Allocation of QoS Connections in MF-TDMA Satellite Systems: A Two-Phase Approach

Transcription

1 VT R Allocaton of QoS Connectons n MF-TDMA Satellte Systems: A Two-Phase Approach Jung-Mn Park, Member, IEEE, Uday Savagaonkar, Edwn K. P. Chong, Fellow, IEEE, Howard Jay Segel, Fellow, IEEE, and Steven D. Jones, Member, IEEE Abstract We address the problem of provdng guaranteed qualty of servce (QoS) connectons over a mult-frequency tme dvson multple access (MF-TDMA) system that employs dfferental phase-shft keyng (DPSK) wth varous modulaton modes. The problem can be dvded nto two parts resource calculaton and resource allocaton. We present algorthms for performng these two tasks, and evaluate ther performance n the case of a Mlstar Extremely Hgh Frequency Satellte Communcaton (EHF-SATCOM) system. In the resource-calculaton phase, we calculate the mnmum number of tmeslots requred to provde the desred level of bt error rate (BER) and data rate. The BER s drectly affected by the dsturbance n the lnk parameters. We use a Markov modelng technque to predct the worst-case dsturbance over the connecton duraton. The Markov model s traned offlne to generate a transton probablty matrx, whch s then used for predctng the worst-case dsturbance level. We provde smulaton results to demonstrate that our scheme outperforms the scheme currently mplemented n the EHF-SATCOM system. The resource-allocaton phase addresses the problem of allocatng actual tmeslots n the MF-TDMA channel structure (MTCS). If we vew the MTCS as a collecton of bns, then the allocaton of the tmeslots can be consdered as a varant of the dynamc bn-packng problem. Because the bn-packng problem s known to be P-complete, obtanng an optmal packng scheme requres a prohbtve amount of computaton. We propose a novel packng heurstc called Reserve Channel wth Prorty (RCP) ft, and show that t outperforms two common bn-packng heurstcs. Manuscrpt receved ovember 2, 22; revsed December 3, 23. A prelmnary verson of portons of ths materal was presented n [3] Ths research was supported n part by the DARPA/ITO AICE Program under contract numbers DABT63-99-C- and 2, by SF under grants AI , AI-9937, and ECS-9889, and by the Colorado State Unversty George T. Abell Endowment. J.-M. Park s wth the Bradley Department of Electrcal and Computer Engneerng, Vrgna Tech, Blacksburg, VA 246 USA (phone: , fax: , e-mal: jungmn@vt.edu). U. Savagaonkar s wth the Intel Communcatons Technologes Lab n Hllsboro, OR, USA (e-mal: uday.r.savagaonkar@ntel.com). E. K. P. Chong s wth the Department of Electrcal and Computer Engneerng and Department of Mathematcs, Colorado State Unversty, Fort Collns, CO 8523 USA (e-mal: echong@colostate.edu). H. J. Segel s wth the Department of Electrcal and Computer Engneerng and Department of Computer Scence, Colorado State Unversty, Fort Collns, CO 8523 USA (e-mal: hj@colostate.edu). S. D. Jones s wth the Johns Hopkns Unversty Appled Physcs Laboratory, Johns Hopkns Road, Laurel, MD 2723 (e-mal: Steven.Jones@jhuapl.edu). Index Terms Satellte, resource allocaton, QoS, MF-TDMA, bn packng, Markov modelng, predcton. T I. ITRODUCTIO HE mult-frequency tme dvson multple access (MF- TDMA) scheme s a hybrd soluton that combnes the strengths of the frequency dvson multple access (FDMA) and tme dvson multple access (TDMA) technques, and hence s favored by many modern satellte communcaton systems. Ths technque allows for effcent streamng of traffc whle mantanng flexblty n capacty allocaton. Access to the satellte uplnk employng ths technque s characterzed by a large number of connectons that share lmted system resources. In systems employng MF-TDMA as ther uplnk access method, multple frequency channels are allocated for the uplnk access, and the TDMA scheme s employed n each frequency channel. Thus, each frequency channel s dvded nto several tmeslots that can be assgned to multple connectons. We treat the tmeslots as the resource that needs to be allocated to each connecton. Each connecton s assgned a fxed porton of the resource based on ts qualty of servce (QoS) requrements. Specfcally, we consder two QoS measures data rate and maxmum-allowable bt error rate (BER). It s assumed that each connecton declares ts QoS requrements at the tme of the connecton request. We treat the data rate as a determnstc QoS measure, and the BER as a statstcal QoS measure throughout the duraton of a connecton, a fxed data rate s guaranteed, whereas the maxmum-allowable BER s assured wth a certan probablty. Our am s to provde QoS guarantees to every connecton throughout ts duraton. To acheve ths objectve, we concentrate on two specfc problems that are lmted to the uplnk of the MF-TDMA satellte systems resource calculaton and resource allocaton. Specfcally, we focus on the above two problems appled to the Mlstar Extremely Hgh Frequency Satellte Communcaton (EHF-SATCOM) system. Ths satellte system s desgned to provde relable communcatons for the US Mltary s strategc and tactcal forces. (See Secton II-A for more detals.) It s mpractcal to reconfgure a connecton once t s allocated a poston on the MF-TDMA channel structure (MTCS). A typcal reconfguraton of the MTCS for the Mlstar EHF-SATCOM system could take as long as 4 seconds or longer. Ths s a consderable delay relatve to the

2 VT R 2 average connecton duraton for the system. Hence, reconfguraton of the MTCS, and consequently that of a connecton, s undesrable. At the same tme, the number of tmeslots allocated to a connecton drectly affects the QoS of the lnk. To elaborate, n the case of systems employng multple modulaton modes wth an MF-TDMA channel structure, the two QoS measures under consderaton are drectly related to the number of tmeslots allocated, the modulaton mode beng used, and the dsturbance level n the system va the lnk-budget equatons. The dsturbance level n turn depends on varous system and envronmental parameters such as transmtter power and ran rate. We wll descrbe these relatons brefly n Secton II-B. Whle some of the parameters contrbutng to the dsturbance level are determnstc, others are not. The aggregated effect of the nondetermnstc parameters changes the mnmum number of tmeslots needed to guarantee the QoS level of a connecton durng ts duraton. We present a Markov model-based predcton (MMP) scheme for predctng the worst-case dsturbance level over the connecton duraton. We use ths predcton to compute the number of tmeslots requred n the worst case. Açar and Rosenberg [] also have nvestgated the problem of resource calculaton, but ther study consdered Asynchronous Transfer Mode (ATM) over MF-TDMA satellte lnks, and they used performance