CALL ADMISSION CONTROL IN WIRELESS MULTIMEDIA NETWORKS

Transcription

1 CALL ADMISSION CONTROL IN WIRELESS MULTIMEDIA NETWORKS Novella Bartoln 1, Imrch Chlamtac 2 1 Dpartmento d Informatca, Unverstà d Roma La Sapenza, Roma, Italy novella@ds.unroma1.t 2 Center for Advanced Telecommuncatons Systems and Servces (CATSS) Unversty of Texas at Dallas, Dallas, Texas, U.S.A. chlamtac@utdallas.edu Abstract - Ths paper addresses the call admsson control problem for the multmeda servces that characterze the thrd generaton of wreless networks. In the proposed model each cell has to serve a varety of classes of requests that dffer n ther traffc parameters, bandwdth requrements and n the prortes whle ensurng proper qualty of servce levels to all of them. A Sem Markov Process s used to model mult-class multmeda systems wth heterogeneous traffc behavor, allowng for call transtons among classes. It s shown that the derved optmal polcy establshes state-related threshold values for the admsson polcy of handoff and new calls n the dfferent classes, whle mnmzng the blockng probabltes of all the classes and prortzng the handoff requests. It s proven that n restrctve cases the optmal polcy has the shape of a Mult-Threshold Prorty polcy, whle n general stuatons the optmal polcy has a more complex shape. Keywords - Cellular Networks, Sem Markov Decson Processes, Handoff, Call Admsson Control, Randomzed Polces. I. Introducton The advent of the thrd generaton of wreless multmeda servces, brought about the need to adapt the exstng moble cellular networks to make them carry the varous classes of multmeda traffc, voce, vdeo, mages, web documents, data or a combnaton thereof. The user needs to have ubqutous access to a wde varety of servces whle roamng throughout the area covered by the wreless network. In these systems the base staton of each cell n the network has to serve several streams of requests, correspondng to multmeda servces. The wreless multmeda network has to be able to support multple classes of traffc wth dfferent Qualty of Servce (QoS) requrements,.e., dfferent number of channels needed, holdng tme of the connecton, cell resdence tme and prorty. Furthermore, the system wll have to support dynamc transtons of the calls among classes, that may be requred at run tme, accordng to the users needs, correspondng to bandwdth adaptaton requrements and to type of servce changes requred at run-tme. In order to support multmeda applcatons, the system capacty has to be ncreased sgnfcantly. A common way of achevng ths s by employng mcrocells and pcocells [1]. The reducton n cell sze leads to an ncreased spectrum-utlzaton effcency, but also results n more frequent handoffs and makes connecton level QoS more dffcult to acheve. Snce t s mpractcal to completely elmnate handoff drops, the next best alternatve s to provde a probablstc guarantee on qualty. The system can reduce the chances of unsuccessful handoff by assgnng hgher prorty to handoff requests than that assgned to ntal access requests belongng to the same class, because from a user s perspectve, the forced termnaton of an ongong call s less desrable than gettng a busy sgnal due to the block of an ntal access attempt. At the same tme the system must guarantee a proper prortzaton among requests of dfferent classes. In fact, emergency, or very hgh prorty new requests, can have hgher prorty than handoff requests of a low prorty class. For ths reason the choce of the Call Admsson Control (CAC) polcy plays a major role mpact n multmeda wreless networks. The purpose of ths paper s to propose a model to study and optmze the QoS parameters that characterze the traffc n a mult-class envronment, by means of access control polces. Several works have been proposed to analyze the problem of CAC n a mult-class envronment. Some of them [5], [7] only consdered two classes whle comparng dfferent reservaton strateges. In [13] a call admsson polcy named Hybrd Cutoff Prorty Polcy (HCPP) s consdered whle evaluatng the performance of a model that does not allow for class transtons, whle n [11], [12] SMDP models are proposed to be used at runtme to mprove the QoS by means of CAC polces, wthout analyzng the structure of the optmal soluton and wthout consderng the possblty of havng class transtons of calls, except n [11], where a lmted bandwdth requrement adaptaton s consdered to solve the problem of /02/$ IEEE PIMRC 2002

