Efficient On-Demand Data Service Delivery to High-Speed Trains in Cellular/Infostation Integrated Networks

Transcription

1 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. XX, NO. XX, MONTH 2XX 1 Effcent On-Demand Data Servce Delvery to Hgh-Speed Trans n Cellular/Infostaton Integrated Networks Hao Lang, Student Member, IEEE, and Wehua Zhuang, Fellow, IEEE Abstract In ths paper, we nvestgate on-demand data servces for hgh-speed trans va a cellular/nfostaton ntegrated network. Servce requests and acknowledgements are sent through the cellular network to a content server, whle data delvery s acheved va tracksde nfostatons. The optmal resource allocaton problem s formulated by takng account of the ntermttent network connectvty and mult-servce demands. In order to acheve effcent resource allocaton wth low computatonal complexty, the orgnal problem s transformed nto a sngle-machne preemptve schedulng problem based on a tmecapacty mappng. As the servce demands are not known a pror, an onlne resource allocaton algorthm based on Smth rato and exponental capacty s proposed. The performance bound of the onlne algorthm s characterzed based on the theory of sequencng and schedulng. If the lnk from the backbone network to an nfostaton s a bottleneck, a servce pre-downloadng algorthm s also proposed to facltate the resource allocaton. The performance of the proposed algorthms s evaluated based on a real hgh-speed tran schedule. Compared wth the exstng approaches, our proposed algorthms can sgnfcantly mprove the qualty of on-demand data servce provsonng over the trp of a tran. Index Terms Cellular/nfostaton ntegrated network, hghspeed tran, on-demand data servce, resource allocaton. I. INTRODUCTION Recently, the hgh-speed ral has been rapdly developng all over the world [2]. The ral not only can sgnfcantly shorten journey tmes, but also can mprove passenger comforts by hgh-speed Internet servces [3]. The cellular network deployed near the ral lnes can provde seamless coverage. However, the data transmsson rate s lmted for trans movng at extremely hgh speeds because of the Doppler effect [4]. Wth hundreds of passengers onboard and an evergrowng data-ntensve servce demand such as audo/vdeo clp downloadng and bulk data retreval, hgh nformaton traffc congeston n the cellular network s nevtable. An alternatve or complementary soluton s proposed n [4] [7], where tracksde nfostatons (or repeaters) are deployed n close vcnty to the ral lnes and connected to content servers n the Internet. Powerful antennas are nstalled on each tran to communcate wth the nfostatons. The antennas are further connected to a vehcle staton whch can be accessed by the passenger devces based on wreless local Manuscrpt receved 15 May 211; revsed 25 October 211. Ths research s supported by a research grant from the Natural Scence and Engneerng Research Councl (NSERC). Ths work s presented n part at IEEE Globecom 211 [1]. The authors are wth the Department of Electrcal and Computer Engneerng, Unversty of Waterloo, 2 Unversty Avenue West, Waterloo, Ontaro, Canada N2L 3G1 (e-mal: {h8lang, wzhuang@uwaterloo.ca). Dgtal object dentfer XXXXXX area network (WLAN) technologes. Varous medum access control (MAC) protocols are studed for the communcatons between the nfostatons and vehcle statons. For nstance, the IEEE 82.11p MAC can be used for vdeo broadcastng n metro passenger nformaton systems [7], whle the MAC frame structure proposed n [4] can support data delvery to a hgh-speed tran wth a speed up to 36 km/h. In ths work, we consder a cellular/nfostaton ntegrated network archtecture to better utlze the resources of both network nfrastructures [8] [9]. Data servces are provded n an on-demand manner. A cellular network wth seamless coverage s consdered to support control channels for servce requests and acknowledgements to mnmze ther delay and avod congeston, whle data traffc s delvered va tracksde nfostatons to acheve a hgh data transmsson rate. For a large number of onboard passengers, the resource contenton among multple servces should be resolved. Further, the coverage provded by the nfostatons may not be seamless for a low deployment cost. As a hgh-speed tran travels along a ral lne, the wreless lnk from an nfostaton to a vehcle staton s hghly dynamc and subject to perodc dsconnectons, whch makes the resource allocaton challengng. In the lterature, the optmal on-demand broadcast schedulng s nvestgated for satellte and cellular networks [1] [11]. The proposed algorthms can resolve the resource contenton among multple servces. However, the approaches based on a constant rate broadcast lnk are not applcable to data delvery va nfostatons. On the other hand, the data delvery n a vehcular network wth ntermttent lnks s studed based on the moblty patterns of vehcles [8] [12]. Servce predownloadng approaches are proposed to reduce the data fetchng delay when the lnk from the backbone network to an nfostaton s a bottleneck [5] [13]. The solutons deal wth sngle servce delvery for each vehcle [5] [8] [12] or offlne resource allocaton based on servce popularty [13], whch cannot be drectly appled to on-demand data delvery to mass transportaton vehcles such as hgh-speed trans. A servce schedulng problem s dscussed n [1] under the assumpton that the bandwdth from the backbone network to an nfostaton s suffcently large, whle the servce predownloadng s not addressed. How to effcently allocate resources among multple on-demand data servces n such a network wth ntermttent connectvty s an open ssue. In ths paper, we nvestgate the resource allocaton for ondemand data delvery to hgh-speed trans, takng account of both ntermttent network connectvty and mult-servce demands. Specfcally, the contrbuton of ths paper s three-fold: ) The optmal resource allocaton problem s formulated based

2 2 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. XX, NO. XX, MONTH 2XX Symbol A h,k B c n G s (D s ) H K h M h,s (Mh,s d ) N Q s Q r h,k,s ( Q r h,k,s ) Q r ŝ,s S T F T I (T O ) Th (T h o) W h x h,k,s y n,s ω s TABLE I: Summary of mportant symbols used. Defnton The capacty of the kth frame wthn the hth nfostaton The sze of each data block The parttonng pont of vrtual perod The request tme (deadlne) of servce s The number of tracksde nfostatons The number of frames wthn the hth nfostaton The number of blocks to be (already) pre-downloaded at the hth nfostaton for servce s The number of vrtual perods The sze of servce s The numbers of remanng blocks of servce s before (after) the resource allocaton for the kth frame wthn the hth nfostaton The numbers of remanng blocks of servce s when servce ŝ s requested The set of on-demand data servces Frame duraton The startng (endng) tme of a trp The tme for a tran to come nto (go out of) the transmsson range of the hth nfostaton The bandwdth of the lnk from the backbone network to the hth nfostaton The number of blocks delvered to the vehcle staton durng the kth frame wthn the hth nfostaton for servce s The number of blocks delvered to the vehcle staton wthn the nth vrtual perod for servce s The reward of servce s on the trajectory of a tran, data servce demands, and network resources. In order to acheve effcent resource allocaton wth low computatonal complexty, the orgnal frame-based formulaton s transformed nto a capacty-based formulaton, whch s a sngle-machne preemptve schedulng problem wth nteger request tmes, processng tmes, and deadlnes. The transformaton s based on a tme-capacty mappng whch explots the predetermned hgh-speed tran schedule; ) An onlne resource allocaton algorthm s proposed to address the uncertantes n servce demands, and the performance bound s characterzed based on the theory of sequencng and schedulng. Gven