measures dfferent from ours. After the resource-calculaton algorthm determnes the number of tmeslots requred to satsfy the QoS requrements of a connecton, a resource-allocaton algorthm s needed to map the tmeslots onto the MTCS. If we vew the frequency channels of the MTCS as a collecton of bns, then the problem of allocatng resources for the uplnk can be vewed as a varant of the dynamc bn-packng problem. Motvated by potental applcatons, such as computer storage, the classcal bn-packng problem has been actvely researched and analyzed (e.g., [2], [9]). The objectve of the classcal bnpackng problem s to pack the bns wth the gven tems as densely as possble (.e., pack the tems nto as few bns as possble). Because the bn-packng problem s P-complete [9], most of the research has concentrated on fndng upper and lower bounds on the worst-case performance of wellknown smple algorthms (e.g., frst ft and best ft), rather than searchng for an optmal soluton. Although these well-known packng algorthms obtan relatvely good placements for the classcal bn-packng problem, the packng restrctons that are unque to the resource-allocaton problem of the MTCS make the straghtforward applcaton of these algorthms to our problem neffectve. We propose a novel packng algorthm, called Reserve Channel wth Prorty (RCP) ft, for the resource allocaton n an MTCS. To measure the performance of bn-packng algorthms, one mght want to obtan the expected performance of such algorthms under varous probablstc assumptons, such as arrval tmes, departure tmes, and sze of the tems. However, t has been shown that such results are extremely dffcult to obtan theoretcally, even for statc bn packng. Furthermore, even n statc bn packng, obtanng numercal ndcators for a relatvely sophstcated packng procedure under probablstc assumptons s nearly mpossble due to the enormous complexty of the calculatons [2]. Thus, we compare the performance of RCP ft wth other packng algorthms (.e., best ft and frst ft) va smulatons. In the next secton, we ntroduce the Mlstar EHF-SATCOM system and ts MF-TDMA uplnk channel structure, whch was used as the model for the smulaton experments. The resource-calculaton and resource-allocaton phases are descrbed n Secton III and Secton IV, respectvely. We provde the smulaton results n Secton V. Fnally, n Secton VI, we conclude the paper wth a dscusson of the results. In the Appendx, we prove the P-completeness of the resourceallocaton problem. A. Channel Structure II. THE EHF-SATCOM SYSTEM We adopt a satellte system model based on the Mlstar EHF-SATCOM system. Ths satellte system s desgned to provde relable communcatons for the US mltary s strategc and tactcal forces. Concepts for survvablty n a hostle space envronment have shaped the desgn of ths system t s robust aganst both electronc warfare and physcal attacks carred out by the enemy. The Mlstar system s a jont satellte communcatons system that s desgned to provde secure worldwde communcatons for hgh-prorty mltary users (.e., command authortes). The mult-satellte constellaton s capable of lnkng the command authortes wth a wde range of mltary resources (e.g., shps, submarnes, and arcraft). Unlke systems usng lower frequences, Mlstar satellte systems utlzng EHF technology (3 ~ 3 GHz) offer numerous advantages : able to avod nterference and crowdng, whch s problematc n other frequency bands; rapd recovery from the scntllaton caused by a hghalttude nuclear detonaton; mnmal susceptblty to enemy jammng and eavesdroppng; ablty to acheve smaller secure beams wth modest-szed antennas. The EHF-SATCOM system s comprsed of three dstnct parts the space segment, the user segment, and the control segment. The satelltes correspond to the space segment, earth termnals correspond to the user segment, and the control segment conssts of satellte control and plannng elements. The system can support multple voce and data channels orgnatng from many termnals smultaneously. The space segment (satellte) acts essentally as a relay and router n the sky. It receves, demodulates, routes, and re-modulates nformaton flows. The user segment (termnal) s capable of Informaton adapted from

3 VT R 3 transmttng and recevng communcaton sgnals wth the satelltes. Although a sngle termnal can only communcate wth one satellte at a tme, t normally has the capablty to change from one satellte to another as requred. Dependng on the specfc type, a termnal has the capablty to support one or multple voce and data streams. In addton, some types also have the capablty to nterface and control certan aspects of the satellte, such as resource allocaton and antenna pontng. The type of communcaton lnk (access control) between the space segment and the user segment s dfferent for the uplnk and the downlnk. The EHF-SATCOM system uses MF-TDMA as ts uplnk access method and a sngle tmedvson multplexed stream as ts downlnk access method. The uplnk bandwdth s dvded nto several beams, and each beam s made up of several frequency channels. In further dscussons, we assume that 32 frequency channels are avalable for the uplnk, and each frequency channel s composed of 7 TDMA tmeslots per frame. Each termnal ntates communcaton (wth some other termnal) by makng a connecton request. The connecton s supported through the allocaton of the commonly shared resources (.e., set of tmeslots) managed by a satellte. In an MF-TDMA satellte system, tmeslots are allocated n groups, called bursts. Each burst s composed of a sngle strng of contguous tmeslots over whch a termnal transmts ts data. A termnal transmts, to the satellte, ts bursts n the assgned poston of the frame accordng to a transmt burst tme plan (BTP), and receves bursts n the assgned poston of the frame, returned by the transponder, accordng to a receve BTP [8]. ote that a termnal may request multple connectons over tme, and at any gven tme, a termnal may have more than one actve connecton. The length of the burst (.e., number of tmeslots) depends on the modulaton mode and the data rate. The EHF-SATCOM system supports seven dfferent modulaton modes and eleven dfferent data rates for the uplnk. The modulaton mode determnes the burst rate of the transmsson, whch s the rate at whch symbols can be transmtted wthn the burst. That s, the seven modulaton modes each specfy a dfferent burst rate for the termnal s uplnk transmsson. ote that the burst rate s n symbols per second whle the data rate s n bts per second. Because the burst rate s drectly affected by the BER of the connecton accordng to the uplnk budget equaton, the determnaton of the modulaton mode depends on the BER requrement (see () and (2)). ote that BER s