IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 1

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1 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOG 1 A Cross-Layer Framework for Overhead Reducton, Traffc Schedulng, and Burst Allocaton n IEEE OFDMA Networks Ja-Mng Lang, Jen-Jee Chen, ou-chun Wang, and u-chee Tseng Abstract IEEE OFDMA downlnk subframes have a specal 2D channel-tme structure. Allocaton resources from such a 2D structure ncurs extra control overheads that hurt network performance. Exstng solutons try to mprove network performance by desgnng solely ether the scheduler n the MAC layer or the burst allocator n the physcal layer, but the effcency of overhead reducton s lmted. In the paper, we pont out the necessty of co-desgnng both the scheduler and the burst allocator to effcently reduce overheads and mprove network performance. Under the PUSC model, we propose a cross-layer framework that covers overhead reducton, real-tme and non-real-tme traffc schedulng, and burst allocaton. The framework ncludes a two-ter, prorty-based scheduler and a bucket-based burst allocator, whch s more complete and effcent than pror studes. Both the scheduler and the burst allocator are tghtly coupled together to solve the problem of arrangng resources to data traffcs. Gven avalable space and bucket desgn from the burst allocator, the scheduler can well utlze frame resource, reduce real-tme traffc delays, and mantan farness. On the other hand, wth prorty knowledge and resource assgnment from the scheduler, the burst allocator can effcently arrange downlnk bursts to satsfy traffc requrements wth low complexty. Through analyss, the cross-layer framework s valdated to gve an upper bound to overheads and acheve hgh network performance. Extensve smulaton results verfy that the cross-layer framework sgnfcantly ncreases network throughput, mantans long-term farness, allevates real-tme traffc delays, and enhances frame utlzaton. Index Terms burst allocaton, cross-layer desgn, far schedulng, IEEE , WMAX OFDMA 1 INTRODUCTION THE IEEE standard [1] s developed for wde-range broadband wreless access. The physcal layer employs the OFDMA (orthogonal frequency dvson multple access) technque, where a base staton (BS) can communcate wth multple moble subscrber statons (MSSs) smultaneously through a set of orthogonal subchannels. The standard supports the FDD (frequency dvson duplex) and the TDD (tme dvson duplex) modes; ths paper ams at the TDD mode. Under the TDD mode, two types of subcarrer groupng models are specfed: AMC (adaptve modulaton and codng) and PUSC (partal usage of subcarrers). AMC adopts a contguous permutaton strategy, whch chooses adjacent subcarrers to consttute each subchannel and leverages channel dversty by the hgh correlaton n channel gans. However, each MSS needs to report ts channel qualty on every subchannel to the BS. On the other hand, PUSC adopts a dstrbuted permutaton strategy, whch randomly selects subcarrers from the entre frequency spectrum to consttute each subchannel. Thus, the subchannels could be more resstant to nterference and each MSS can report only the average channel qualty to the BS. Because PUSC s more nterference-resstant and mandatory n the standard, ths paper adopts the PUSC model. In ths case, there s no ssue of subchannel dversty (.e., the qualtes of all subchannel are smlar) snce the BS calculates the average qualty for each subchannel based on MSSs reports [2], [3]. J.-M. Lang,.-C. Wang, and.-c. Tseng are wth the Department of Computer Scence, Natonal Chao-Tung Unversty, Hsn-Chu, 30010, Tawan. E-mal: {jmlang, wangyc, yctseng}@cs.nctu.edu.tw J.-J. Chen s wth the Department of Electrcal Engneerng, Natonal Unversty of Tanan, Tanan, 70005, Tawan. E-mal: james.jjchen@eee.org The BS manages network resources for MSSs data traffcs, whch are classfed nto real-tme traffcs (e.g., unsolcted grant servce (UGS), real-tme pollng servce (rtps), and extended rtps (ertps)) and non-real-tme traffcs (e.g., non-real-tme pollng servce (nrtps) and best effort (BE)). These network resources are represented by frames. Each frame conssts of a downlnk subframe and an uplnk subframe. Each downlnk subframe s a 2D array over channel and tme domans, as shown n Fg. 1. The resource unt that the BS allocates to MSSs s called a burst. Each burst s a 2D sub-array and needs to be specfed by a downlnk map nformaton element (DL-MAP IE or smply IE) n the DL-MAP feld. These IEs are encoded by the robust QPSK1/2 modulaton and codng scheme for relablty. Because the IEs occupy frame space and do not carry MSSs data, they are consdered as control overheads. Explctly, how to effcently reduce IE overheads wll sgnfcantly affect network performance snce t determnes frame utlzaton. To manage resources to all data traffcs, the standard defnes a scheduler n the MAC layer and a burst allocator n the physcal layer. However, ther desgns are left as open ssues to mplementers. Ths paper ams at co-desgnng both the scheduler and the burst allocator to mprove network performance, whch covers overhead reducton, real-tme and non-real-tme traffc schedulng, and burst allocaton. The desgn of the scheduler should consder the three ssues: The scheduler should mprove network throughput whle mantan long-term farness. Snce the BS may send data to MSSs usng dfferent transmsson rates (due to network stuatons), the scheduler wll prefer those MSSs usng hgher transmsson rates but should avod starvng those MSSs usng lower transmsson rates.