the lnk from the backbone network to an nfostaton s a bottleneck, we analyze the pre-downloadng capacty and propose a servce pre-downloadng algorthm to facltate the resource allocaton; ) The performance of our proposed algorthms s evaluated based on a real hgh-speed tran schedule. It s shown that our proposed resource allocaton algorthms can sgnfcantly mprove the total reward of delvered servces as compared wth exstng algorthms. By tunng a redundant factor, dfferent tradeoff can be acheved between the overhead and reward of servce pre-downloadng. As many symbols are used n ths paper, Table I summarzes the mportant ones. Proofs of Theorem 1 and all the Lemmas are gven n Appendx. II. SYSTEM MODEL The network topology s shown n Fg. 1. Several tracksde nfostatons are deployed along the ral lne, whereas a cellular network provdes a seamless coverage over the regon. The base statons of the cellular network and the nfostatons are connected to the content servers n the Internet va wrelne lnks 1. When a passenger requests an on-demand data servce, the servce request s sent from the vehcle staton to the correspondng content server va the cellular network. The data traffc of the requested servce s delvered from the content server to the vehcle staton va the nfostatons. After the servce s delvered, an acknowledgement s made by the vehcle staton va the cellular network. For smplcty, we assume that the probablty of traffc congeston n the cellular and backbone networks s low, so that the servce requests and acknowledgements can be delvered wth a neglgble delay. Moreover, the data transmsson rate from a vehcle staton to a passenger devce s suffcently large. A data block can be successfully delvered to a passenger devce f t s delvered to the vehcle staton. For the communcatons between the nfostatons and the vehcle staton, we consder the MAC frame structure proposed n [4] whch s specfcally desgned for hgh-speed trans wth a speed up to 36 km/h. Tme s parttoned nto frames wth equal duraton T F. At the begnnng of each frame, one of the powerful antennas whch are nstalled on the tran s selected as the master antenna to broadcast a beacon sgnal to the nfostatons n the vcnty. The nfostatons whch can detect the beacon sgnal transmt ther unque dentfcaton sgnals as acknowledgments. Each of the antennas on the tran uses the acknowledgements for channel estmaton and tunes to the 1 Note that a wreless lnk s possble for an nfostaton wth two sets of wreless transcevers [6].

3 LIANG and ZHUANG: EFFICIENT ON-DEMAND DATA SERVICE DELIVERY TO HIGH-SPEED TRAINS IN CELLULAR/INFOSTATION INTEGRATED NETWORKS 3 A. Tran Trajectory Orgn Staton cumulatve capacty T I T 1 o T 1 Backbone Network T 2 o T 2 T 3 o T 3 Destnaton Termnal TO dstance tme c5 c4 c3 c2 c1 TI G1 G2 D2 D1 TO tme Consder a sngle trp of a tran from an orgn staton to a destnaton termnal wthn the tme duraton [T I, T O ]. A total number of H tracksde nfostatons are deployed along the ral lne. For nstance, we have H = 3 n Fg. 1. Each nfostaton covers a segment of the ral lne based on ts wreless transmsson range. Denote Th and T h o as tme nstants for the tran to come nto and go out of the transmsson range of the hth (h [1,, H]) nfostaton, respectvely. For solated nfostatons, we have Th o T h+1 for 1 h H 1. Takng nto account the duraton of a trp, we have T I T1 and TH o T O. In Fg. 1, the transmsson perod and dle perod are the tme duratons when the tran s n and out of the coverage area of an nfostaton, respectvely. Hgh-Speed Tran (Vehcle Staton) Base Staton Tracksde Infostaton Router Central Controller Content Server Wrelne Lnk Wrelne/Wreless Lnk Wreless Lnk Transmsson Perod Idle Perod Cellular Network Coverage Area Infostaton Coverage Area Fg. 1: System model and tme-capacty mappng. nfostaton wth the hghest lnk gan. Then all the nfostatons whch have detected the beacon sgnal start to broadcast data blocks. Ths scheme s referred to as the blnd nformaton ranng. If a group of nfostatons are deployed n close vcnty wth overlapped coverage area, an addtonal zone controller [4] should be deployed to control the group of nfostatons and schedule the broadcastng to reduce nterference and mprove data throughput. In ths paper, we manly focus on a network wth solated nfostatons and ntermttent lnk connectvty. However, the analytcal model can be drectly extended to a network wth some densely deployed nfostatons, by replacng each nfostaton n the current model wth a zone controller to take charge of schedulng the group of nfostatons n close vcnty. A central controller s deployed and can communcate wth the cellular network, nfostatons, and content servers. The central controller allocates the network rado resources based on the tran trajectory and data servce demands. The tran trajectory defnes the locaton of a tran at a specfc tme, whle the rado resources depend on the wreless channel condton from an nfostaton to a vehcle staton. Snce each tran moves on a predetermned ral lne and the schedule of a hgh-speed tran s hghly stable 2, the nformaton of tran trajectory and network resources can be obtaned by the central controller n advance wth hgh accuracy. However, the demand of a data servce s not known a pror untl the servce request s receved by the content server and delvered to the central controller. 2 Accordng to a recent report, the accuracy of tran departure tmes of Huhang hgh-speed ralway (also know as the Shangha-Hangzhou hgh-speed ralway) s about 99.5% [14] [15]. B. Data Servce Demands A set S of on-demand data servces are supported over the trp. The request of servce s (s S) s receved by the content server at tme G s. If servce s s delvered to the vehcle staton before ts deadlne D s, a reward ω s can be obtaned by the servce provder. We consder G s T I and D s T O, assumng that all other servces can be delvered to the passengers when they are off-board. Erasure codng based servce delvery s consdered [4] [13]. The nformaton data of servce s s encoded and segmented nto a large number Q s of blocks, each havng an equal sze of B bts. Servce s can be decoded when at least Q s (Q s < Q s ) dstnct blocks are receved. The advantage of usng erasure codng s that no recovery scheme s requred for the transmsson error or loss of a specfc block. The nfostatons only need to keep transmttng (or ranng accordng to [4]) the encoded blocks untl the servce can be decoded at the vehcle staton, whch sgnfcantly smplfes the protocol desgn for hghspeed tran applcatons subject to a hghly dynamc wreless channel condton. C. Network Resources The duraton that the tran s wthn the coverage of the hth nfostaton corresponds to a number of frames, gven by K h = (Th o T h )/T F. Note that the small dfference between Th and the begnnng tme of the frst frame s omtted. The kth frame begns and ends at tmes Th +(k 1)T F and Th + kt F, respectvely. We defne the capacty (A h,k ) of the kth frame as the maxmum number of blocks that can be delvered from the hth nfostaton to the vehcle staton wthn ths frame. The value of A h,k s determned by the wreless channel condton accordng to (3) n [4]. If the wreless channel s n deep fadng such that no block can be delvered to the vehcle staton, we have A h,k =. A roundrobn scheduler 3 s appled when multple trans are present n the coverage area of an nfostaton. If the kth frame wthn the hth nfostaton coverage s not allocated to the vehcle staton 3 A scheduler wth prortzaton can potentally mprove the performance of resource allocaton when multple trans are smultaneously wthn the coverage of an nfostaton. However, as the tme for two hgh-speed trans to meet s extremely short accordng to the real tran schedule (e.g., the one consdered n Secton VI), the performance mprovement can be very lmted.