one of the QoS requrements (.e., BER and data rate) of a connecton. Gven the modulaton mode and the data rate, the burst length s unquely determned usng a system-specfc look-up table. Although choosng a modulaton mode correspondng to a hgher burst rate conserves the amount of resource (.e., number of tmeslots) allocated to a connecton, t also causes an ncrease n the BER. A hgher burst rate drectly translates to a hgher BER (see () and (2)), and hence there s a tradeoff between capacty and QoS n the EHF-SATCOM uplnk scheme. After the length of the burst s computed, the tmeslots are allocated on the MTCS. The MTCS can be vewed as a twodmensonal array, where the rows represent frequency channels, and the columns represent tmeslot ndexes (see Fg. ). When allocatng tmeslots on the MTCS, the followng restrctons are appled: Restrcton : The set of tmeslots used by a termnal to support a gven sngle connecton must be contguous on one frequency (.e., must form a sngle burst). Restrcton 2: A termnal cannot use tmeslots that overlap n tme to support multple connectons. frequency channels tmeslots Fg.. MF-TDMA channel structure (MTCS). The MTCS can be vewed as a two-dmensonal array, where the rows represent frequency channels, and the columns represent tmeslot ndexes. These restrctons are due to the hardware and operatonal lmtatons of the EHF-SATCOM system. Earth termnals for ths system employ a hgh power amplfer for the uplnk. onlneartes n the amplfer create nter-modulaton products when multple carrers are present at the same tme wth the amplfer operatng at full output power. The power n the nter-modulaton products wll result n reduced power n the carrers. Thus, Restrcton 2 s mposed to avod ntermodulaton products [6], [7]. The reason for Restrcton s to ease the assgnment problem for the satellte resources and smplfy the routng n the payload. It follows from the two restrctons and the gven channel structure that a termnal cannot be assgned more than 7 tmeslots n a sngle frame. When a connecton s set up between two termnals va satellte, t can be establshed as full-duplex or half-duplex. When the full-duplex mode s used, ether termnal can transmt at any tme, and hence two uplnk bursts must be assgned, one for each termnal. For the smulaton results n Secton V, we assume that the system always operates n the full-duplex mode. B. Tmeslot Calculaton To assgn the approprate number of tmeslots for each connecton request, we need to calculate the maxmum allowable burst rate. Once the burst rate s computed, the requred modulaton mode can be obtaned from a systemspecfc look-up table. Assumng that the system uses bnary...

4 VT R 4 DPSK, and that the requred BER P b s gven, the correspondng Eb / (sgnal-to-nose rato (SR) per bt) on the uplnk can be calculated as Eb / Pb = e. () 2 The SR per bt n turn depends on varous envronmental and system parameters (.e., lnk parameters) accordng to the followng equaton: Eb / = Pt + Gt + Lf + Lr + Lc + Gc + Gr (2) log( R ) log( kt ), where P : transmtter power n db, t G : transmtter antenna gan n db, t L : free-space loss n db, f L r : ran loss n db, L : loss due to catastrophc falure n db, c G : codng gan n db, c G : recever antenna gan n db, r R : burst rate n symbols per second, b b k : Boltzmann s constant ( J/K), T : system nose temperature (assumed to be constant at K). The above equaton and ts counterpart for the downlnk are called the lnk-budget equatons. All of the above lnk parameters have an mpact on the behavor of the system, some greater than others. It s known that at the frequences at whch EHF-SATCOM systems operate, ran loss s the sngle most mportant parameter, asde from loss due to catastrophc falures []. In our model, we assume that all of these parameters, except for ran loss, are known n advance. ote that consderng the ran loss as the only non-determnstc parameter does not make our model restrctve. In fact, the effect of uncertantes about the other parameters can be aggregated nto the ran loss value (va (2)), and then t can be converted to an effectve ran rate usng (3) (see below). The effectve ran rate represents the aggregated effect of all the non-determnstc parameters on the SR per bt value. The relaton between ran loss and ran rate s gven by L = l k R α. (3) r Here, l s the length of the termnal to satellte path that s n ran (usually assumed to be the dstance from the termnal to the freezng heght along the path, f t s ranng, or zero, f t s not ranng). The parameter R s the ran rate descrbed n mm/hr, and k p and α are frequency-dependent parameters wth values of.4 and.9, respectvely, at 44.5 GHz (uplnk frequency of the Mlstar EHF-SATCOM system) []. The nomnal values of the other parameters and the value of the ran loss, as computed above, can jontly be used to determne the burst rate (and consequently the modulaton mode) requred to acheve the requested BER, once the ran rate s p known. A. Problem Descrpton III. RESOURCE CALCULATIO The resource-calculaton phase deals wth the problem of determnng the amount of resource(s) requred to provde the requested QoS. As already mentoned, we treat the tmeslots as the only resource n the system. Thus, n the resourcecalculaton phase, we need to determne the number of tmeslots requred to set up a communcaton connecton wth the requested level of QoS. As explaned n Secton II-B, gven a fxed number of tmeslots, the BER and data rate depend on each other through the lnk-budget equatons. A compromse s acheved by selectng a proper modulaton mode. We assume that the satellte system s equpped wth a means of measurng the BER n the uplnk and the downlnk. Thus, the desred value of BER can easly be mantaned as follows: ) Observe the BER at regular ntervals. 2) At every epoch, use the observed value of BER and the present burst rate to compute the burst rate requred to provde the desred BER. 3) Change the modulaton mode to the one that corresponds to the burst rate computed n the second step. Ths scheme would be suffcent f the prmary objectve s to control the BER. But the connecton requests requre a fxed data rate as well as a guaranteed BER. If the values of the lnk parameters (see (2)) change durng a connecton s duraton, ths causes a correspondng change n the BER. To prevent the BER from exceedng the maxmum-allowable level, whle mantanng a constant data rate, the burst rate has to be constantly changed to compensate for the changes n the lnk parameters. Wth a fxed data rate, changng the burst rate requres changng the number of tmeslots allocated for the connecton. Ths means that the tmeslots must be reallocated. However, tmeslot reallocaton n the EHF-SATCOM system s a tme-consumng process, and hence ths alternatve s not vable. One way to guarantee the BER and yet provde a fxed data rate s to provde some safety margn n the SR by startng the communcaton n a modulaton mode correspondng to a burst rate that s lower than what s requred by the present BER. Thus, despte the varatons n the envronmental and system parameters, the safety margn should make up for the ncreased dsturbance (.e., any factor that s detrmental to the transmsson sgnal), mantanng the desred BER. In the current mplementaton of the system, expermentally determned values are used for the parameters appearng n the lnk-budget equatons. Specfcally, as a safety margn, a 2dB allowance s added on to the Eb / computed usng these parameters, and a modulaton mode s selected accordngly. We wll refer to ths method as the 2 db scheme. Ths method s not very effcent, and one mght squander a lot of tmeslots, yet not always satsfy the BER requrement (and thus may