2 2 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOG The scheduler should satsfy the delay constrants of real-tme traffcs to avod hgh packet droppng ratos. However, t should also meet the requrements of nonreal-tme traffcs. To well utlze the lmted frame space, the scheduler has to reduce IE overheads when assgnng resources to MSSs data traffcs. Ths requres the knowledge of avalable frame space and burst arrangement desgn from the burst allocator. On the other hand, the desgn of the burst allocator should address the three ssues: The burst allocator should arrange IEs and downlnk bursts for the MSSs resource requests from the scheduler n the OFDMA channel-tme structure to well utlze the frame space and reduce the control overhead. Under the PUSC model, snce all subchannels are equally adequate for all MSSs, the problem of arrangng IEs and downlnk bursts wll become a 2D mappng problem, whch s NP-complete [4]. To smplfy the burst arrangement problem, an advance plannng for the MSSs resource requests n the scheduler s needed. Ths requres a co-desgnng for the scheduler and the burst allocator. To satsfy traffc requrements such as real-tme delay constrants, the burst allocator has to arrange bursts based on the traffc schedulng knowledge from the scheduler. For example, those bursts for urgent realtme traffcs should be allocated frst to avod packet droppng. Smplcty s a crtcal concern because a frame s typcally 5 ms [5], whch means that the burst allocaton scheme needs to be executed every 5 ms. In the lterature, pror studes desgn solely ether the scheduler [6] [10] or the burst allocator [4], [11] [14] to address the reducton of IE overheads. Nevertheless, we pont out the necessty of the cross-layer desgn by the followng three reasons: Frst, the amount of IE overheads hghly depends on the number of scheduled MSSs and the number of fragmented bursts, where pror work handles the two ssues by the scheduler and the burst allocator, respectvely. However, f we just take care of ether one of them, the effcency of overhead reducton s lmted. Second, wthout consderng burst arrangements, the scheduler may fal to satsfy MSSs requrements because extra IE overheads wll occupy the lmted frame space. Thrd, wthout consderng the schedulng assgnments, the burst allocator may kck out some mportant data of MSSs (due to out of frame space). Ths may cause unfarness among MSSs and hgh packet droppng ratos of real-tme traffcs. Therefore, t s necessary to co-desgn both the scheduler and the burst allocator due to ther nseparable dependency. In ths paper, we propose a cross-layer framework that contans a two-ter, prorty-based scheduler and a bucket-based burst allocator. The scheduler assgns prortes to MSSs traffcs n a two-ter manner and allocates resources to these traffcs based on ther prortes. In the frst ter, traffcs are dfferentated by ther types. Urgent real-tme traffcs are assgned wth the hghest level-1 prorty to avod ther packets beng dropped n the next frame. Then, a γ rato (0 < γ < 1) of non-urgent real-tme traffcs are assgned wth level-2 prorty and nonreal-tme traffcs are gven wth level-3 prorty. The above desgn has two advantages. Frst, we can avod generatng too many urgent real-tme traffcs n the next frame. Second, nonreal-tme traffcs can have opportunty to be served to avod beng starved. In the second ter, traffcs wth the same type (.e., the same prorty level n the frst ter) are assgned wth dfferent prortes calculated by ther 1) current transmsson rates, 2) average transmsson rates, 3) admtted data rates, and 4) queue lengths. The BS can have the knowledge of the above four factors because all downlnk traffcs are queued n the BS and MSSs wll report ther average channel qualtes to the BS [15]. Unlke tradtonal prorty-based solutons that are partal to non-real-tme traffcs [10], our novel two-ter prorty schedulng scheme not only prevents urgent real-tme traffcs from ncurrng packet droppng (through the frst ter) but also mantans long-term farness (through the second ter). The network throughput s also mproved by gvng a hgher prorty to those MSSs usng hgher transmsson rates (n the second ter). In addton, the scheduler can adjust the number of MSSs to be served and assgn resources to traffcs accordng to the burst arrangement manner (from the burst allocator) to sgnfcantly reduce IE overheads. Ths desgn s neglected n pror studes and has sgnfcant mpact on overhead reducton and network performance. On the other hand, the burst allocator dvdes the free space of each downlnk subframe nto a specal structure whch conssts of several buckets and then arranges bursts n a bucket-by-bucket manner. Gven k requests to be flled n a subframe, we show that ths burst allocaton scheme generates at most k plus a small constant number of IEs. In addton, the burst allocator wll arrange bursts accordng to the prorty desgn from the scheduler so that the burst allocaton can satsfy MSSs traffc requrements. The above bucket-based desgn ncurs very low computaton complexty and can be mplemented on most low-cost WMAX chps [16]. Explctly, n our cross-layer framework, both the scheduler and the burst allocator are tghtly coupled together to solve the problems of overhead reducton, real-tme and non-realtme traffcs schedulng, and burst allocaton. Major contrbutons of ths paper are four-fold. Frst, we pont out the necessty of co-desgnng both the scheduler and the burst allocator to mprove network performance and propose a cross-layer framework that covers overhead reducton, real-tme and non-real-tme traffc schedulng, and burst allocaton. Our framework s more complete and effcent than pror studes. Second, we develop a two-ter prorty-based scheduler that dstrbutes resources among MSSs accordng to ther traffc types, transmsson rates, and queue lengths. The proposed scheduler mproves network throughput, guarantees traffc requrements, and mantans long-term farness. Thrd, a low-complexty bucket-based scheme s desgned for burst allocaton, whch sgnfcantly mproves the utlzaton of downlnk subframes. Fourth, we analyze the upper bound of the amount of IE overheads and the potental throughput degradaton caused by the proposed burst allocator, whch s used to valdate the smulaton experments and provde gudelnes for the settng of the burst allocator. Extensve smulatons are also conducted, and ther results valdate that our cross-layer framework can acheve hgh network throughput, mantan long-term farness, allevate real-tme traffc delays, and mprove downlnk subframe utlzaton. The rest of ths paper s organzed as follows: Secton 2 surveys related work. Secton 3 gves the problem formulaton.

3 A CROSS-LAER FRAMEWORK FOR OVERHEAD REDUCTION, TRAFFIC SCHEDULING, AND BURST ALLOCATION IN IEEE OFDMA NETWORKS 3 The cross-layer framework s proposed n Secton 4. Secton 5 analyzes the expected network throughput of the proposed framework. Extensve smulaton results are gven n Secton 6. Conclusons are drawn n Secton 7. 2 RELATED WORK Most of pror studes on resource allocaton n OFDMA networks solely mplement ether the scheduler or the burst allocator. For the mplementaton of the scheduler, the study of [6] proposes a schedulng scheme accordng to MSSs sgnalto-nose ratos to acheve rate maxmzaton. The work of [7] proposes a utlty functon to evaluate the tradeoff between network throughput and long-term farness. In the work of [8], an opportunstc scheduler s proposed by adoptng the nstantaneous channel qualty of each MSS to mantan farness. However, these studes do not consder the delay requrements of real-tme traffcs. The work of [9] tres to mnmze the blockng probablty of MSSs traffc requests and thus the packet droppng ratos of real-tme traffcs may be reduced. Nevertheless, all of the above studes [6] [9] do not address the ssue of overhead reducton. The work of [10] tres to reduce IE overhead from the perspectve of the scheduler, where the to be served n each subframe s reduced to avod generatng too many IEs. However, wthout the help of the burst allocator, not only the effcency of overhead reducton becomes nsgnfcant but also some mportant data (e.g., urgent real-tme traffcs) may not be allocated wth bursts because of out of frame space. In ths case, some MSSs may encounter serous packet droppng. On the other hand, several studes consder mplementng the burst allocator. The work of [17] proposes a new control message for perodc resource assgnment to reduce duplcate sgnalng. Reference [18] suggests pggybackng IEs on data packets to ncrease the utlzaton of downlnk subframes. However, both studes [17], [18] nvolve n modfyng the standard. The work of [4] proposes two heurstcs for burst allocaton: The frst heurstc scans the free space n a downlnk subframe row by row to