4 4 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. XX, NO. XX, MONTH 2XX under consderaton, we have A h,k =. Snce the MAC s frame based, servce request tme (or deadlne) s rounded to the begnnng tme of a frame. Full-duplex nfostatons are consdered such that data fetchng from the content server and data delvery to the vehcle staton can be acheved smultaneously. Two cases are consdered for the lnk from the backbone network to an nfostaton: 1) The bandwdth of the lnk (e.g., a hgh data-rate wrelne lnk [4]) s suffcently large so that the capacty of each frame can be fully utlzed; 2) The lnk (e.g., a T1 based wrelne lnk at 1.5Mbps [16] or an IEEE 82.16j based wreless lnk [6]) s a bottleneck wth lmted bandwdth W h to the hth nfostaton. For the second case, data servces can be pre-downloaded at the nfostatons to acheve hgh rado resource utlzaton [8]. We consder an unlmted buffer space at the nfostatons. III. PROBLEM FORMULATION AND TRANSFORMATION In ths secton, we frst formulate the optmal resource allocaton problem. Then we ntroduce a tme-capacty mappng to transform the orgnal problem formulaton nto a capactybased problem formulaton. A. Problem Formulaton The objectve n servce provsonng s to maxmze the total reward of delvered servces over a trp of the tran. Defne x h,k,s as the number of blocks delvered to the vehcle staton durng the kth frame wthn the hth nfostaton coverage for servce s. The resource allocaton varable over the trp of the tran s gven by X = {x h,k,s h {1, 2,, H, k {1, 2,, K h, s S. For a specfc X, defne ψ X,s as a delvery ndcator of servce s, whch equals 1 f servce s s delvered before ts deadlne and otherwse. Based on erasure codng, we have ψ X,s = 1 f H Kh h=1 k=1 x h,k,s = Q s, and ψ X,s = f H Kh h=1 k=1 x h,k,s < Q s. Note that we do not consder the case H Kh h=1 k=1 x h,k,s > Q s because, for erasure codng based servce delvery, the resources are underutlzed by delverng more than Q s blocks for servce s. The optmal resource allocaton problem s formulated as (P1) max ω s ψ X,s (1) X subject to s S x h,k,s Z +, h {1, 2,, H, s S k {1, 2,, K h (2) H K h x h,k,s Q s, s S (3) h=1 k=1 x h,k,s =, f G s T h + kt F or D s T h + (k 1)T F, h {1, 2,, H, s S k {1, 2,, K h (4) x h,k,s A h,k, h {1, 2,, H, s S k {1, 2,, K h. (5) Constrant (2) mples that negatve resource allocaton s not allowed, where Z + = N { represents the set of nonnegatve ntegers. Constrant (4) states that the blocks of a servce can only be delvered after the request tme and before the deadlne. Wth (5), the number of blocks that can be delvered to the vehcle staton durng the kth frame wthn the hth nfostaton coverage s lmted by the capacty A h,k of the frame. Problem P1 s a mxed nteger programmng (MIP) problem whch cannot be solved effcently [17]. The man dffculty of analyzng problem P1 comes from the nteger nature of constrant (2). However, based on further nvestgaton, we observe that problem P1 can be potentally consdered as a problem of sequencng and schedulng [18] because of the constant request tme, deadlne, sze (n terms of the number of blocks), and reward of each servce. However, the exstng theory of sequencng and schedulng cannot be drectly appled to analyze problem P1 snce the servces are not schedulable contnuously over tme because of the ntermttent lnk connectvty. Moreover, the data transmsson rate (n terms of A h,k ) from nfostatons to a vehcle staton s not a constant. Therefore, the duraton to complete each servce s dependent on the tme when the servce s requested and scheduled. In order to better characterze problem P1 and develop effcent algorthms to solve t, we consder a problem transformaton n the rest of ths secton such that the tme ndces are vrtually mapped to cumulatve capacty values, as shown n Fg. 1. Here we defne the cumulatve capacty at tme t (t [T I, T O ]) as the summaton of the capactes of all frames wthn [T I, t]. The problem transformaton conssts of two steps,.e., tme-capacty mappng and capacty-based problem formulaton as presented n the followng. Here problem P1 s referred to as the frame-based problem formulaton. B. Tme-Capacty Mappng For a specfc trp of the tran, the maxmum number of blocks that can be delvered to the vehcle staton s lmted by H Kh h=1 k=1 A h,k. [ Defne a tme-capacty mappng ] functon Kh k=1 A h,k f(t) : [T I, T O ], 1,, H h=1 whch maps tme t to the correspondng cumulatve capacty. Based on the nformaton of tran trajectory and network rado resources, we have the followng lemma. Lemma 1. The value of f(t) s gven by (t T h t )/T F A ht,j + h t 1 Kl, f(t) = f h t 1 and t Th o t ht Kl, otherwse { where h t = arg max h T h t f t T1, and h t = otherwse. Wthout loss of generalty, we consder the summaton b l=a ( ) equals zero f b < a. Intutvely, more blocks can be potentally delvered to the vehcle staton as tme t ncreases. Ths property s nherent for f(t) and stated by the followng lemma. Lemma 2. The mappng f(t) s a non-decreasng functon wth respect to t (t [T I, T O ]). (6)

5 LIANG and ZHUANG: EFFICIENT ON-DEMAND DATA SERVICE DELIVERY TO HIGH-SPEED TRAINS IN CELLULAR/INFOSTATION INTEGRATED NETWORKS 5 In problem P1, only constrant (4) s drectly related to the tme ndces. Therefore, we can apply the tme-capacty mappng functon f(t) on constrant (4) to transform t nto a capacty-based constrant. Based on Lemma 1 and Lemma 2, the followng theorem holds. Theorem 1. For problem P1, (4) s equvalent to a capactybased constrant gven by x h,k,s =, f G c s k K l A h,j + k 1 K l or Ds c A h,j +, s S h {1, 2,, H, k {1, 2,, K h (7) where G c s = f (G s ) and D c s = f (D s ). In (7), G c s and D c s can be consdered as the vrtual request tme and deadlne of servce s, respectvely, whch are defned based on the cumulatve capacty. C. Capacty-Based Problem Formulaton By replacng (4) n problem P1 wth (7), we can obtan problem P2. Snce all constrants of problem P2 are defned based