2 the hghly varyng resource avalablty. In ths paper we propose a model that takes nto account an heterogeneous, mult-class envronment, that allows for call transtons among classes, respondng to multmeda traffc requrements of 3G wreless systems. Ths model s exploted to evaluate the behavor of a wde class of polces and s optmzed by means of stochastc analyss wth SMDPs. Lnear programmng methods permt to dscard non statonary and randomzed polces from the search for the optmum. The structural analyss of the optmal long-run cost functon s nstead realzed through dynamc programmng methods that allow the structural analyss of the optmal CAC polcy. It s shown that the optmal polcy establshes staterelated threshold values for handoff and new calls n the dfferent classes. It s also shown that under certan assumptons the optmal polcy has the shape of what we call Mult-prorty Threshold Polcy (MTP) that, to the best of our knowledge, has not been proposed before. MTP s an adaptaton of a resource utlzaton polcy proposed n [4] under the name of Upper Lmt (UL) polcy to solve the problem of admttng mult-rate traffc n ATM wreless networks wthout takng nto account the handoff prortzaton problem. Under MTP two threshold values are defned for each class, T New and T Hoff. A class- call s accepted as long as enough bandwdth s avalable and the total number of busy channels s such that the acceptance of another class- call does not cause the occupancy level to exceed the threshold T New or T Hoff dependng on f the call s new or f t s a handoff call respectvely. The handoff calls of the hghest prorty stream of request are always accepted. The defnton of a threshold value even for handoff calls allows for the case n whch a low prorty handoff call could be dened servce n the hope to make place for hgh prorty calls, even f newly orgnated (e.g., emergency new calls). The results of our analyss have an mmedate practcal applcaton as the optmal polcy can easly be computed once basc statstc parameters defnng the traffc of requests are known, by solvng an optmzaton problem by means of very commonly used methods of operatons research [8], [10], [14], [15]. II. A Mult-class Sem Markov Decson Model for CAC We consder a decson model that allows for multple class calls that dffer n ther QoS requrements and traffc parameters, allowng for call transtons among classes. Each cell n the system has to gve servce to N classes of call requests that we assume to be generated accordng to a Posson dstrbuton wth mean arrval rates λ New 0 N for new calls, λ Hoff, 0 H for handoff calls, where the condton H N takes nto account the possblty that some classes of traffc do not have handoffs. There are C channels avalable n each cell assumng a Fxed Channel Allocaton (FCA) scheme. Each new or handoff call of class has a class dependent bandwdth requrement that s measured n number of unt channels and represented wth b. The unencumbered communcaton tme and the cell resdence tme of a class- call are assumed to be exponentally dstrbuted wth mean rate µ c and µe respectvely. We use µ µ c µe, 1, 2,..., N}. We now ntroduce the notaton that wll be used throughout the secton. The state of the SMDP s represented through an N- dmensonal vector x (x 1, x 2,..., x N ) n whch the varable x represents the number of ongong class- calls. The state space Λ s defned n the followng way Λ x : } b x C; x 0. =1 When the system s n state x, an accept/reject decson must be made for each type of possble arrval,.e., an orgnaton of a class- new call, or the arrval of a class- handoff call. Thus, the acton space B can be expressed by B = (a New 1, a New 2,..., a New N, a Hoff 1,..., a Hoff N ) : } a New, a Hoff j 0, 1},, j = 1,..., N. where the ndcators a New and a Hoff j denote the acceptance (1) or the denal of servce (0) of class- new calls or handoff respectvely. A call may transt from one class to another satsfyng bandwdth adaptaton requrements due to the traffc condtons, or accordng to the user s needs to change type of servce at runtme. Ths could happen when a user asks for new addtonal servces whle havng an ongong connecton. For example a user wth an ongong voce call could ask for addtonal bandwdth to set a vdeo-conference wthout nterruptng hs connecton. In ths case the call would transfer from the voce class to the vdeo class. The transton from a class to another class j occurs wth negatve exponental dstrbuton wth mean rate π j. These transtons take place between states characterzed by a dfferent number of busy channels (n bandwdth unts) but wth the same total number of ongong calls as shown n Fgure 1. If the system s n state x Λ and the acton a B s chosen, then the dwell tme of the state x s τ(x, a) where