5 VT R 5 have to reconfgure the connecton more often). Here, we ntroduce a MMP scheme to predct the worst-case SR per bt n terms of the effectve ran rate. We then choose a modulaton mode that can accommodate ths predcted worst-case SR. The prncples nvolved n managng the uplnk and the downlnk are very smlar. Thus, we wll restrct our dscusson only to the uplnk. All our results are also demonstrated only for the uplnk. B. Markov Model-Based Predcton ) Basc Approach Gven a connecton request, the resource-calculaton phase reles on determnng the worst-case dsturbance over the duraton of the connecton so that suffcently many tmeslots can be allocated to the connecton to meet the requred BER wth a probablty no less than some prescrbed value. To determne the worst-case dsturbance, we use a Markov model to characterze the dsturbance process, n terms of the effectve ran rate. The use of a Markov model s, n prncple, not restrctve ndeed, any process of arbtrary complexty can be approxmated arbtrarly well by a suffcently large Markov model. The man caveat s the sze of the model requred. In the case of a nose profle that s prmarly affected by weather condtons, we have found that a model wth manageable sze suffces. Even f the model turned out to requre an unmanageable number of states, our method extends to the use of hdden Markov models, sgnfcantly enlargng the famly of processes that can be captured wth a manageable number of states. But, as ponted out above, practcal consderatons render such an extenson of our method unnecessary. Below, we descrbe the specfc Markov model we used to characterze the effectve ran rate process, how we estmate the parameters of the model, and how we use the model to calculate the worst-case dsturbance wth a probablty no less than some prescrbed threshold value. 2) Tranng the Markov Model The Markov model conssts of 8 states. Each state represents the varable part of the dsturbance n terms of the effectve ran rate (measured n mm/hr), and whether the dsturbance s ncreasng or decreasng. The states through 39 represent the ran rates of mm/hr through 39 mm/hr, and that the dsturbance s ether ncreasng or s constant. Furthermore, the states 4 through 79 represent the ran rates of mm/hr through 39 mm/hr, and that the dsturbance s strctly decreasng. A tranng profle s used to count the relatve frequences of varous state transtons, whch are then used to compute the transton probabltes. Thus, the tranng process provdes us wth an estmate of the probablty transton matrx P, where the entry P j denotes the probablty of state transton from state to state j. 3) Computng the Supremum Assume that the duraton of the connecton s known n advance, and that t s (an nteger) unts of tme. Denote the set of states by Ω. Let {P j :, j Ω} be the set of transton probabltes obtaned from the tranng process. Wthout loss of generalty, let us assume that the startng tme of the connecton s zero, and that the state of the system at ths tme s x. Denote the state of the system at tme nstant n by a random varable X n. Thus, we have X = x. Let us use the notaton ranrate( x ) to denote the ran rate n state x,.e., x f x 39 ranrate( x) = (4) x 4 f 4 x 79. Gven a probablty threshold p, we wsh to fnd the smallest value r such that Pr R r, R r,..., R r X = x p, (5) where we use { } n R to represent ranrate( X ). If we could compute the left-hand sde of (5) for any value of r (between to 39), then we can easly determne the smallest r satsfyng that nequalty. Clearly, r has to be greater than or equal to ranrate( x ), because otherwse the left-hand sde of (5) wll be zero. Thus, t suffces to consder the case where r ranrate( x ). For each r, let us defne a set S( r) { Ω : ranrate( ) r},.e., S(r) s the set of states n whch the ran rate s less than or equal to r. Then the probablty on the left-hand sde of (5) can easly be computed as follows: Pr { R r,..., R r X = x} = Pr { X S( r),..., X S( r) X = x} = Pr { X S( r),..., X S( r) X = x} = Pr X S( r),..., X S( r) X = x, X = x P x S ( r) x S ( r) { } 2 { } = Pr X S( r),..., X S( r) X = x P 2 { X S r X 3 S r X 2 x2} { X S r X S r X x } = Pr ( ),..., ( ) = n x x x2 S ( r) x S ( r) = Pr ( ),..., ( ) = x3 S ( r) x x ( Px x Px x ) 2 Px ( ) 2 x3 Px x P 2 x x x2 S( r) x S ( r) = Px ( ) x P x 2 x P x x P 2 xx. x S( r) x S ( r) x 2 S( r) x S ( r) Thus, the probablty can be computed n S(r) computatons. Gven a probablty threshold, we search for the smallest r {ranrate( x), ranrate( x) +,,39} satsfyng (5) a smple bnary search suffces for ths purpose. 4) Computng the umber of Tmeslots Once the supremum of the effectve ran rate over the connecton duraton s obtaned, the burst rate requred to satsfy the BER requrement s computed usng (2) and (3). Usng the computed burst rate, the correspondng modulaton mode s selected. As mentoned prevously, gven the modulaton mode and the data rate, the sze of the burst (.e., number of tmeslots) s determned usng a system-specfc look-up table. Ths s the number of tmeslots that wll be allocated (f possble) to set up the communcaton connecton. The method of allocatng these tmeslots on the MTCS, whle conformng to the allocaton restrctons (see Secton II-A), s