on the number of blocks, we can smplfy problem P2 by ntroducng a capacty-based formulaton. By defnton, we have f(t I ) = and f(t O ) = H h=1 Kh k=1 A h,k. Then the set {T I, T O, G s, D s s S of tme ndces can be represented by a set C of unque cumulatve capacty, gven by C = s S {f (G s ), f (D s ) {f (T I ), f (T O ) { H K h = s S {G c s, Ds c, A h,k. (8) h=1 k=1 Let C = N + 1 (N 1) and c n (1 n N + 1) be the cardnalty and elements of set C, respectvely. Wthout loss of generalty, we consder an ascendng order of the elements n C,.e., c 1 < c 2 < < c N+1. An example s shown n Fg. 1, where two servces are consdered wth request tmes G 1 and G 2, and deadlnes D 1 and D 2, respectvely. Then we have N = 4 and c n (1 n 5) gven by c 1 =, c 2 = G c 1, c 3 = G c 2, H K h c 4 = D1 c = D2, c c 5 = A h,k (9) h=1 k=1 where D 1 and D 2 are mapped to the same cumulatve capacty c 4 snce no block can be delvered durng an dle perod. Note that f G c 2 < D1 c D2 c < H Kh h=1 k=1 A h,k, we have N = 5, whle each element n C (other than c 1 and c 6 ) corresponds to the request tme or deadlne of a servce. We partton the trp of the tran nto N non-overlapped vrtual perods accordng to the cumulatve capacty values n C. Wthn the nth vrtual perod (defned by [c n + 1, c n+1 ]), no new servce s requested and no exstng servce expres snce all servce request tmes and deadlnes are consdered n the calculaton of set C. Therefore, for a feasble resource allocaton, changng the sequence of servce schedulng wthn a vrtual perod does not affect the servce delvery performance. Ths property s formally stated by the followng lemma. Lemma 3. Consder a feasble resource allocaton varable X wth four elements x h1,k 1,s 1, x h1,k 1,s 2, x h2,k 2,s 1, x h2,k 2,s 2. Suppose x h1,k 1,s 1, x h2,k 2,s 2 1, x h1,k 1,s 2, x h2,k 2,s 1. All blocks of the two frames (.e., the k 1 th frame wthn the h 1 th nfostaton coverage and the k 2 th frame wthn the h 2 th nfostaton coverage) belong to the same vrtual perod, whle the two frames are not dentcal. Construct another resource allocaton varable X by replacng the elements x h1,k 1,s 1, x h1,k 1,s 2, x h2,k 2,s 1, x h2,k 2,s 2 n X wth x h1,k 1,s 1 1, x h1,k 1,s 2 + 1, x h2,k 2,s 1 + 1, x h2,k 2,s 2 1 and keepng all other elements unchanged. Then we have the same feasbltes and objectve functon values for X and X. Based on Lemma 3, the optmal resource allocaton can be acheved by consderng the total number of blocks delvered for each servce wthn each vrtual perod. Defne y n,s as the number of blocks delvered to the vehcle staton for servce s wthn the nth vrtual perod. Then the resource allocaton varable over the trp of the tran s gven by Y = {y n,s n {1, 2,, N, s S. Defne the delvery ndcator of servce s as η Y,s. We have η Y,s = 1 f N n=1 y n,s = Q s, and η Y,s = f N n=1 y n,s < Q s. Then problem P2 can be transformed nto a capacty-based formulaton as follows (P3) max ω s η Y,s (1) Y s S subject to y n,s Z +, n {1, 2,, N, s S (11) N y n,s Q s, s S (12) n=1 y n,s =, f G c s c n or D c s c n, n {1, 2,, N (13) y n,s c n+1 c n, n {1, 2,, N(14) s S where (14) states that the number of blocks whch can be delvered to the vehcle staton durng the nth vrtual perod s lmted to c n+1 c n. IV. RESOURCE ALLOCATION Based on the problem transformaton, tme ndces are vrtually transformed to the cumulatve capacty values, over whch the servces are contnuously schedulable. Accordng to the theory of sequencng and schedulng, problem P3 defnes a sngle-machne preemptve schedulng problem wth nteger request (or release) tmes (G c s), processng tmes (Q s ), and deadlnes (D c s) (formal notaton: 1 G c s, preempton ω s η Y,s ), whch can be solved by a dynamc programmng algorthm at complexty O( S L 2 G L2 ω), where L G s the number of dstnct request tmes, and L ω represents the sum of the nteger reward [18] [21]. The complexty s known as pseudo-polynomal [21] snce the representaton of all rewards ω s (s S) by ntegers may result n a large L ω and a hgh computatonal complexty accordngly. Moreover,

6 6 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. XX, NO. XX, MONTH 2XX for on-demand data servces, the servce demands are not known a pror. In order to acheve effcent resource allocaton for on-demand data servce delvery to hgh-speed trans, we devse an onlne algorthm n ths secton. As the onlne algorthm s devsed based on problem P3, ts performance bound can be characterzed based on the theoretcal results of the sngle-machne preemptve schedulng problem, to be dscussed n the followng. As the tran moves from the orgn staton to the destnaton termnal, the onlne algorthm allocates the network resources to multple servces frame-by-frame. Consder the kth frame wthn the hth nfostaton coverage, wth x h,k,s blocks { delvered for servce s (s S g h,k ), where Sg h,k = s s S, Gs Th + (k 1)T F represents the set of requested servces. The resource allocaton algorthm s detaled n Algorthm 1, where Q r h,k,s and Q r h,k,s are the numbers of remanng blocks of servce s before and after the kth frame, respectvely. The algorthm needs to be performed only when S g h,k. For a newly requested servce s,.e., S g h,k, f h = 1, k = 1 s S g h,k \ Sg,K, f h 1, k = 1 (15) S g h,k \ Sg h,k 1, otherwse we have Q r h,k,s = Q s; Otherwse, we have { Qr Q r h,k,s =, f k = 1,K,s Q r h,k 1,s, f k > 1. (16) In (15) and (16), k = 1 corresponds to the frst frame wthn an nfostaton coverage. In (16), f k = 1, we have h 1 snce the servce s consdered to be new n one of the prevous frames. Algorthm 1 teratvely allocates the capacty of a frame (A h,k ) to the on-demand data servces n descendng order of ther utltes, untl the capacty of the frame s fully utlzed. In step 3, S A represents the set of actve servces whch can possbly be delvered before ther deadlnes, gven by S A = s s Sg h,k, Q r h,k,s >, Ds c Q k r h,k,s + A h,j K l + m. (17) In step 7, U s represents the utlty