3 x -1 j- transton -j transton x -1 class j arrval class j completon x class arrval class completon x 1 j- transton -j transton x 1 p a xy = (λ new where a new a new λ hoff = a hoff = 0 f y / Λ. Class- departure: y = x e a hoff )/Γ 1, 2,..., N} (3) p a xy = x µ /Γ 1, 2,..., N}. (4) Fg. 1 A 2-class model wth class transtons. Class j transton: y = x e e j p a xy = x π j a trans j /Γ 1, 2,..., N}, where a trans j = 0 f y / Λ and a trans j = 1 otherwse. (5) τ(x, a) = 1/ [ N =1 x µ (λ New a New x π j ) λ Hoff a Hoff (1) where π 0 1,, N}. The system s forced to pay a penalty H f a handoff call of class s refused. If the servce s dened to an ntal attempt of access n class, the system wll have to pay a lower penalty L H. It may happen that H < L j for some ndexes j, meanng that the prorty of class-j calls s hgher than the prorty of class enough that even a class- handoff call may be nterrupted n the hope of makng place for new calls n class j. Ths can happen n presence of very hgh prorty traffc, lke emergency calls. Equaton 1 shows the dependency of the dwell tme of the states of the process both on the decson a and on the state x. The set of rate that characterzes the process s bounded above by the maxmum outgong rate. Hence we conclude that the process s unformzable. Addng dummy transtons from states to themselves, a unform Posson process can be constructed whch governs the epochs at whch transtons take place. The unform rate wll be an upper bound on the total outgong rate from each state. The followng defnton of Γ fts our needs. Γ = [Cµ λ Hoff =1 λ New C π j ]. (2) The transton probabltes of the unformzed process are then Class- arrval: y = x e Dummy transtons from each state to tself: y = x p a xy = 1 Γ [Γ N x a trans j π j )] 1, 2,..., N}. (λ new a new =1 λ hoff a hoff x µ (6) Otherwse: the transtons between other states that are not consdered n ths lst have probablty 0. The unformzed cost functon s: r(s, a) = 1 Γ =1 [λ New (1 a New ) L λ Hoff (1 a Hoff ) H ]. (7) Studyng the propertes of the descrbed unformzed process, t can be confrmed, wthout loss of generalty, that the decson model can be restrcted to nclude the only processes wth no transent states and wth only one communcatng class,.e., to the only unchan processes. We ndcate wth S the fnte set of all feasble couples of vectors of the knd (state, decson). The unchan property, together wth the fnteness of S mples the exstence of a unque statonary state probablty dstrbuton whch s ndependent of the ntal state of the process. The exstence of a statonary polcy allows us to conclude that an optmal soluton can be expressed through a decson varable x sa that represents the probablty for the system to be n state s and contemporaneously to take the decson a. The Lnear Programmng (LP) formulaton assocated wth our SMDP for the mnmzaton of the cost pad n a long-run executon s gven by:

4 Mnmze (s,a) S r(s, a) x s,a constraned to x sa 0 (s,a) S x sa = 1 (s, a) S a B x ja = (s,a) S pa sj x sa j Λ. (8) Once known the parameters that characterze the traffc behavor n the consdered cell, the lnear programmng problem gven by Equaton 8 can be solved by means of the well known methods of the operatons research [9], thus obtanng the optmal polcy for CAC. Ths problem can also be solved at run-tme, and t can be used to calculate the steady state probabltes that are necessary to obtan the values of the man QoS parameters. III. Optmzaton of the Mult-Class Model We now want to obtan general propertes of the optmal CAC polcy. For ths purpose we keep on analyzng the optmzaton problem. The decson process formulated n Secton II allows the search for the optmal polcy n a wde general class that also ncludes the so called fractonal or randomzed polces. Statonary randomzed polces are characterzed by state-related non-determnstc decsons,.e. n each state the decson s made wth a certan fxed probablty that defnes the consdered polcy. Nevertheless fractonal polces can be excluded from our study snce, by analyzng the shape of the restrant matrx of the lnear programmng formulaton gven by Equaton 8, we can prove the exstence of an optmal determnstc soluton. To nvestgate the shape of the optmal polcy we recur to Derman s theorem [6] accordng to whch every