try to fully utlze the space, but t may generate a large number of IEs. The second heurstc pre-segments a subframe nto several rectangles, and a request wll choose a rectangle larger than t for allocaton; however, ths scheme requres pror knowledge of the request dstrbuton. The work of [11] allocates bursts for large requests frst. Nevertheless, larger requests may not be necessarly more mportant or urgent. Several studes consder allocatng bursts n a column-by-column manner. In the work of [12], bursts wth the same modulaton and codng scheme are combned nto a large one. However, ths scheme s not complant to the standard because a burst may contan requests from multple MSSs. The study of [13] pads zero bts n each column s end, whch may cause low subframe utlzaton. The work of [14] adopts a backward, column-wse allocaton scheme, where the bursts are allocated from the rght-down sde to the left-up sde of the subframe. However, ths scheme requres 3n bursts for n MSSs n the worst case. As can be seen, exstng research efforts may pad too many useless bts, generate too many IEs, or leave unused slot holes. Few studes mplement both the scheduler and the burst allocator, but they do not consder reducng IE overhead. The studes of [19], [20] try to arrange resources to MSSs to maxmze ther data rates and mantan farness. However, they do not consder the delay requrements of real-tme subchannels preamble frame DL: downlnk UL: uplnk DL UL DL UL DL UL DL UL frame control header FCH DL_MAP UL_MAP DL-MAP_IE burst 1 (5, 1, 7, 4) burst 3 (5, 11, 4, 6) X tme unts burst 2 (8, 6, 5, 7) Fg. 1: The structure of an IEEE OFDMA downlnk subframe under the TDD mode. traffcs. The studes of [21], [22] develop an one-ter prortybased scheduler to allocate resources to each MSS to exactly satsfy ts demand. Thus, the delay requrement of real-tme traffcs could be guaranteed but network throughput may be degraded. Nevertheless, all of the studes [19] [22] neglect the ssue of overhead reducton, whch may lead to low subframe utlzaton and low network throughput. We wll show by smulatons n Secton 6 that, wthout reducng IE overhead, the QoS (qualty of servce) requrements of MSSs traffcs may not be satsfed, especally when the network becomes saturated. Table 1 compares the features of pror studes and our cross-layer framework. It can be shown that our cross-layer framework covers all of the features. In addton, our crosslayer framework has the least computaton complexty n burst allocaton. Thus, t can be mplemented on most of WMAX low-cost chps. 3 RESOURCE ALLOCATION PROBLEM We consder the downlnk communcaton n an OFDMA network usng the TDD mode. The mandatory PUSC model s adopted so that there s no ssue of subchannel dversty (because MSSs wll report only ther average channel qualtes to the BS, as mentoned n Secton 1). The BS supports multple MSSs n a pont-to-multpont manner, where each MSS has ts admtted real-tme and non-real-tme traffc rates. The BS has to arrange the rado resource to the MSSs accordng to ther traffc demands. The rado resource s dvded nto frames, where each frame s further dvded nto a downlnk subframe and an uplnk subframe (referrng to Fg. 1). A downlnk subframe s modeled by a 2D array wthx tme unts (n the tme doman) and subchannels (n the frequency doman). The basc unt n the X array s called a subchannel-tme slot (or smply slot). Each downlnk subframe s composed of three portons: preamble, control, and data. The control porton contans a DL- MAP and a UL-MAP to ndcate the downlnk and uplnk resource allocaton n the current frame, respectvely. The downlnk allocaton unt s a subarray, called a downlnk burst (or smply burst), n the X array. Each burst s denoted by (x,y,w,h), where x s the startng tme unt, y s the startng subchannel, w s the burst s wdth, and h s the burst s heght. An MSS can own more than one burst n a subframe. However, no two bursts can overlap wth each other. Fg. 1 gves some

4 4 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOG TABLE 1: Comparson of pror work and our cross-layer framework features network long-term rate real-tme subframe burst allocaton throughput farness satsfacton traffc utlzaton complexty references [6] [8] N/A references [9] N/A reference [10] N/A references [4], [12], [14] O(n),O(n),O(n 2 ) references [11], [13] O(n) reference [19], [20] O(n 2 ),O(n) references [21], [22] O(n) our framework O(n) n s the. The rate satsfacton s to evaluate the degree of starvaton of non-real-tme traffcs. examples. Bursts 1 and an coexst, but bursts 2 and 3 cannot coexst. Each burst requres one IE n DL-MAP to descrbe ts sze and locaton n the subframe. Accordng to the standard, each burst carres the data of exact one MSS. Explctly, from the scheduler s perspectve, the number of bursts (and thus IEs) wll ncrease when more MSSs are scheduled. On the other hand, from the burst allocator s perspectve, more IEs are requred when an MSS s data are dstrbuted over multple bursts. An IE requres 60 bts encoded by the QPSK1/2 modulaton and codng scheme [5]. Snce each slot can carry 48 bts by QPSK1/2, an IE occupes 5 4 slots, whch has sgnfcant mpact on the avalable space to allocate bursts n a downlnk subframe. The resource allocaton problem s formulated as follows: There are n MSSs n the network, where each MSS M, = 1..n, s admtted wth an average real-tme data rate of R rt (n bts/frame) and a mnmal non-real-tme data rate of R nrt (n bts/frame). Let C be the current transmsson rate 1 (n bts/slot) for the BS to send data tom, whch may change over frames. The objectve s to desgn a cross-layer framework contanng both the scheduler and the burst allocator to arrange bursts to MSSs, such that we can reduce IE overhead, mprove network throughput, acheve long-term farness, allevate realtme traffc delays, and maxmally utlze downlnk subframes. In addton, the desgn of the cross-layer framework should not be too complcated so that t can execute wthn a frame duraton (.e., 5 ms) and mplemented n most low-cost WMAX chps. Note that the farness ndex (FI) n [23] s adopted to evaluate the long-term farness of a scheme as follows: SD = T 1 j=0 FI = ( n =1 SD ) 2 n n =1 (SD ) 2, where SD s the share degree of M whch s calculated by (Ãrt ) (f c j)+ãnrt (f c j) T (R rt +R nrt ), (1) where Ãrt (x) and Ãnrt (x) are the amounts of real-tme and non-real-tme traffcs allocated to M n the xth frame, respectvely, f c s the current frame ndex, and T s the wndow sze (n frames) over whch we measure farness. We denote U d (x) the utlzaton of the xth downlnk subframe, whch s defned by the rato of the number of slots used to transmt data to X. Thus, the average downlnk utlzaton over T frames T 1 j=0 U d(f c j) T s paper.. Table 2 summarzes the notatons used n ths 1. The estmaton of the transmsson rate hghly depends on the path loss, fadng, and propagaton model. Here, we assume that the BS can accurately estmate the transmsson rate for each MSS and wll dscuss how to conduct the estmaton n Secton 6. (1) C (2) (R rt, R nrt ) (4) & FS (3) (B rt, B nrt ) two-ter, prorty-based scheduler prorty rule allocaton rule bucket-based burst allocator (6) downlnk IEs and bursts (7) (A rt, A nrt ) (5) (Q rt, Q nrt ) Fg. 2: The system archtecture of the proposed cross-layer framework, where = 1..n. 4 THE PROPOSED CROSS-LAER FRAMEWORK Fg. 2 shows the system archtecture of our cross-layer framework, whch s composed of two components: the two-ter, prorty-based scheduler and the bucket-based burst allocator. The transmsson rate C for each MSS M (label 1 n Fg. 2) s perodcally reported to the scheduler and the burst allocator. Each M s admtted rates R rt and R nrt (label 2) are sent to the scheduler when M frst assocates wth the BS or when R rt and R nrt change. The scheduler also montors the current amounts of queued real-tme and non-real-tme data B rt and B nrt (label 3). The burst allocator nforms the scheduler of the bucket sze and the avalable free space FS n the current downlnk subframe (label 4) to help the scheduler dstrbute resources among MSSs traffcs, where FS =X (FCH sze) (UL-MAP sze) (sze of DL-MAP control felds), (2) where FCH s the frame control header. The UL-MAP sze can be known n advance snce the uplnk subframe s allocated before the downlnk subframe. The DL-MAP control felds contan all parts of DL-MAP except IEs, whch are yet to be decded by the burst allocator. The scheduler s msson s to generate each M s real-tme and non-real-tme resource assgnmentsq rt andq nrt (label 5) to the burst allocator. Based on Q rt and Q nrt, the burst allocator arranges IEs and bursts to each M (label 6). The actual real-tme and non-real-tme traffcs allocated to M are wrtten as A rt and A nrt (label 7) and are fed to the scheduler for future schedulng.