of servce s. We consder two knds of utltes,.e., Smth rato and exponental capacty [2]. For Smth rato based algorthm, U s = ω s /Q s. Intutvely, a servce wth a hgher reward or smaller sze can obtan a hgher utlty. For the exponental capacty based algorthm, the utlty functon ncorporates the number of remanng blocks ( Q r h,k,s ) whch corresponds to the current condton of each servce, and s gven by ( ) ln max s S g Q Q r h,k,s 1 s h,k U s = ω s 1 max s S g h,k Q s. (18) The complexty of Algorthm 1 s O (max h,k {A h,k S ). Defne the compettve rato of Algorthm 1 as the maxmal Algorthm 1 Resource Allocaton Algorthm Input: k, h, G c s, Ds, c ω s, Q s, Q r h,k,s (s Sg h,k ) Output: x h,k,s, Q r h,k,s (s Sg h,k ) 1: Intalze x h,k,s =, Q r h,k,s = Qr h,k,s for s Sg h,k, m = A h,k ; 2: whle m do 3: S A calculaton; 4: f S A = then 5: break; 6: end f 7: U s calculaton, for s S A ; 8: s = arg max s SA {U s ; 9: Update x h,k,s x h,k,s + 1, Qr h,k,s Q r h,k,s 1, m m 1; 1: end whle rato (corresponds to the worst-case performance of Algorthm 1 wth respect to the randomness n servce requests) of the total reward of delvered servces based on the optmal soluton of problem P3 to that of the delvered servces based on Algorthm 1. The compettve rato of the Smth rato and exponental capacty based algorthm s gven by 2 max s S {Q s and max s S {Q s / ln(max s S {Q s ), respectvely [2]. Snce we have 1/ ln(max s S {Q s ) < 2 for typcal on-demand data servces whch consst of a large number of blocks, the exponental capacty based algorthm can mprove the performance of resource allocaton n worstcase scenaros, at the cost of hgher computatonal complexty n step 7. However, the computatonal complexty can be potentally reduced. For nstance, a straghtforward approach s to mantan a queue of all actve servces and sort the servces n descendng order of ther utltes. In ths way, the headof-lne (HOL) servce always represents the servce wth the hghest utlty to be scheduled. For the resource allocaton n each frame, the order s updated only for the newly requested servces or the servces wth some blocks beng delvered. As a result, step 7 and step 8 do not need to be recalculated for each actve servce durng each teraton wth respect to m. V. SERVICE PRE-DOWNLOADING When the lnk from the backbone network to an nfostaton s the bottleneck of servce delvery, the capacty A h,k of a frame s underutlzed f less than A h,k blocks are fetched from the content server wthn the frame. In order to address ths problem, a servce pre-downloadng mechansm can be mplemented [5], [8], [13]. In the cellular/nfostaton ntegrated network, after a servce request s receved by the content server, the data blocks of the servce can be pre-downloaded to the nfostatons to be vsted by the vehcle staton, and then delvered to the vehcle staton upon ts arrval. A smple servce pre-downloadng approach s to buffer all data blocks of the avalable servces at each nfostaton. However, ths approach s not only nfeasble (because of the lmted bandwdth of the bottleneck lnk) but also neffcent (as some pre-downloaded blocks cannot be transmtted to the vehcle staton durng ts short vst to each of the nfostatons).

7 LIANG and ZHUANG: EFFICIENT ON-DEMAND DATA SERVICE DELIVERY TO HIGH-SPEED TRAINS IN CELLULAR/INFOSTATION INTEGRATED NETWORKS 7 In the followng, we propose a servce pre-downloadng approach to facltate the resource allocaton of Algorthm 1. Let S g ŝ = {s s S, G s Gŝ denote the set of requested servces at tme Gŝ. We want to determne the number of blocks (M h,s ) to be pre-downloaded at the hth (h [1,, H]) nfostaton for servce s S g ŝ. Next, we frst analyze the pre-downloadng capacty to determne the maxmum number of blocks to be pre-downloaded at each nfostaton, and then present a servce pre-downloadng algorthm to calculate M h,s. A. Pre-Downloadng Capacty and Redundant Factor Takng account of the lmted capacty of each frame, the number of blocks to be pre-downloaded at the hth nfostaton ( s S M h,s) should be lmted by the sum capacty of all frames wthn the nfostaton coverage ( k K h A h,k ). On the other hand, for a gven tme t (t < Th o ), the duraton of servce pre-downloadng to the hth nfostaton s gven by Th o t. Note that the transmsson perod wth duraton Th o T h s taken nto account snce full-duplex nfostatons are consdered. Wth the bandwdth W h of the bottleneck lnk, the maxmum number of blocks that can be fetched from the content server durng Th o t s (T h o t)w h/b. Then the pre-downloadng capacty of the hth nfostaton at tme t s { Q c h,t = mn A h,k, (Th o t)w h /B. (19) k K h As dscussed n Secton II, servce s can be successfully decoded f Q s blocks are receved by the vehcle staton before D s. However, because of the resource contenton among multple servces, the number of pre-downloaded blocks of servce s s dependent on other servce demands. Therefore, we ntroduce a redundant factor β (β ) for servce predownloadng. Specfcally, for each servce, the number of predownloaded blocks at the nfostatons to be vsted s β tmes the number of remanng blocks to be delvered. The larger the β, the more blocks can be pre-downloaded for each servce and the less number of servces can be pre-downloaded. Note that β can be larger than one snce some pre-downloaded blocks of a servce may not be delvered to the vehcle staton when new servces wth hgh prortes arrve. B. Servce Pre-Downloadng Algorthm Based on the pre-downloadng capacty and redundant factor, a servce pre-downloadng algorthm s devsed. When the request of a servce ŝ s receved at tme Gŝ, the servce pre-downloadng varables (M h,s ) are calculated accordng to Algorthm 2, where Q r ŝ,s represents the number of remanng blocks of servce s at tme Gŝ. In step 5, only the set of actve servces whch can possbly be delvered before ther deadlnes s consdered. The mnmum operaton n step 9 s performed over two terms correspondng to the