6 VT R 6 descrbed n Secton IV. The process of provdng guaranteed QoS connectons va the EHF-SATCOM system s summarzed n Fg. 2. If the dsturbance crosses the allowed safety margn (.e., the effectve ran rate of the actual dsturbance becomes more than what was predcted), the actual BER exceeds the maxmumallowable BER requrement of the connecton, and thus mght requre the connecton to be reconfgured. A hgher value of p n (5) mples that these stuatons are less probable to occur. But ths also costs more n terms of the number of tmeslots allocated for the connecton. Thus, there s a tradeoff between resource utlzaton effcency and frequency of reconfguraton. Fg. 2 Process of provdng guaranteed QoS connectons. A. Problem Descrpton IV. RESOURCE ALLOCATIO After the number of tmeslots has been calculated, a message s sent to the resource controller requestng these tmeslots. In the resource-allocaton phase, the controller nvokes a resource-allocaton algorthm to allocate the tmeslots onto the MTCS. Allocatng the tmeslots effcently s not a trval problem as s proven n the Appendx, t s n fact P-complete. 2 Of specal concern s the fragmentaton or checkerboardng that mght prevent a burst from beng allocated although the total space s suffcent for t. Due to the dynamc nature of the connecton request arrvals, dversty of the burst szes, and the allocaton restrctons, frequency channels are prone to have many fragmented spaces wthn them. Because bursts cannot be splt nto smaller peces to ft these fragmented spaces, ths can result n the wastage of the uplnk transmsson capacty. It s apparent that reducng the fragmentaton s crucal for obtanng effcently packed channels. The problem of allocatng tmeslots for the uplnk can be vewed as a varant of the bn-packng problem. Most of the research efforts n ths area have concentrated on acqurng 2 To be precse, we prove the offlne verson of ths problem to be Pcomplete. Ths, however, does not prove that the onlne verson s equally dffcult to solve. The onlne verson can be cast n the framework of Markov Decson Processes (MDP), but because of the curse of dmensonalty, ths approach s mpractcal. It s nterestng though to note that some heurstc technques such as Hndsght Optmzaton used for solvng MDPs rely on fndng the optmal offlne soluton, whch s extremely dffcult to fnd for ths problem. close bounds on the worst-case performance of well-known packng schemes, such as frst ft and best ft, appled to the statc case [9]. We use frst ft and best ft as benchmarks to evaluate the performance of our scheme, RCP ft. Ther formal defntons are gven below. Frst ft: Let B, B 2,... be the sequence of bns wth each bn havng a maxmum capacty of C. The tems x, x2,..., x n wll be placed n that order startng from the frst bn (.e., B ). To place x, fnd the least j such that B j s flled to level C x α, and place leftmost empty poston (assumng that x nto B j n the B j s capacty s ndexed from left to rght). ow B j s flled to level α + x, whch s less than or equal to C. Best ft: Let B, B 2,... be the sequence of bns wth each bn havng a maxmum capacty of C. The tems x, x2,..., x n wll be placed n that order startng from the frst bn. To place x, fnd j such that B j s flled to level α C x, where α s as large as possble. If two or more bns wth the same value of α exst, then select the bn wth the smallest ndex. ow, place x nto B n the smallest empty space large enough to ft t. For our applcaton, frequency channels represent the equalcapacty bns, and the bursts represent the tems that need to be packed. The objectve s to maxmze the utlzaton of the MTCS, where utlzaton s defned as the percentage of tmeslots that are actually allocated. The statc model of bn packng s not drectly applcable to our applcaton, because t fals to take nto account the dynamc arrvals and departures of the tems. Coffman et al. formulated the dynamc bnpackng model and analyzed the frst-ft algorthm wthn ths context [3]. However, they dd not consder the problem of managng space wthn a bn to reduce fragmentaton. In [2], chols and Conkln dscuss an approach specfc to Mlstar EHF-SATCOM systems, but ther approach s lmted to the statc case. B. The RCP-ft Algorthm ) General Idea As already mentoned, frst-ft and best-ft algorthms are wdely known algorthms for solvng the generc bn-packng problem. These algorthms blndly pack the gven tems wthout any knowledge of the arrval statstcs of the tems or the specal packng restrctons that mght exst n a specfc applcaton. Therefore, t s possble for an algorthm to outperform these two packng schemes, f these factors are taken nto consderaton. As already noted, reducng the fragmentaton s crucal for obtanng effcently packed channels. Three factors can cause fragmentaton n the tmeslots of the MTCS dversty of the burst szes, dynamc arrvals and departures of the connecton requests, and the allocaton restrctons. The fragmentaton caused by the frst two factors s unavodable regardless of the j

7 VT R 7 packng scheme. Let us consder the allocaton restrctons for the tmeslot-allocaton problem. Restrcton, mentoned n Secton II-A, also apples to the bn-packng problem, whereas Restrcton 2 s unque to our problem. Because of Restrcton 2, the possble allocaton space for any group of bursts comng from a sngle termnal (PASST) s restrcted to 7 tmeslots, whch s the length of one frame. From here on, we wll denote ths space smply as PASST. Allocatng tmeslots accordng to Restrcton 2 can cause fragmentaton wthn the frequency channels, especally when the total uplnk-traffc load on the system s dstrbuted among a small number of actve termnals. Ths case s llustrated n Fg. 3(a). In ths example, there are four bursts assocated wth two actve termnals A and B, and the bursts are allocated usng frst ft. The letters n the whte boxes represent the termnal assocated wth each burst, and the shaded boxes represent the PASST for termnal B. We assume that the connecton requests are comng from the two termnals n the order reqa(3), reqb(2), reqa(3), and reqa(), where reqx(y) represents a request comng from termnal X of sze y tmeslots. In the fgure, the fourth request s allocated n the fourth tmeslot (.e., fourth column) of the second frequency channel because of Restrcton 2. The fragmentaton caused by ths allocaton wll prohbt any bursts longer than four tmeslots from beng allocated n the second channel. frequency frequency 2 2 tmeslots A B A (a) A tmeslots B A A A (b) Fg. 3. Allocaton example: (a) wthout channel reservaton, and (b) wth channel reservaton. Four bursts assocated wth two actve termnals are beng allocated. The fragmentaton (caused by Restrcton 2) descrbed above can be avoded by groupng all the bursts that belong to the same termnal and placng them n a sngle frequency channel. Consder a groupng of bursts n whch each frequency channel s assocated wth a specfc termnal, that s, all bursts wthn a channel are from the same termnal. Ths groupng can be done by reservng a frequency channel for bursts assocated wth the same termnal, whch we call channel reservaton. Ths s the underlyng dea behnd RCP ft. An example of tmeslot allocaton usng channel reservaton s llustrated