5 A CROSS-LAER FRAMEWORK FOR OVERHEAD REDUCTION, TRAFFIC SCHEDULING, AND BURST ALLOCATION IN IEEE OFDMA NETWORKS 5 notaton n X FS T C C avg R rt/rnrt B rt/bnrt Q rt /Qnrt A rt /Anrt I rt/inrt S nrt θ IE B TABLE 2: Summary of notatons defnton the number of admtted MSSs n the network the number of unts n tme doman of a downlnk subframe the number of subchannels n frequency doman of a downlnk subframe the free space (n slots) n a downlnk subframe the wndow sze (n frames) the bucket sze (n slots) the current transmsson rate (n bts/slot) for the BS to send data to MSS M the average transmsson rate (n bts/slot) for the BS to send data to M n recent T frames the admtted data rate (n bts/frame) of M s real-tme/non-real-tme traffcs the amount of real-tme/non-real-tme queued data (n bts) of M M s real-tme/non-real-tme resource assgnments (n bts) generated by the scheduler the amount of real-tme/non-real-tme data (n bts) allocated to M by the burst allocator M s mportance factors to allocate real-tme/non-real-tme traffcs the non-real-tme rate satsfacton rato of M n recent T frames the sze of an IE (n slots) the number of buckets n a downlnk subframe In our cross-layer framework, the prorty rule defned n the scheduler helps the burst allocator to determne how to arrange bursts for MSSs traffcs. On the other hand, the allocaton rule defned n the burst allocator also helps the scheduler to determne how to assgn resources to MSSs traffcs. Both the prorty and allocaton rules are lke tenons n the cross-layer framework, whch make the scheduler and the burst allocator tghtly cooperate wth each other. Due to the NP-complete nature of the burst allocaton problem and the hardware constrants of low-cost WMAX chps, t s neffcent and yet nfeasble to derve an optmal soluton to arrange IEs and bursts n a short frame duraton. Therefore, to keep our burst allocator smple and effcent, we adopt a bucket concept as follows: The avalable free space FS n the current subframe s slced horzontally nto a number of buckets, each of sze (see Fg. 3 for an example). The sze actually serves as the allocaton unt n our scheme. As to be seen, the scheduler always keeps (Q rt + Q nrt ) as a multple of for each M. In ths way, the burst allocator can easly arrange bursts n a bucket-by-bucket manner, well utlze frame resource, and generate qute few bursts and thus IEs (whch wll be proved havng an upper bound later n Secton 4.2). In addton, the long-term farness s acheved because the actual allocaton (A rt,anrt ) by the burst allocator s lkely to be qute close to the assgnment (Q rt, Qnrt ) by the scheduler, for each = 1..n. 4.1 Two-Ter, Prorty-Based Scheduler In each frame, the scheduler wll generate resource assgnments (Q rt,qnrt ), = 1..n, to the burst allocator. To generate these assgnments, the scheduler adopts a two-ter prorty rule. In the frst ter, traffcs are dfferentated by ther types and gven prorty levels accordng to the followng order: P1. Urgent real-tme traffcs whose packets wll pass ther deadlnes at the end of ths frame. P2. Real-tme traffcs ranked top γ rato (0 < γ < 1) sorted by ther mportance. P3. Non-real-tme traffcs sorted by ther mportance. Then, n the second ter, traffcs wth the same type are assgned wth dfferent prortes by ther mportance, whch s calculated by ther 1) current transmsson rates, 2) average transmsson rates, 3) admtted data rates, and 4) queue lengths. In partcular, for prorty level P2, we rank the mportance of M s real-tme traffc by I rt = C C C avg Brt R rt. (3) Here, the mportance I rt nvolves three factors multpled together: 1) A hgher transmsson ratec gvesm a hgher ratng to mprove network throughput. C 2) A hgher rato C avg gves M a hgher ratng to prevent starvaton for MSSs wth low average rates, where C avg s the average transmsson rate for the BS to send data to M n the most recent T frames. Specfcally, supposng that an MSS encounters a bad channel condton for a long perod (.e., a lower C avg value), we stll prefer ths MSS f t can now enjoy a hgher transmsson rate (.e., C > C avg ). In addton, C C avg a hgher value means that the MSSs s currently n a better condton so that we gve t a hgher prorty to mprove the potental throughput. 3) A hgher rato Brt gves M R rt a hgher ratng to favor MSSs wth more backlogs. Smlarly, for prorty level P3, we rank the mportance of M s non-real-tme traffc by I nrt = C C C avg 1 S nrt, (4) wheres nrt s the non-real-tme rate satsfacton rato ofm n the most recent T frames, whch s calculated by S nrt = T 1 j=0 Anrt (f c j). (5) T R nrt A small S nrt means that M s non-real-tme traffc may be starved. Thus, a smaller S nrt gves M a hgher ratng. The above two-ter prorty rule not only prevents urgent real-tme traffcs from ncurrng packet droppng (through the frst ter) but also mantans long-term farness (through the second ter). The network throughput s also mproved by gvng a hgher prorty to those MSSs usng hgher transmsson rates (n the second ter). In addton, by gvng a γ rato of non-urgent real-tme traffcs wth level-2 prorty, not only the amount of urgent real-tme traffcs n the next frame can be reduced, but also non-real-tme traffcs can have opportunty to send ther data.