predownloadng capacty and redundant factor, respectvely. For the frst term, a summaton j 1 =1 M h,s s subtracted snce the correspondng capacty s used to pre-download servces wth hgher prortes, whle for the second term, a summaton l=h Gŝ +1 M l,s j s subtracted snce ths amount of blocks s Algorthm 2 Servce Pre-Downloadng Algorthm Input: G s, D s, G c s, Ds, c ω s, Q s, Q r ŝ,s (s Sg ŝ ) Output: M h,s (h {1,, H, s S g ŝ ) 1: Intalze M h,s = for h {1,, H, s S g ŝ ; 2: U s calculaton, for s S g ŝ ; 3: Sort servces n S g ŝ n descendng order of ther utltes and obtan the ordered set {s 1, s 2,, s S g ŝ ; 4: for j = 1 to S g ŝ do 5: f Q r ŝ,s j = or Ds c j < G c ŝ + Qr ŝ,s j then 6: Contnue; 7: end f 8: for h = h Gŝ + 1{ to H do 9: M h,sj = mn Q c j 1 h,gŝ =1 M h,s, 1: end for 11: end for βq r ŝ,s j l=h Gŝ +1 M l,s j ; to be pre-downloaded to the nfostatons before nfostaton h. The utlty (U s ) of servce s s gven by the resource allocaton Algorthm 1. The complexty of Algorthm 2 s O (H S ). Let Mh,s d denote the number of blocks already predownloaded at nfostaton h for servce s. Because of the arrval of servces wth hgher prortes, we may have M h,s < Mh,s d. Therefore, the number of blocks to be pre-downloaded for servce s at nfostaton h s gven by max{, M h,s Mh,s d. For each nfostaton, the data blocks of the servces are fetched from the content server n descendng order of ther utltes. When multple trans are travelng on parallel hgh-speed rals between the orgn staton and destnaton termnal [14], Algorthm 2 s appled by lettng S g ŝ represent the set of servces requested by all the trans. When a tran comes nto the transmsson range of an nfostaton, the pre-downloaded blocks are scheduled for transmsson accordng to Algorthm 1. After all pre-downloaded blocks are delvered, the remanng blocks of avalable servces are drectly fetched from the content servers. VI. NUMERICAL RESULTS In order to evaluate performance of the proposed resource allocaton algorthms, we consder a real tran schedule based on the Huhang hgh-speed ralway [22]. The ralway s specally desgned for hgh-speed trans wth a maxmum speed of 35 km/h. There are ten statons on the ralway and the locaton of each staton (n terms of the dstance from the Shangha staton) s gven n Table II. Snce no moblty trace s avalable, we consder a synthetc tran moblty model proposed n [23]. Each tran moves at a constant speed when t travels from one staton to another. When a tran leaves (arrves at) a staton, t accelerates (decelerates) accordng to a constant acceleraton (deceleraton). For smplcty, we consder the deceleraton equals to the negatve value of the acceleraton (α). A typcal value for the acceleraton α of a hgh-speed tran s gven by.4 m/s 2 [24]. Fve sample trajectores of the hgh-speed trans are shown n Fg. 2, for two trans from Hangzhou (G743 and G732) and three trans from Shangha (G741, G731, and G7362). The

8 8 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. XX, NO. XX, MONTH 2XX TABLE II: Locatons of statons on the ralway. Staton Shangha Hongqao Songjang Dstance (km) Staton Jnshan Jashan Jaxng Dstance (km) Staton Tongxang Hanng Yuhang Dstance (km) Staton Hangzhou Dstance (km) 22 Dstance (km) Hangzhou 2 18 Yuhang Jaxng G743 4 Hongqao G732 G741 2 G731 G7362 Shangha Tme (mn) Fg. 2: Trajectory of the hgh-speed trans. startng tme of tran G743 (6:5 am) based on the February 211 schedule s chosen to be tme. Note that the trans G731 and G732 need less tme to travel between Hongqao and Hangzhou snce they do not stop at two ntermedate statons, Jaxng and Yuhang. For the wreless channel condton, we use a typcal settng for a hgh-speed tran [4], wth T F = 53µs, B = 24 bts, and H = 4. The wreless communcaton between an nfostaton and the vehcle staton s establshed based on a carrer frequency of 2.4GHz and an approxmate data rate of 5Mbps. On each tran operatng on Huhang hgh-speed ralway, 13 antennas can be deployed wth a separaton dstance of 15 m between adjacent antennas. The dstance between each nfostaton and the ral lne s 3 m. The transmsson range of each nfostaton s approxmately 5 m. The servce requests arrve at a tran accordng to a Posson process wth average rate λ. The number of blocks of each servce (Q s ) s unformly dstrbuted wthn [Q mn = 5, Q max = 5] (correspondng to a servce sze wthn [1.5, 15] Mbytes). The lfetme (D s G s ) of each servce s exponentally dstrbuted wth average value 2 mnutes. The reward of each servce (ω s ) s unformly dstrbuted wthn [1, 1] 4. 4 In realty, the reward of each servce may depend on many factors such as the servce sze, urgency (delvery deadlne), and prorty. How to map these factors to the reward for practcal hgh-speed tran applcatons s stll an open ssue and left for our future work. In addton to the proposed resource allocaton algorthms, we consder three exstng algorthms for comparson,.e., frst-n-frst-out (FIFO), earlest due date (EDD), and RAPID [12]. For the FIFO and EDD algorthms, the servces are scheduled accordng to an ascendng order of ther request tmes and deadlnes, respectvely. RAPID s a typcal sngleservce resource allocaton algorthm for a network wth ntermttent lnks. Snce the RAPID algorthm s orgnally proposed for randomzed node moblty, we have modfed the algorthm to ncorporate the pre-determned tran schedule for far comparson. To calculate the utlty functon, we modfy the algorthm by replacng the tme ndces wth cumulatve capacty values based on the tme-capacty mappng. Moreover, the transfer opportunty [12] (whch determnes the maxmum number of blocks that can be delvered from an nfostaton to the vehcle staton) s changed from a constant defned by the orgnal work to the sum of the capacty of all frames wthn each nfostaton, whch s a varable wth respect to dfferent nfostatons accordng to the tran schedule. A. Performance of Resource Allocaton Algorthms The performance of our proposed resource allocaton algorthm