n Fg. 3(b). In the fgure, the same set of bursts used n Fg. 3(a) s allocated usng channel reservaton. ote that n Fg. 3(b), there s no fragmentaton n the second channel, allowng any burst shorter than seven tmeslots to be allocated. otce that the sze of the PASST assocated wth termnal B has not changed from Fg. 3(a). However, ths arrangement of bursts has allowed the PASST for termnal B to be contguous, whch mproves the utlzaton of the tmeslots. We have already explaned that channel reservaton can be used to pack the bursts n a more space-effcent manner. However, we have mplctly assumed that t c, where t and c are the number of actve termnals and the number of frequency channels, respectvely. Obvously, f t > c, t would be mpossble to reserve an exclusve channel for each of the actve termnals requestng a connecton. Consequently, some of the frequency channels need to be allocated wth a mxture of bursts from dfferent termnals. These mxed channels undermne the effectveness of the channel reservaton scheme, and should be kept to a mnmum. 2) The Algorthm Before descrbng the detals of RCP ft, we defne the followng terms: Channel tag: Specfes whether a gven channel s reserved, unreserved, or empty. Reserved channel: A frequency channel that s reserved for bursts comng from a specfc termnal. All bursts allocated n ths channel are comng from the same termnal. Unreserved channel: A frequency channel that can be shared by bursts comng from multple termnals. Ths channel s characterzed by a heterogeneous mx (.e., n terms of termnals) of bursts allocated wthn the channel. Empty channel: A frequency channel that s completely empty. There are no bursts allocated n the channel. Termnal load: Ths value s used to quantfy the traffc generated by each termnal. It represents the uplnk-traffc load that each termnal s generatng. Termnal load ρ s defned as d l ρ =, (6) τ where d : mean duraton of the connectons from termnal (n frames); l : mean burst length per frame of the connectons from termnal (n tmeslots/frame); τ : mean nterarrval tme of the connecton requests comng from termnal (n frames). In (6), d and τ are measured n unts of frames, and l s measured n unts of tmeslots per frame. Hence, termnal load s a quantty measured n (tmeslots/frame). Because a frame s of a fxed duraton, ths measure s equvalent to (tmeslots/tme). If >, some bursts must be allocated n an unreserved t c channel that s already occuped by bursts comng from dfferent termnals. The unreserved channels undermne the effectveness of channel reservaton, and contrbute to the fragmentaton of the MTCS. An unreserved channel s created

8 VT R 8 only f the followng condtons are satsfed when tryng to allocate a burst (see Fg. 4): There s no reserved channel that s assocated wth the termnal of the burst. There s no empty channel. There s no (prevously created) unreserved channel that has enough space to accommodate the burst. When an unreserved channel must be created (to allocate the burst), t s created by selectng a reserved channel and changng t nto an unreserved channel. To mnmze the number of unreserved channels, the crteron for selectng the reserved channel (whch wll be changed nto an unreserved channel) s based on the traffc load created by the termnal assocated wth each reserved channel. We assume that the traffc load s unequally dstrbuted among termnals, and that the system can detect these dfferences. 3 It s lkely that termnals sharng the same uplnk resource (.e., termnals wthn the same beam or termnals n dfferent beams that are usng the same satellte uplnk) wll each generate dfferent amounts of uplnk traffc. For example, certan termnals mght be sendng hgh-resoluton mages, requrng large amounts of channel resources, whle other termnals mght be sendng text messages that requre much less resources. To quantfy the traffc generated by each termnal, a quantty called termnal load (see (6)) s calculated for each termnal. After the termnal load value s calculated for each termnal assocated wth a reserved channel, a reserved channel s selected whose termnal has the smallest termnal load. Ths reserved channel s changed to an unreserved channel (by changng the channel tag), and the burst s allocated wthn t. In Fg. 4, we descrbe the steps of RCP ft usng a flowchart. ote that n the tmeslot allocaton step, once a frequency channel s selected, the burst s allocated n the smallest empty space avalable wthn the frequency channel that s large enough to ft t. To llustrate how the RCP-ft algorthm can actually be used to allocate bursts, here we gve an example allocaton scenaro. We assume the followng: Channel structure s MF-TDMA (6 tmeslots 4 channels). Connecton requests are comng from fve termnals A, B, C, D, and E. The order of the connecton requests s reqa(3), reqb(8), reqa(8), reqc(2), reqd(6), reqe(2), reqa(5), reqc(4), and reqe(8). The order of the termnal load generated by each termnal (from largest to smallest) s A, B, C, D, and E. For smplcty, we consder the statc case only (.e., connecton termnatons are not consdered). The frst request s accommodated by placng a burst of sze three n tmeslots one through three of Channel (see Fg. 3 When a termnal has traffc to send, t wll request a channel access va the resource controller. The resource controller can keep a hstorcal record of the connecton requests attrbuted to each termnal, ncludng parameters such as connecton duraton and burst length of the connecton. Usng ths record, 5(b)). The frst channel s tag s changed to reserved, whch means that ths channel should be packed only wth termnal A s bursts. The second burst s placed n Channel 2, and ths channel s reserved for termnal B. Smlar procedures are followed for the fourth and ffth bursts. The thrd burst s placed n the frst channel wthout any change n the channel tag because ths channel has already been reserved for termnal A. To accommodate the sxth request comng from termnal E, one of the reserved channels must be changed to an unreserved channel because all the channels have already been reserved for other termnals. Accordng to the RCP-ft algorthm, we choose Channel 4, whch s reserved for termnal D, and allocate termnal E s burst n ths channel. Recall that termnal D s termnal load value s smaller than that of termnal A, B, or C. The last burst (for termnal E) s allocated n Channel 4 because ths channel s unreserved and has enough space to accommodate the burst. Fg. 4 Flowchart for RCP ft. (a) (b) Fg. 5. Allocaton example: (a) frst-ft, (b) RCP-ft. the resource controller can keep track of the resources allocated to each termnal, and estmate the traffc load generated by each termnal.