6 6 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOG subchannels preamble other control felds (1) X tme unts two-ter, prortybased scheduler resource assgnments ( Q, Q ) 1 1 ( Q, Q ) 2 2 ( Q, Q ) 3 3 ( Q, Q ) 4 4 prorty rule bucket-based burst allocator subchannels preamble other control felds (1) X tme unts ( Q1, Q1 ) ( Q3, Q3 ) rt ( bkt nrt ( Q4, Q4 ) Q1, Q1 ) (4) ( Q2, Q2 ) extra slots 6 reserved IEs 1st possblty P1/P2 P3 2nd possblty P1/P2 P3 Fg. 3: An example of the bucket-based burst allocaton wth three buckets and four resource assgnments. Below, we present the detaled operatons of our scheduler. Let e be a bnary flag to ndcate whether an IE has been allocated for M, = 1..n. Intally, we set all e = 0, = 1..n. Besdes, the free space FS s deducted by ( 1) θ IE to preserve the space for potental IEs caused by the burst allocator (ths wll be dscussed n the next secton), where θ IE = 5 4 s the sze of an IE. 1) Let U rt be the data amount of M s urgent real-tme traffc n the current frame. For allm wthu rt > 0, we sort them accordng to ther C values n a descendng order. Then, we schedule the free space FS for each of them as follows, untl FS 0: a) Reserve an IE form by settngfs = FS θ IE. Then, set e = 1. b) If FS > 0, assgn resource Q rt = mn{fs C,U rt } to M and set FS = FS Qrt C. Then, deduct Q rt from B rt. 2) After step 1, f FS > 0, we sort all M that have realtme traffcs accordng to ther I rt values (by Eq. (3)). Then, we schedule the resource for each of them as follows, untl ether all MSSs n the top γ rato are examned or FS 0: a) If e = 0, reserve an IE for M by settng FS = FS θ IE and e = 1. b) If F S > 0, assgn more resource δ = mn{fs C,B rt} to M. Then, set Q rt = Q rt + δ and FS = FS δ C. Deduct δ from B rt. 3) After step 2, f FS > 0, we sort all M accordng to ther I nrt values (by Eq. (4)). Then, we schedule the resource for each of them as follows, untl ether all MSSs are examned or FS 0: a) If e = 0, reserve an IE for M by settng FS = FS θ IE and e = 1. b) If F S > 0, assgn more resource δ = mn{fs C,B nrt } tom. Then, setq nrt = δ and FS = FS δ C. Deduct δ from B nrt. 4) Snce the bucket sze s the allocaton unt n our burst allocator, n ths step, we wll do a fne-tunng on Q rt and Q nrt such that (Q rt + Q nrt ) s algned Step 1 Step 2 Step 3 Step 4 start sort MSSs, by ther C s n a decreasng order sort MSSs, by rt ther I s n a decreasng order sort MSSs, by nrt ther I s n a decreasng order assgn, resource to M s urgent traffc & reserve 1 IE success pck MSS M FS > 0? fal, assgn resource to M s real-tme traffc & reserve 1 IE f needed, assgn resource to M s non-real-tme traffc & reserve 1 IE f needed do fne-tunng on the total resource assgnment end yes yes pck MSS M success from top rrato FS > 0? fal success pck MSS M fal yes FS > 0? Fg. 4: The flowchart of the two-ter, prorty-based scheduler. to a multple of for each M. To do so, we wll gradually remove some slots from Q nrt and then Q rt, untl ( Qrt +Qnrt C mod ) = 0. One excepton s when most of data n Q rt are urgent, whch makes removng any resource from M mpossble. In ths case, we wll add more slots to M untl ( Qrt +Qnrt C mod ) = 0. The above adjustment (.e., removal and addton) may make the total resource assgnment below or beyond the avalable resource FS. If so, we wll further remove some slots from the MSSs wth less mportant or add some slots to the MSSs wth more mportance, untl the total resource assgnment s equal to the ntal free space gven by the burst allocator. no no no

7 A CROSS-LAER FRAMEWORK FOR OVERHEAD REDUCTION, TRAFFIC SCHEDULING, AND BURST ALLOCATION IN IEEE OFDMA NETWORKS 7 Fg. 4 llustrates the flowchart of the scheduler. To summarze, our scheduler generates the resource assgnment accordng to three prortes: (P1) urgent traffcs, (P2) real-tme traffcs, and (P3) non-real-tme traffcs. Step 1 frst schedules those MSSs wth urgent traffcs to allevate ther real-tme traffc delays. Step 2 schedules those top γ rato of MSSs to reduce the that may have urgent traffcs n the followng frames. Ths step also helps reduce the IE overhead of future frames caused by urgent traffcs, whch s neglected by pror studes. Step 3 schedules those MSSs wth lower non-real-tme satsfacton ratos to prevent them from starvaton. Fnally, step 4 reshapes all assgnments such that each (Q rt +Q nrt ) s dvsble by. Ths step wll help the burst allocator to fully utlze a downlnk subframe. We then analyze the tme complexty of our scheduler. In step 1, sortng MSSs by therc values takeso(nlgn) tme and schedulng the resources for the MSSs wth urgent traffcs takes O(n) tme. In step 2, sortng MSSs by ther I rt values requres O(nlgn) tme and schedulng the resources for the top γ rato of MSSs requres at most O(γn) tme. In step 3, sortng MSSs by ther I nrt values costs O(nlgn) tme and schedulng the resources for the MSSs wth non-real-tme traffcs takes O(n) tme. In step 4, reshapng all requests spends at most O(n) tme. Thus, the total tme complexty s O(nlgn+n+nlgn+ γn+nlgn+n+n) = O(nlgn). 4.2 Bucket-Based Burst Allocator Ideally, the free space FS n Eq. (2) should accommodate each resource assgnment (Q rt,qnrt ) calculated by the scheduler and ts correspondng IE(s). However, snce the burst allocaton problem s NP-complete, our bucket-based heurstc wll try to squeeze as more MSSs assgnments nto FS as possble and allocate one burst per assgnment wth a very hgh possblty. If more than one burst s requred, more IEs are needed, n whch case some assgnments orgnally arranged by the scheduler may be trmmed down or even kcked out by the burst allocator. Gven the free space FS by Eq. (2), bucket sze, and assgnments (Q rt,qnrt ) s from the scheduler, our bucket-based heurstc works as follows: 1) Slce FS horzontally 2 nto buckets, each of a heght, where s dvsble by. Fg. 3 shows an example by slcng FS nto three buckets. 2) Let k be the number of resource assgnments gven by the scheduler. We reserve (k + 1) θ IE slots for IEs at the left sde of the subframe. In fact, the scheduler has also reserved the space for these IEs, and ts purpose wll become clear later on. Fg. 3 gves an example. Snce there are four assgnments,4+3 1 IEs are reserved. 