Generally speaking, each node greedily replicaes he packe ha brings he maximum replicaion benefi unil he sorage is full. Suppose node v has already replicaed z packes of daa iem d. When node v conacs anoher node, i downloads a packe of he daa iem d max which has he maximum replicaion benefi B max (z max ) from he encounering node. Noe ha he informaion required for calculaing he replicaion benefi can be colleced by node v beforehand as aforemenioned in Secion V-B. If he sorage is full, node v decides wheher o remove a packe o make room for he newly downloaded packe.
If node v removes a packe of daa iem d, he accumulaed replicaion benefi of daa iem d will be decreased by B (z ). We find ou he daa iem d min which has he minimum B min (z min ) among all he daa iems. If B min (z min ) is less han B max (z max ), he sorage replacemen brings benefi, so a packe of daa iem d min is replaced by ha of daa iem d max. Oherwise, here is no updae o he sorage. VI. PERFORMANCE EVALUATIONS In his secion, we evaluae he performance of our specrum-aware replicaion scheme based on synheic and realisic races. A. Schemes for Comparisons To evaluae he performance of our specrum-aware replicaion scheme (), we compare i wih hree exising replicaion schemes which do no consider primary user appearance:. : A conac duraion aware replicaion scheme []; 2. : A replicaion scheme where he sorage space is evenly allocaed among all he daa iems; 3. : A replicaion scheme where he sorage allocaion is proporional o he daa query rae; i.e., frequenly accessed daa will be replicaed wih more sorage space. For all hese schemes, he daa replicaion is a daa packe level and erasure coding is used. B. Synheic Trace ) Simulaion Seings: We generae a synheic race in which here are 2 mobile nodes and 2 daa iems in he nework. We se 2 locaions, and he channel availabiliy a each locaion is deermined by our model for primary user appearance (he ransiion probabiliies among differen saes are randomly generaed). Considering ha he node moving speed is relaively slow, we assume i akes ime unis o ransiion from one locaion o anoher. Each daa iem is generaed by some node which is randomly seleced, and can be reconsruced by 2 coded packes. In our simulaions, we assume each node has equal sorage space and can replicae a mos coded packes. Following exising works [], [6], he daa query paern is based on Zipf-like disribuion in which he query rae of he ih mos popular daa iem is proporional o i θ. Here θ shows how skewed he query paern is, and is se o.8 in defaul according o sudies on real Web races [29]. We vary he channel bandwidh (β), he number of channels (C), and he Zipf parameer (θ), o sudy heir effecs on he (average) daa rerieval probabiliy. The channel bandwidh is he per channel ransmission capaciy. Tha is, if here are c available channels, he maximum number of packes ha can be ransmied in one ime uni is cβ. We also invesigae he effec of primary user appearance on he performance. Specifically, we model some channels as unlicensed channels which are never accessed by primary users (following Secion IV-A) and sudy how he percenage of unlicensed channels affecs he daa rerieval probabiliy. In all simulaions, he firs half of he race is used for warmup o collec necessary nework informaion. All he daa and queries are generaed during he second half of he race. The presened resuls are averaged over runs. 2) Simulaion Resuls: Figure 2(a) shows he effec of channel bandwidh on he daa rerieval probabiliy. For all schemes, he daa rerieval probabiliy increases as he channel bandwidh increases, since more packes can be ransmied upon conac. Among he four schemes, performs he bes, since i considers he effec of primary user appearance on he daa replicaion sraegy, which is ignored by he oher hree schemes. Compared o, and, improves he daa rerieval probabiliy by 75%, 38% and 32% when he channel bandwidh is packe per ime uni. When he channel bandwidh reaches packes per ime uni, he improvemen changes o 2%, 44% and 2%. When he channel bandwidh is less han 5 packes per ime uni, performs he bes among he oher hree schemes. ouperforms since allocaes more sorage space o he daa iems of high query rae. ouperforms due o he following reason. The replicaion sraegy in is based on he daa ransmission capaciy upon each conac. Wihou considering he primary user appearance, he daa ransmission capaciy canno be calculaed accuraely, which affecs he performance of. When he channel bandwidh exceeds 5 packes per ime uni, ouperforms. Increasing he channel bandwidh makes daa replicaion less resriced by he daa ransmission capaciy upon each conac. This reduces he effec of inaccurae calculaion of daa ransmission capaciy on he performance of. Meanwhile, considers he node conac paern which is no considered in, and hus performs beer. Figure 2(b) shows he effec of he number of channels on he daa rerieval probabiliy. For all schemes, he daa rerieval probabiliy increases as he number of channels increases, since here are generally more available channels o be used for daa ransmission upon conac. When here are channels in he nework, Figure 2(c) shows he effec of unlicensed channels on he daa rerieval probabiliy. For all schemes, he daa rerieval probabiliy increases as he percenage of unlicensed channels increases, since