9 VT R 9 Fg. 5(a) and 5(b) show the MTCS after the bursts have been allocated usng the frst-ft and RCP-ft algorthms, respectvely. The shaded regons represent empty tmeslots. The fgures clearly llustrate that packng wth RCP ft causes less fragmentaton. We clam that packng bursts va RCP ft results n mproved utlzaton of the MTCS by reducng the fragmentaton (compared to frst ft and best ft). Smulaton results of Secton V support ths clam. V. SIMULATIO RESULTS A. Resource Calculaton Usng Markov Model-Based Predcton ) Smulaton Detals and Performance Measures The smulatons were performed on computer-generated Markov and non-markov dsturbance profles. We performed several dfferent smulatons usng Markov as well as non- Markov profles. Each smulaton used two dfferent profles (wth the same probablty dstrbuton) one for the tranng phase and one for the predcton phase. Profles used n dfferent smulatons had dfferent dstrbutons sgnfyng dfferent coarseness levels n the dsturbance profles. We say that a profle s coarser than the other f the state-transton probabltes for the former profle are hgher than those for the latter. The tranng phase used profles that were,, sample ponts (spaced at two seconds) n length. In the predcton phase,, connecton requests were generated accordng to a Posson-arrval process wth a mean nterarrval tme of 2 seconds. The connecton-holdng tmes were dstrbuted unformly between zero and 4 seconds (these were approxmated to the closest number of sample ponts). The smulatons were used to compare the performance of the MMP scheme wth that of the 2 db scheme currently mplemented n the Mlstar EHF-SATCOM system. For comparng the performance of the two technques, the followng two measures were used. Slot allocaton factor: Let S mn be the mnmum number of tmeslots requred to satsfy the BER requrement of connecton wthout reconfgurng the connecton. ote that ths can be determned by observng the dsturbance profle, but only after the connecton has been completed. Let be the number of tmeslots allocated by algorthm A for connecton (where A represents ether the 2 db scheme or the MMP scheme). Then the slot allocaton factor (SAF) of algorthm A s defned as SAF A A mn {all calls} ( ) =. mn S {all calls} S S Intutvely, SAF(A) ndcates the normalzed number of tmeslots wasted by algorthm A on the average. An algorthm wth a lower SAF value wastes fewer number of tmeslots. As resource-allocaton effcency s of utmost concern over wreless lnks, we beleve that ths performance metrc mrrors the resource constrants faced by most satellte systems. S A Fracton of nstants the QoS s not satsfed: The performance metrc SAF defned above provdes a measure of algorthm effcency. An algorthm wth low SAF s more effcent compared to an algorthm wth larger SAF, as t wastes fewer tmeslots. But, SAF gves only a one-sded vew of the performance of the algorthm. If one compares two algorthms purely based on SAF, then an algorthm allocatng no tmeslots would be the best. But clearly ths s not an acceptable soluton. What we are nterested n s an algorthm that attempts to meet the QoS requrements of the users as much as possble, and yet s frugal wth the tmeslots. Thus, we defne our second metrc fracton of nstants the QoS s not satsfed. Ths metrc s defned as the number of connectons for whch the BER requrement s not satsfed, dvded by the total number of connectons. Ths crteron measures the effectveness of the algorthm n terms of provdng the requred BER level. 2) Smulaton Results and Dscusson For brevty, we provde smulaton results only for two dsturbance profles. Fgs. 6 and 7 show the performance of the two schemes for the case of a moderate, non-markov profle, whereas Fgs. 8 and 9 show the results for a very coarse, non- Markov profle. We can see that for Fg. 6, our scheme outperforms (.e., results n lower SAF values compared to) the 2 db scheme for probablty thresholds lower than.8. For Fg. 7, our scheme always outperforms (.e., results n lower values for the fracton of nstants the QoS s not satsfed compared to) the 2 db scheme. On the other hand, for Fg. 8, the 2 db scheme always outperforms our scheme n terms of SAF. But t should be noted that the fracton of nstants QoS s not satsfed s as hgh as.26 for the 2 db scheme usng the same profle (see Fg. 9). Ths value s ntolerably hgh, as connecton reconfguraton can take as long as 4 seconds n a Mlstar EHF-SATCOM system. Thus, the MMP scheme acheves a compromse between bandwdth effcency and frequency of reconfguraton, as opposed to the 2 db scheme, whch does not acheve ths compromse. Also, the MMP scheme has the advantage of beng able to tune ts parameter (.e., probablty threshold) to adjust to the dsturbance profles. B. Resource Allocaton Usng RCP Ft The performance of RCP ft was smulated usng a system modeled after the Mlstar EHF-SATCOM system descrbed n Secton II. The followng assumptons were made. Connecton requests arrve accordng to a Posson process. Duraton of a connecton s exponentally dstrbuted. Mnmum requred BER for each connecton s fxed at -5. Data rate for each connecton s randomly pcked from the eleven rates supported by the EHF-SATCOM system, wth equal probablty. Parameters (.e., transmtter power, transmt/receve antenna gan, free space loss, loss due to catastrophc falure, codng gan, and system nose temperature) of the uplnk budget equaton (see (2)) are fxed at system-specfc nomnal values.