3) We then assgn bursts to satsfy these resource assgnments accordng to ther prortes orgnally defned n the scheduler. Snce each assgnment (Q rt,qnrt ) may have data mxed n categores of P1, P2, and P3, we redefne ts prorty as follows: a) An assgnment wth data n P1 has a hgher prorty than an assgnment wthout data n P1. b) Wthout the exstence of data n P1, an assgnment wth data n P2 has a hgher prorty than an assgnment wthout data n P2. 2. We can also slce FS vertcally, but the effect wll be the same. start Step 1 Step 2 Step 3 slce FS nto buckets reserve ( k 1) θ bkt IE + slots for IEs fll ( Q, Q ) nto the current bucket & swtch to the next bucket f needed no Step 4 sort resource assgnments based on prortes pck ( Q, Q ) all buckets are full? end success feed back actual allocatons ( A, A )' s to the scheduler yes Fg. 5: The flowchart of the bucket-based burst allocator. Then, bursts are allocated n a bucket-by-bucket manner. Specfcally, when an assgnment (Q rt,qnrt ) s examned, t wll be placed startng from the prevous stop pont and fll up the bucket from rght to left, untl ether (Q rt,qnrt ) s satsfed or the left end of the bucket s encountered. In the later case, we wll move to the rght end of the next bucket and repeat the above allocaton process agan. In addton, ths cross-bucket behavor wll requre one extra IE for the request. The above operaton s repeated untl ether all assgnments are examned or all buckets are exhausted. Fg. 3 gves an example, where the four assgnments are prortzed by (Q rt 3,Q nrt 3 ) > (Q rt 1,Q nrt 1 ) > (Q rt 4,Q nrt 4 ) > (Q rt 2,Q nrt 2 ). Assgnment (Q rt 1,Q nrt 1 ) requres two IEs snce t nvolves n one cross-bucket behavor. 4) Accordng to the allocaton n step 3, we place each resource assgnment (Q rt,qnrt ) nto ts burst(s). Besdes, the amount of actual allocaton s wrtten nto each (A rt,anrt ) and fed back to the scheduler for future schedulng. Fg. 5 llustrates the flowchart of the burst allocator. We make some remarks below. Frst, because there are buckets, there are at most ( ) 1 cross-bucket burst assgnments and thus at most ( ) 1 extra IEs are needed. To accommodate ths need, some assgnments may be trmmed down slghtly. Ths s why (Q rt,qnrt ) and (A rt,anrt ) are not necessarly the same. However, the dfference should be very small. Second, the bucket whch s located at the boundary of reserved IEs and data (e.g., the thrd bucket n Fg. 3) may have some extra slots (e.g., the lower-left corner of the thrd bucket). These extra slots are gnored n the above process for ease of presentaton, but they can be used to allocate bursts to further mprove space effcency. Thrd, snce each crossbucket behavor wll requre one extra IE and there are buckets, the number of IEs requred s bounded, as proved n Theorem 1. Theorem ( 1. In) the bucket-based burst allocator, the k + 1 IEs reserved n step 2 are suffcent for the burst allocaton n step 3. fal

8 8 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOG Proof: Gven bucketsˆb 1,ˆb 2,, andˆb, we can concatenate them nto one vrtual bucket ˆb ( ) wth 1 jonts. We then allocate one vrtual burst for each request from the scheduler n ˆb, so we have at most k vrtual bursts. Then, we replace each vrtual burst by one real burst. However, we requre one extra real burst whenever the replaced vrtual burst ( crosses ) one jont. The worst case occurs when each of 1 jonts s crossed by one vrtual burst. In ths case, ( ) we requre k + 1 real bursts to replace all vrtual bursts. Snce ( each real) burst requres one IE, we have to reserve at most k + 1 IEs. In comparson, a nave burst allocaton wll requre the worst case of 3k IEs f the allocaton goes n a row-major or column-major way [14] (because each request may requre up to three IEs). In our scheme, the bucket sze can be dynamcally adjusted to reflect the gran sze of our allocaton. A larger gran sze may cause fewer IEs, but sacrfce resource utlzaton; a smaller gran sze may cause more IEs, but mprove resource utlzaton. We wll dscuss the effect of n Secton 6.6. We then analyze the tme complexty of our burst allocator. Snce we allocate bursts n a zgzag manner, the tme complexty s proportonal ( to the number ) of bursts. By Theorem 1, we have at most k + 1 bursts. Snce we have k n and s usually smaller than n, the tme complexty s ( ) O k + 1 = O(n). To conclude, the proposed scheduler and burst allocator are dependent wth each other by the followng two desgns: Frst, the scheduler reserves the extra IE space caused by the bucket partton and arranges resources to MSSs traffcs so that the resource assgnments can algn to buckets. Thus, we can enhance the possblty that the burst allocator fully satsfes the resource assgnments from the scheduler. Second, the burst allocator follows the prorty rule n the scheduler to arrange bursts. Thus, even f the frame space s not enough to satsfy all traffcs, urgent real-tme traffcs can be stll arranged wth bursts to catch ther approachng deadlnes. 5 ANALSIS OF NETWORK THROUGHPUT LOSS B THE BUCKET-BASED SCHEME Gven an deal scheduler, we analyze the loss of network throughput caused by our bucket-based burst allocator. To smplfy the analyss, we assume that the network has only traffcs of prorty levels P1 and P3, and each MSS has nfnte data n P3. (Traffcs of P2 wll eventually become urgent traffcs of P1.) Then, we calculate the dfference between the expected throughput by our burst allocator and the maxmum throughput by an deal one. In the deal burst allocator, the number of IEs s equal to the number of resource assgnments from the scheduler. Also, the frame resource s always allocated to urgent traffcs (P1) frst and then to non-real-tme traffcs (P3) wth the hghest transmsson rate. It follows that two factors may degrade network throughput by our burst allocator: 1) extra IEs ncurred by step 3 n Secton 4.2 and 2) the data paddng of low-rate non-real-tme traffcs at the boundary between the data n P1 and P3. Specfcally, each burst must begn wth the data n P1 followed by the data n