s evaluated by extensve smulatons under dfferent system parameters, such as servce arrval rate, tran schedule, servce sze, and servce lfetme. The total reward of delvered servces versus average servce arrval rate (λ) s shown n Fg. 3 for tran G732. The standard devatons are llustrated for reference. The total reward s low for the FIFO and EDF algorthms snce they do not ncorporate the tran trajectory and data servce demands. Although the EDF algorthm performs well when most servces can be delvered before ther deadlnes, ts performance degrades as λ ncreases [25]. For a large λ, the total rewards acheved by the RAPID algorthm and our proposed algorthm mprove snce more servces can be potentally scheduled. However, the ncrement dwndles snce the network throughput becomes saturated. The RAPID algorthm performs better than the FIFO and EDF algorthms snce the moblty nformaton of the tran s taken nto account. By further ncorporatng the demands of multple servces, our proposed resource allocaton algorthm acheves the best performance. In comparson wth the exstng algorthms, the performance gan acheved by our proposed algorthm mproves as the servce arrval rate ncreases, whch s a desrable property for hgh-speed trans wth hundreds of passengers onboard and an ever-growng servce demand. Although the compettve factor of the exponental capacty based algorthm s hgher than that of the Smth rato based algorthm, the performance of resource allocaton s comparable snce a worst case scenaro for the algorthm (.e., there s a large servce wth hgh reward whch consumes most of the network resources [2]) happens wth a low probablty for the hgh-speed tran applcatons. Fg. 4 shows the total reward of delvered servces versus λ for tran G741. For the same λ value, tran G741 has a hgher total reward than tran G732, because the former has a longer trp duraton, as shown n Fg. 2, resultng n more delvered servces.

9 LIANG and ZHUANG: EFFICIENT ON-DEMAND DATA SERVICE DELIVERY TO HIGH-SPEED TRAINS IN CELLULAR/INFOSTATION INTEGRATED NETWORKS 9 Total reward of delvered servces Exponental Capacty Smth Rato RAPID FIFO EDF Total reward of delvered servces Exponental Capacty Smth Rato RAPID FIFO EDF λ (servce/s) Average servce sze (Mbytes) Fg. 3: Impact of servce arrval rate (G732). Fg. 5: Impact of servce sze Total reward of delvered servces Exponental Capacty Smth Rato RAPID FIFO EDF Total reward of delvered servces Exponental Capacty Smth Rato RAPID FIFO EDF λ (servce/s) τ (s) Fg. 4: Impact of servce arrval rate (G741). Fg. 6: Impact of servce lfetme. Fg. 5 shows how the total reward of delvered servces changes wth the average servce sze, wth Q mn = 5 and Q max varyng accordng to the average. We can see that the total reward decreases as the average downloadng fle sze ncreases. For a larger average servce sze, more resources are needed to delver each servce. As a result, a less number of servces can be delvered under the lmted resources. The total reward of delvered servces ncreases wth the average servce lfetme (τ), as shown n Fg. 6. For a larger τ, more nfostatons can be vsted by an vehcle staton before a servce expres, whch ncreases the probablty of delverng the servce. However, the ncrement dwndles when τ s large snce the network throughput becomes saturated. From Fgs. 4-6, we can see that our proposed resource allocaton algorthms outperform the exstng algorthms under dfferent system parameters. As smlar performance s observed for Smth rato and exponental capacty utltes, n the followng performance evaluaton, we consder the Smth rato based algorthm as an example. B. Performance of Servce Pre-Downloadng Algorthm The effect of the bottleneck lnk bandwdth (W h ) n servce pre-downloadng s shown n Fg. 7 for tran G743, where all nfostatons have the same bandwdth W h = W (h [1,, H]). The total reward s sgnfcantly mproved by the servce pre-downloadng. As the bandwdth ncreases, the total reward mproves slowly wthout servce pre-downloadng snce all data blocks need to be fetched drectly from the content servers upon the arrval of a vehcle staton, whch underutlzes the capacty of the wreless channel (n frames). On the other hand, wth servce pre-downloadng, a hgher reward can be acheved even for a small W h snce the dsconnected perod of a vehcle staton s effectvely exploted by the nfostatons to pre-download data blocks. Fg. 8 and Fg. 9 show that the redundant factor (β) has a crtcal mpact on the resource allocaton performance. As demonstrated n Fg. 8, the number of pre-downloaded blocks ncreases as β ncreases. However, the ncrement decreases for a large β because of a saturated throughput of the bottleneck

10 1 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. XX, NO. XX, MONTH 2XX Total reward of delvered servces Wth servce pre downloadng Wthout servce pre downloadng W (bt/s) x 1 5 Fg. 7: The total reward wth and wthout servce pre-downloadng (λ =.2 servce/s). Number of pre downloaded blocks 3.5 x λ =.5 servce/s λ =.1 servce/s β Fg. 8: Number of pre-downloaded blocks versus redundant factor (W = 1 4 bt/s). lnk. Also, the number of pre-downloaded blocks ncreases wth λ. From Fg. 9, we can see that, as β ncreases, the total reward frst ncreases and then decreases. When β s small, more servces can be pre-downloaded at each nfostaton whle the number of blocks pre-downloaded for each servce s small. The hghest total reward s acheved at β =.6 and β = 1.4 for α =.5 servce/s and α =.1 servce/s, respectvely. Ths observaton ndcates that, for a lower servce arrval rate, more blocks should be pre-downloaded for each servce, and vce versa. However, further nvestgaton s needed to determne the optmal value of β and to strke a balance between the overhead of servce pre-downloadng and the total reward of delvered servces. VII. CONCLUSIONS In ths paper, we formulate an optmal resource allocaton problem for on-demand data delvery to hgh-speed