more packes can be ransmied upon conac by using more available channels. When all channels are unlicensed, and have he same daa rerieval probabiliy of 9% since daa replicaion is only deermined by he node conac paern. Figure 2(d) shows he effec of Zipf parameer θ on he daa rerieval probabiliy. For, and, he daa rerieval probabiliy increases as θ increases. Increasing θ makes he query paern much skewer, which increases he query rae of popular daa iems. These hree schemes generally replicae more packes of popular daa iems, so heir daa rerieval probabiliy increases. For, he performance is similar o ha of when he Zipf parameer is.2 or.4. Small θ indicaes similar query rae for all daa iems, so he replicaion sraegy of is similar o ha of. When θ increases, he popular daa iems are given higher
daa rerieval probabiliy.8.6.4.2 2 3 4 5 6 7 8 9 channel bandwidh (a) Daa rerieval probabiliy vs. channel bandwidh (C =, θ =.8) daa rerieval probabiliy.8.6.4.2 5 5 2 25 3 # of channels (b) Daa rerieval probabiliy vs. # of channels (β =2, θ =.8) daa rerieval probabiliy.8.6.4.2 2 4 6 8 percenage of unlicensed channels (%) (c) Daa rerieval probabiliy vs. percenage of unlicensed channels (β =3, C =, θ =.8) Fig. 2. query rae, bu are no reaed differenly in. Thus, he daa rerieval probabiliy of almos says fla a around 32% wih he increase of θ. C. Realisic Traces ) Simulaion Seings: The performance of our scheme is also evaluaed on realisic races. However, mos realisic races are inappropriae for our simulaions. They do no record where each conac happens, and hence i is difficul o model he channel availabiliy upon each conac. We find ha in he Darmouh race [22] and he UCSD race [3], each mobile node records he nearby associaed wireless access poins (APs), which may be used o model he locaions. A conac happens if wo nodes are a he same locaion a he same ime. The amoun of daa ha can be ransmied upon conac depends on he channel availabiliy a ha locaion, which can be simulaed using our model for primary user appearance (he ransiion probabiliies among differen saes are randomly generaed). The Darmouh race was colleced by several housand wireless lapops which were carried by sudens and faculy a he Darmouh College campus over five years. In our simulaion, we focus on he daa colleced beween Sepember, 22 and December, 22. If wo nodes are associaed wih he APs in he same building, hey are assumed o be a he same locaion. There are 85 locaions in oal by grouping APs of he same building ogeher. We sor all users in a descending order of race lengh, and selec he firs 5 users for simulaion. We se 2 channels and 2 daa iems. The daa rerieval probabiliy.8.6.4.2.2.4.6.8.2.4 zipf parameer (d) Daa rerieval probabiliy vs. Zipf parameer (β =5, C =) Comparison of and oher schemes on he synheic race channel bandwidh is 5 packes per second. Tha is, if here are c available channels, he daa ransmission capaciy is he combined size of 5c packes per second. Each daa iem is generaed by some node which is randomly seleced, and can be reconsruced by 2 coded packes. The sorage space of each node is he combined size of coded packes. The daa query paern is based on Zipf-like disribuion wih θ =.8. The UCSD race was colleced by approximaely 3 wireless PDAs which were carried by UCSD freshmen for an - week period beween Sepember 22, 22 and December 8, 22. There are 52 APs, and each AP corresponds o one locaion. Similar o he Darmouh race, we sor all users in an descending order of race lengh, and selec he firs 5 users for simulaion. The oher simulaion seings are he same as he Darmouh race. In boh Darmouh race and UCSD race, we vary he ime consrain o sudy is effec on he (average) daa rerieval probabiliy. In all simulaions, he firs half of he race is used for warmup o collec necessary nework informaion. All he daa and queries are generaed during he second half of he race. The presened resuls are averaged over 2 runs. 2) Simulaion Resuls: Figure 3 shows he effec of ime consrain on he daa rerieval probabiliy on he Darmouh race and he UCSD race, respecively. For all schemes, he daa rerieval probabiliy increases as he ime consrain increases. This is because increasing he ime consrain creaes more conac opporuniies o rerieve he requesed daa iems. Among he four schemes, performs he bes, since i considers he effec of primary user appearance on
daa rerieval probabiliy.8.6.4.2 2 3 4 5 6 7 8 9 ime consrain ( 5 secs) he daa replicaion sraegy, which is ignored by he oher hree schemes. Compared o, and, improves he daa rerieval probabiliy by 2%, 9%, 47% for he Darmouh race (5%, 4%, 28% for UCSD race) wih ime consrain 5 secs. When he ime consrain reaches 6 secs, he improvemen changes o 2%, 69%, 38% for Darmouh race (2%, 44%, 35% for UCSD race). VII. CONCLUSIONS This paper sudied he daa replicaion problem in inermienly conneced cogniive radio neworks. Differen from exising replicaion schemes in radiional DTNs, he proposed specrum-aware daa replicaion scheme oinly considers node conac paern and primary user appearance in deermining where o replicae he daa. We formulaed he specrum-aware daa replicaion problem as an opimizaion problem which ries o maximize he average daa rerieval probabiliy of he nework subec o ime and sorage consrains. 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