P3. Furthermore, f the data n P3 covers more than one column, t must be sent at the hghest transmsson rate. If the data n P3 covers less than a column, t may be sent at a non-hghest transmsson rate. In the rght-hand sde of Fg. 3, t shows these two possbltes, where P2 s empty. Note that n the frst possblty, all data n P3 must be transmtted at the hghest rate; otherwse, the shaded area wll be allocated to the data n P3 of other MSSs usng the hghest rate. Followng the above formulaton, our objectve s to fnd the throughput loss L by our burst allocator compared wth the deal one: L = E[Õ] c hgh +E[ S], (6) where Õ s the random varable representng the number of extra IEs caused by buckets and S s the random varable representng the throughput degradaton (n bts) caused by the low-rate paddng n the shaded area of the second possblty n the rght-hand sde of Fg. 3. To smplfy the analyss, we assume that there are only two transmsson rates c hgh and c low, where c hgh > c low. The probablty that an MSS s n ether rate s equal. 5.1 Calculaton of E[Õ] We frst gve an example to show how our analyss works. Suppose that we have three MSSs and three buckets. Each bucket has two arrangement unts, each havng slots. Thus, there are totally sx arrangement unts, denoted by O 1,O 2,O 3,O 4,O 5, and O 6. Resources allocated to the three MSSs can be represented by two separators. For example, we lst three possble allocatons: 1) O 1 O 2 O 3 O 4 O 5 O 6, 2) O 1 O 2 O 3 O 4 O 5 O 6, and 3) O 1 O 2 O 3 O 4 O 5 O 6. In arrangement 1, we need no extra IE. In arrangement 2, MSS 2 receves no resource, but MSS 1 needs one extra IE. In arrangement 3, MSS 2 requres two IEs. We wll use arrangement unts and separators to conduct the analyss. Suppose that we havenmsss, (= B) number of buckets, and X B(= α) arrangement unts (.e., each bucket has X arrangement unts). Ths can be represented by arbtrarly placng (n 1) separators along a sequence of α arrangement unts. Bucket boundares appear after each th arrangement unt such thats a multple ofx. Note that only (B 1) bucket boundares can cause extra IEs as mentoned n Secton 4. Whenever no separator appears at a bucket boundary, one extra IE s needed. There are totally (α+(n 1))! α!(n 1)! ways to place these separators. Let Ẽ be the random varable representng the number of bucket boundares, where each of them s nserted by at least one separator. The probablty of (Ẽ = e) s calculated by Prob[Ẽ CB 1 e = e] = (α (B 1 e)+(n 1 e))! (α (B 1 e))!(n 1 e)!. (7) (α+(n 1))! α!(n 1)! Note that the term Ce B 1 s the combnatons to choose e boundares from the (B 1) bucket boundares. Each of these e boundares s nserted by at least one separator. The remanng (B 1 e) bucket boundares must not be nserted by any separator. To understand the second term n the numerator of Eq. (7), we can denote by x 0 the number of separators before the frst arrangement unt and by x the number of separators after the th arrangement unt, = 1..α. Explctly, we have x 0 +x 1 + +x α = n 1, x {0,1,2, }. However, whenẽ = e, (B 1 e) of thesex s must be 0. Also, e of these x s must be larger than or equal to 1. Then, ths

9 A CROSS-LAER FRAMEWORK FOR OVERHEAD REDUCTION, TRAFFIC SCHEDULING, AND BURST ALLOCATION IN IEEE OFDMA NETWORKS 9 problem s equvalent to fndng the number of combnatons of y 0 +y 1 + +y j + +y α (B 1 e) = n 1 e, y j {0,1,2, }. It follows that there are (α (B 1 e)+(n 1 e))! Therefore, E[Õ] can be obtaned by (α (B 1 e))!(n 1 e)! combnatons. B 1 E[Õ] = (number of extra IEs when Ẽ = e) Prob[Ẽ = e] e=0 B 1 = (B 1 e) CB 1 e e=0 5.2 Calculaton of E[ S] (α (B 1 e)+(n 1 e))! (α (B 1 e))!(n 1 e)!. (α+(n 1))! α!(n 1)! (8) Recall that E[ S] s the expected throughput degradaton caused by the transmsson of a burst at a low rate and the burst contans some data paddng of non-real-tme traffcs. To calculate E[ S], let us defne ÑL as the random varable of the usng the low transmsson rate c low. Snce there s no throughput degradaton by MSSs usng the hgh transmsson rate c hgh, the overall expected throughput degradaton s n E[ S] = E[ S ÑL = m] Prob[ÑL = m]. (9) m=1 Let Ũ be the random varable representng the data amount of M s urgent traffc, = 1..n. Here, we assume that Ũ s unformly dstrbuted among [1,R], where R N. Let X j L be the random varable representng the amount of throughput degradaton (n bts) due to the data paddng ofm j s non-realtme traffc when usngc low. Snce the throughput degradaton caused by MSSs usng c hgh s zero, we have m E[ S ÑL = m] = E. (10) j=1 Explctly, XL and X j L are ndependent of each other for any j, so we have m m [ ] E = E XL j. (11) j=1 X L j j=1 Now, let us defne I U as an ndcator to represent whether or not M has urgent traffc such that I U = 1 f M has urgent traffc; otherwse, I U = 0. Snce the bursts of low-rate MSSs wthout urgent traffcs wll not contan the data paddng of non-real-tme traffcs, no throughput degradaton wll be caused by them. So, we can derve E[ X j L ] = E[ X j L Ij U = 1] Prob[Ij U = 1] ( R ) f(ũj = u) = Prob[Ij U = 1], (12) R u=1 where ( u f(ũj = u) = c low (c hgh c low ) X L j u c low ) s a functon to represent the throughput degradaton caused by a low-rate MSS wth non-real-tme data paddng when Ũ j = u. By combnng Eqs. (9), (10), (11), and (12), we can derve that ( n m R ) E[ S] = f(ũj = u) Prob[Ij U = 1] R m=1 j=1 u=1 Prob[ÑL = m]. (13) Fnally, the throughput loss by our burst allocator can be calculated by combnng Eqs. (8) and (13) nto Eq. (6). 