trans n a cellular/nfostaton ntegrated network. The problem s transformed nto a sngle-machne preemptve schedulng problem wth nteger request tmes, processng tmes, and deadlnes. An onlne resource allocaton algorthm wth the Smth rato and exponental capacty based utlty functons s proposed. The performance bound of the onlne algorthm s characterzed based on the theory of sequencng and schedulng wth respect to the sngle-machne preemptve schedulng problem. Further, a servce pre-downloadng algorthm s presented to acheve effcent resource allocaton when the lnk from the backbone network to an nfostaton s a bottleneck. It s demonstrated that the proposed resource allocaton algorthm can mprove the total reward of delvered servces over the exstng approaches such as FIFO, EDF, and RAPID, and that the servce pre-downloadng algorthm can sgnfcantly mprove the effcency of resource allocaton when the bandwdth of the lnk to the nfostaton s a lmtng factor. By tunng the redundant factor, dfferent tradeoff can be acheved between the overhead of servce pre-downloadng (n terms of the number of predownloaded blocks) and total reward of delvered servces. Total reward of delvered servces λ =.5 servce/s λ =.1 servce/s β Fg. 9: Total reward of delvered servces versus redundant factor (W = 1 4 bt/s). Further work ncludes a jont formulaton of the servce predownloadng problem and resource allocaton problem, and the desgn of a more effcent utlty functon for the onlne algorthm. Moreover, for practcal hgh-speed tran applcatons, how to map the qualty of servce (QoS) parameters such as the servce sze, relatve deadlne, and mportance/prorty to the reward of each servce s an nterestng topc and left for our future work. APPENDIX A: PROOF OF LEMMA 1 Two cases are consdered for a gven t. Case 1: t s n a transmsson perod (.e., h, Th t T h o ); Case 2: t s n an dle perod (.e., h, Th t T h o). Case 1: At tme t, the nfostaton wth whch { the vehcle staton can communcate s h t = arg max h T h t. The number of frames wthn the h t th nfostaton coverage before tme t s (t Th t )/T F, and the sum capacty of these frames s gven by (t T h t )/T F A ht,j. On the other hand,

11 LIANG and ZHUANG: EFFICIENT ON-DEMAND DATA SERVICE DELIVERY TO HIGH-SPEED TRAINS IN CELLULAR/INFOSTATION INTEGRATED NETWORKS 11 f h t > 1, the sum capacty of the frames wthn the coverage of nfostatons [1,, h t 1] s gven by h t 1 Kl. Case 2: The nfostaton { most recently vsted by the tran s h t = arg max h T h t. Snce no block can be delvered durng an dle perod, the cumulatve capacty s gven by the sum capacty of all frames n nfostatons [1,, h t ],.e., ht Kl. APPENDIX B: PROOF OF LEMMA 2 Consder two tme nstants t 1 and t 2, such that T I t 1 < t 2 T O. There are four cases. Case 1: Both t 1 and t 2 are n a transmsson perod; Case 2: Both t 1 and t 2 are n an dle perod; Case 3: t 1 s n a transmsson perod whle t 2 s n an dle perod; Case 4: t 1 s n an dle perod whle t 2 s n a transmsson perod. Snce the proof s smlar for the dfferent cases, we show the proof of Case 1 n the followng. If both t 1 and t 2 are n the same transmsson perod,.e., = h t2, we have h t1 f (t 1 ) = (t 2 T ht1 )/T F (t 2 T ht2 )/T F A ht1,j + A ht2,j + h t1 1 h t2 1 K l K l = f (t 2 ). (2) The nequalty n (2) s due to (t T )/T ht1 F beng a nondecreasng functon of t, and A h,j beng non-negatve. If t 1 and t 2 are n dfferent transmsson perods,.e., h t1 + 1 h t2, we have f (t 1 ) (T o ht1 T ht1 )/T F h t1 K l = (t 2 T ht2 )/T F A ht1,j + h t2 1 h t1 1 K l A ht2,j + h t2 1 K l K l = f (t 2 ). (21) The frst nequalty n (21) holds as T h t1 t 1 T o h t1. APPENDIX C: PROOF OF THEOREM 1 For suffcency, we frst consder the condton G s T h + kt F. Snce f(t) s a non-decreasng functon wth respect to t accordng to Lemma 2, we have G c s = f (G s ) f ( T h + kt F ) = = (T h +kt F T h )/T F K l A h,j + k K l A h,j +. (22) Smlarly, we can obtan Ds c k 1 A h,j + Kl for D s Th + (k 1)T F. For necessty, we cannot derve (4) drectly from (7) snce f(t) s not a bjectve functon and thus s not reversble. Instead, we resort to (2) and (5) of problem P1. We frst prove the nequalty part based on contradcton. Consder Kl n (7). Suppose G s < G c s > k A h,j + Th + kt F, snce f(t) s a non-decreasng functon of t, we have G c s = f(g s ) f ( T h + kt F ) = k K l A h,j +. (23) As (23) contradcts wth G c s > k A h,j+ Kl, we have G s Th + kt F. Kl n (7). Next, consder G c s = k A h,j + Suppose G s < Th + kt F. Snce the servce request tme s rounded to the begnnng tme of a frame, we have G s Th + (k 1)T F. By applyng functon f(t) on both sdes of the nequalty, we have G c s = f(g S ) f ( k 1 Th ) K l + (k 1)T F = A h,j + k K l A h,j +. (24) Wth G c s = k A h,j + Kl, the frst and second nequaltes n (24) should take equal sgns. Based on the second equalty k 1 A h,j + Kl = k A h,j + Kl, we have A h,k =. Accordng to (5), the summaton of the resource allocaton varables for the kth frame wthn the hth nfostaton coverage s upperbounded by A h,k,.e., s S x h,k,s A h,k. Moreover, snce x h,k,s can take only non-negatve values as stated by (2), we have x h,k,s =, s S. Ths result ndcates that for G c s = k A h,j + Kl n (7), we already have x h,k,s = for G s < Th + kt F n problem P1. The dscusson Kl s smlar and omtted on Ds c k 1 A h,j+ here. Snce both suffcency and necessty are satsfed, (4) s equvalent to (7) for problem P1. APPENDIX D: PROOF OF LEMMA 3 Defne c p h,k = k 1 A h,j + K as the cumulatve capacty of all frames pror to the kth frame wthn the hth nfostaton coverage. Snce x h1,k 1,s 1, x h2,k 2,s 2 1, the two frames under consderaton should have non-zero capacty,.e., A h1,k 1, A h2,k 2 >. Wthout loss of generalty, we consder all blocks of the two frames belong to the nth vrtual perod,.e., {c ph1,k1 + 1, c ph1,k1 + 2,, c ph1,k1 + A h1,k 1 [c n + 1, c n+1 ] (25) {c ph2,k2 + 1, c ph2,k2 + 2,, c ph2,k2 + A h2,k 2 [c n + 1, c n+1 ]. (26)