10 VT R Ran loss s calculated usng (3), where the ran rate values are obtaned from a smulated ran profle. Channel structure: MF-TDMA (7 tmeslots 32 channels) The system operates only n full-duplex mode. Fgs. and compare the three packng algorthms (.e., frst ft, best ft, and RCP ft) when the connecton requests are unbased. Here, unbased means that all termnals generate the same amount of uplnk traffc. For all three packng algorthms, the algorthm s appled wthout volatng the allocaton restrctons of Secton II-A. For comparng the performance of the three packng schemes, the followng two measures were used. Utlzaton: Utlzaton s defned as the percentage of tmeslots that are actually beng allocated. Tmeslot rejecton rato (TRR): The tmeslot rejecton rato s defned as where T t t r max a t mn( r, max ) mn(, ) dt, T t r s the number of requested tmeslots at tme t, t a s the number of allocated tmeslots at tme t, max s the maxmum capacty of the MTCS n terms of tmeslots, and T s the observaton nterval. Intutvely, TRR ndcates the normalzed number of tmeslots rejected because of the fragmentaton n the MTCS. Fgs. and show the utlzaton and the TRR versus load factor wth the number of termnals requestng a connecton on the uplnk fxed at thrty. The load factor s the mean duraton of the connectons dvded by the nterarrval tme of the connecton requests. It can be seen from the curves that RCP ft outperforms the other packng algorthms n terms of the performance measures mentoned above. When the load factor s, packng the tmeslots wth RCP ft nstead of best ft ncreases the utlzaton by 7% and decreases the TRR by 3%. ote that all three packng schemes result n relatvely low utlzaton and hgh TRR. These results are partly caused by the fact that the data rate-ber combnaton of some of the connectons requres a long burst length, some as long as 64 tmeslots n length, whch s very dffcult to allocate due to any exstng fragmentaton n the MTCS. Fgs. 2 and 3 compare the three packng algorthms when the connecton requests are based. Here, based means that certan termnals have greater termnal load values than those of others, and the bas factor s used to quantfy ths value. For example, f the bas factor of a termnal s 24, then t means that the termnal has a termnal load value that s 24 tmes greater than that of unbased termnals. slot allocaton factor MMP algorthm 2dB algorthm probablty threshold Fg. 6. SAF n the case of a moderate non-markov profle. fracton of nstants QoS not satsfed MMP algorthm 2dB algorthm probablty threshold Fg. 7. Fracton of nstants QoS s not satsfed for the case of a moderate non-markov profle. slot allocaton factor.5.5 MMP algorthm 2dB algorthm probablty threshold Fg. 8. SAF n the case of a very coarse non-markov profle. fracton of nstants QoS not satsfed MMP algorthm 2dB algorthm probablty threshold Fg. 9. Fracton of nstants QoS s not satsfed for the case of a very coarse non-markov profle.

11 VT R utlzaton (%) frst-ft best-ft RCP-ft load factor Fg.. Utlzaton for unbased requests, 3 termnals. tmeslot rejecton rato (%) frst-ft best-ft RCP-ft load factor Fg.. Tmeslot rejecton rato for unbased requests, 3 termnals. utlzaton (%) frst-ft best-ft RCP-ft load factor Fg. 2. Utlzaton for based requests, 3 termnals, two based termnals, both wth bas factor = 24. tmeslot rejecton rato (%) frst-ft best-ft RCP-ft load factor Fg. 3. Tmeslot rejecton rato, 3 termnals, two based termnals, both wth bas factor = 24. Fgs. 2 and 3 show the plots for utlzaton and TRR versus load factor wth 3 termnals. Here, the number of based termnals s fxed at two, and the bas factor for these termnals s set to 24. We can see that the relatve performance mprovement obtaned by RCP ft s ncreased when the connecton requests are based (compared wth Fgs. and ). For example, a utlzaton mprovement of 29% s obtaned when RCP ft s used nstead of best ft at a load factor of. Ths mples that RCP ft s especally effectve when a few termnals heavly domnate the uplnk-traffc load. Comparng Fgs. and wth Fgs. 2 and 3, we can see that rrespectve of the packng scheme, the overall packng effcency s decreased when the connecton requests are based. VI. COCLUSIOS We descrbed a scheme for provdng QoS connectons over MF-TDMA satellte systems. We dvded the problem nto two parts resource calculaton and resource allocaton. For the resource calculaton part, we used a Markov model-based predcton scheme and compared ts performance wth the scheme currently mplemented n the Mlstar EHF-SATCOM systems. For comparng the performance of these schemes, we used two performance measures. We demonstrated that for a moderate dsturbance profle, there exsts a range of probablty thresholds for whch our scheme performs better than the currently mplemented scheme n terms of both performance measures. Moreover, for a very coarse profle, we showed that our scheme attans a compromse between frequency of reconfguraton and resource-utlzaton effcency. For the resource allocaton part, we descrbed a novel packng algorthm that can be used to allocate tmeslots n the uplnk of an EHF-SATCOM system. The packng effcency of the proposed algorthm was benchmarked usng smulaton results; we compared the utlzaton and the TRR wth two other packng schemes best ft and frst ft. The smulaton results showed that RCP ft performs better than the other two packng schemes n both the cases consdered (based and unbased connecton requests). Furthermore, the proposed algorthm s especally effectve when the uplnk-traffc load s heavly domnated by a small number of termnals. Our results were obtaned usng specfcatons and parameters of an actual Mlstar EHF- SATCOM system. The proposed algorthms are applcable to conventonal satellte systems employng the MF-TDMA uplnk access method wth smlar specfcatons. APPEDIX: P-COMPLETEESS OF THE DYAMIC RESOURCE-ALLOCATIO PROBLEM We prove that the dynamc verson of the resourceallocaton problem (DRAP) s P-complete. We wll do so by reducng the bn-packng problem (BPP) to the statc verson of the resource-allocaton problem (SRAP) and then by reducng the SRAP to DRAP. To proceed wth the proof, these problems need to be defned formally. As s commonly done n