6 PERFORMANCE EVALUATION To verfy the effectveness of our cross-layer framework, we develop a smulator n C++ based on the archtecture n [15], as shown n Fg. 6. The smulator contans three layers: The traffc generatng module n the upper layer creates the MSSs demands accordng to ther real-tme and non-real-tme traffc requrements. In the MAC layer, the queung module mantans the data queues for each MSS and the schedulng module conducts the actons of the scheduler. In the PH (physcal) layer, the channel estmatng module smulates the channel condtons and estmates the transmsson rate of each MSS and the burst allocatng module conducts the actons of the burst allocator. The arrows n Fg. 6 show the nteracton between all the modules n our smulator. In partcular, the traffc generatng module wll generate traffcs and feed them to the schedulng module for allocatng resources and the queung module for smulatng the queue of each traffc. The channel estmatng module wll send the transmsson rates of MSSs to both the schedulng and burst allocatng modules for ther references. In addton, the schedulng module and the burst allocatng module wll nteract wth each other, especally for our scheme. The smulator adopts an FFT (fast Fourer transform) sze of 1024 and the zone category as PUSC wth reuse 1. The frame duraton s 5 ms. In ths way, we have X = 12 and = 30. Sx modulaton and codng schemes (MCSs) are adopted, denoted by a set M CS = {QPSK1/2, QPSK3/4, 16QAM1/2, 16QAM3/4, 64QAM2/3, 64QAM3/4}. For the traffc generatng module, the types of real-tme traffcs nclude UGS, rtps, and ertps; the types of non-real-tme traffcs nclude nrtps and BE. Each MSS has an admtted real-tme data rate R rt of bts and an admtted non-real-tme data rate R nrt of bts per frame. In each frame, each MSS generates 0 2R rt amount of real-tme data and R nrt 4R nrt amount of non-real-tme data. For the channel estmatng module, we develop two scenaros to estmate the transmsson rate of each MSS. The frst scenaro, called the SUI (Stanford unversty nterm) scenaro, s based on the SUI path loss model recommended by the task group [24]. In partcular, each MSS wll roam nsde the BS s sgnal coverage (whch s the largest area that the BS can communcate wth each MSS usng the lowest QPSK1/2 MCS) and move followng the random waypont model wth the maxmal speed of 20 meters per second [25]. The transmsson rate of each MSSM s determned by ts receved SNR (sgnalto-nose rato): SNR(BS,M ) = 10 log 10 ( P(BS,M ) BW N o ),

10 10 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOG upper layer traffc generatng module real-tme traffc (UGS, rtps, ertps) non-real-tme traffc (nrtps, BE) MAC layer schedulng module two-ter, prorty-based scheduler HRF MPF RMF QG queung module RT NT RT NT RT NT RT NT MSS 1 MSS 2 MSS 3 MSS n (RT: real-tme traffc NT: non-real-tme traffc) PH layer channel estmatng module SUI scenaro Markov scenaro burst allocatng module bucket-based burst allocator reference [4] for RMF HRF & MPF QG Fg. 6: The archtecture of our C++ smulator. TABLE 3: The amounts of data carred by each slot and the mnmum requred SNR thresholds of dfferent MCSs ndex MCSs data carred mnmum by each slot requred SNR 1 QPSK 1/2 48 bts 6 dbm 2 QPSK 3/4 72 bts 8.5 dbm 3 16QAM 1/2 96 bts 11.5 dbm 4 16QAM 3/4 144 bts 15 dbm 5 64QAM 2/3 192 bts 19 dbm 6 64QAM 3/4 216 bts 21 dbm TABLE 4: The smulaton parameters used n the SUI scenaro parameter value P BS 1000 mllwatts subchannel bandwdth (BW) 10 MHz path loss model SUI Tx/Rx antenna gan BS: 16 db/16 db; MSS: 8 db/8 db antenna hght BS: 30 meters; MSS: 2 meters thermal nose -100 dbm where BW s the effectve channel bandwdth (n Hz), N o s the thermal nose level, and P(BS,M ) s the receved sgnal power at M, whch s defned by P(BS,M ) = G BS G M P BS, L(BS,M ) where P BS s the transmsson power of the BS; G BS and G M are the antenna gans at the BS and M, respectvely, and L(BS,M ) s the path loss from the BS tom. GvenM s SNR, the BS can determne M s MCS based on Table 3. Specfcally, the BS wll choose the hghest MCS whose mnmum requred SNR s smaller than SNR(BS,M ). Table 4 lsts the parameters used n the SUI scenaro. The second scenaro, called the Markov scenaro, adopts a sx-state Markov chan [26] to smulate the channel condton of each MSS, as shown n Fg. 7. Specfcally, let MCS[] be the th MCS, = Suppose that an MSS uses MCS[] to ft ts channel condton at the current frame. The probabltes that the MSS swtches to MCS[ 1] and MCS[ + 1] n the next frame are both 1 2 p c, and the probablty that t remans unchanged s 1 p c. For the boundary cases of = 1 and 6, the probabltes of swtchng tomcs[2] andmcs[5], respectvely, are both p c. Unless otherwse stated, we set p c = 0.5 and the ntal value of each MSS s randomly selected from 2 to 5. 1 pc MCS[1] p c 1 pc MCS[2] 1 pc MCS[3] 1 pc 1 pc 1 pc MCS[4] MCS[5] MCS[6] Fg. 7: A sx-state Markov chan to model the channel condton. We compare our cross-layer framework aganst the hgh rate frst (HRF) scheme [21], the modfed proportonal far (MPF) scheme [10], the rate maxmzaton wth farness consderaton (RMF) scheme [20], and the QoS guarantee (QG) scheme [22]. HRF always frst selects the MSS wth the hghest transmsson ratec to serve. MPF assgns prortes to MSSs, where an MSS wth a hgher C value and a lower amount of receved data s gven a hgher prorty. RMF frst allocates resources to those unsatsfed MSSs accordng to ther mnmum requrements, where MSSs are sorted by ther transmsson rates. If there remans resources, they are allocated to the MSSs wth hgher transmsson rates. Smlarly, QG frst satsfes the mnmum requrements of each MSS s traffcs, whch are dvded nto realtme and non-real-tme ones. Then, the remanng resources are allocated to those MSSs wth hgher transmsson rates. Snce both HRF and MPF mplement only the scheduler, we adopt the scheme n [4] as ther burst allocators. In our framework, we use B = 5 buckets and set γ = 0.3 n P2 unless otherwse stated. In Secton 6.6, we wll dscuss the effects of these two parameters on the system performance. The duraton of each experment s at least 2000 frames. 6.1 Network Throughput We frst compare the network throughput under dfferent (.e., n), where the network throughput s defned by the amount of MSSs data (n bts) transmtted by the BS durng 2000 frames. We observe the case when the network becomes saturated, where there are MSSs to be served. Fg. 8 shows the smulaton results under both the SUI and the Markov scenaros, where the trends are smlar. Explctly, when the grows, the throughput ncreases but wll eventually steady when there are too many MSSs (.e., n 80). The throughput under the SUI scenaro s lower than that under the Markov scenaro because some MSSs may move around the boundary of the BS s coverage, p c