polcy that s optmal under a dscounted cost crteron wth a dscount factor α close to 1 s also optmal under the average cost crteron. Thence we restrct our study to the optmzaton of a dscounted cost functon over an nfnte horzon W α (s), that has the followng formulaton obtaned by means of dynamc programmng methods, made possble by the certanty of the exstence of an optmal determnstc soluton. W α (s) = 1 N s µ W α (s e ) η Γ =1 =1 =1 (C s )µ W α (s) =1 (λ new λ hoff )W α (s) λ new mn a B anew [W α (s e ) W α (s)] (1 a new )ˆL } =1 λ hoff mn a B a hoff [W α (s e ) W α (s)] (1 a hoff )Ĥ} [π j s W α (s e e j ) (C s )π j W α (s)] =1 (9) where ˆL L /α and Ĥ H /α. Then the optmal polcy chooses the best acton to take n each state wth the followng rule: Hgh prorty customers of class are accepted only f α (s) W α (s e ) W α (s) Ĥ. Low prorty customers of class are accepted only f α (s) W α (s e ) W α (s) ˆL. An N-dmensonal property of monotony and convexty n the number of ongong calls n each class can be proven by means of dynamc programmng methods. Snce α (s) s non-negatve and non-decreasng n the number of ongong calls n class, thence we can fnd nteger values t L (s) and t H (s) such that [ t L (s) = arg mn α (s) > ˆL }], and [ }] t H (s) = arg mn α (s) > Ĥ. Therefore, the optmal polcy regardng the decson to accept or refuse to serve requests belongng to any one of the classes, cannot be easly reduced to a fxed thresholds polcy lke MTP or HCPP, the threshold value for each class strctly depends on the level of occupancy of the other classes. Each threshold has to be evaluated for the possble levels of occupancy, for example by means of the LP method seen n Secton II concernng the optmzaton problem of Equaton 8. Snce there s an optmal statonary polcy, f the traffc parameters do not change sgnfcantly at runtme, the optmal polcy can be evaluated once for all, by means of the lnear programmng formulaton of ths optmzaton problem. The computatonal complexty of ths optmal soluton s proportonal to the sze of the restrant matrx

5 of the problem, but f an average traffc behavor can be dentfed, the soluton can be computed once for all the tme the esteem of the traffc parameters s suffcently accurate. From Equaton 9 we can see that f µ does not depend on the class, that s µ µ, 1, 2,..., N}, and f the bandwdth requrements are the same n every class, that s b b, 1, 2,..., N}, then the optmal dscounted cost functon over an nfnte horzon W α (s) does not depend on the partcular state s, but on ts total occupancy level only and the polcy MTP can be proven to be optmal n ths partcular case. Thence MTP s not optmal even wthout class transtons, unless wth some assumptons,.e. the dfferent classes, even though wth dfferent prortes, have the same bandwdth requrements and the same cell resdence and call holdng tmes,.e., MTP s optmal only for non multmeda traffc. HCPP s optmal n an even more restrctve case, that s only f the classes of requests have also the same prorty,.e. wth only one class of traffc, thus obtanng the well known CPP [2]. IV. Conclusons In ths paper we conducted an analyss and optmzaton of QoS of wreless networks by means of nnovatve models created wth the methodology of SMDPs. SMDPs, n a very general shape, are proven to be an excellent method of evaluaton of QoS parameters and CAC polces, creatng a parametrc model that makes us able to compare the behavor of several admsson polces, whle optmzng an objectve functon n the shape of an average cost over an nfnte horzon. SMDPs can be used to optmze blockng probabltes of new and handoff calls of several classes of multmeda requests. SMDPs reveal that the optmal polcy establshes staterelated threshold values for handoff and new calls n the dfferent classes. It was proven that only f the classes have the same bandwdth requrements and the same servce tme,.e. for prortzed non-multmeda traffc, the optmal polcy has the shape of MTP. [4] S. K. Bswas, B. Sengupta, Call Admssblty for Multrate Traffc n Wreless ATM Networks, n Proceedngs of IEEE INFOCOM 97, pp [5] J. Chen, M. Schwartz, Two-ter resource allocaton for a multmeda mcro-cellular moble system, IBM Research, Hawthorne, New York, submtted for publcaton. [6] C. Derman, Fnte state Markovan decson processes. Academc Press, [7] B. Epsten, M. Schwartz, Reservaton Strateges for Multmeda Traffc n a Wreless Envronment n IEEE 45th Vehcular Technology Conference, Chcago IL, July [8] K. Hastngs, Introducton to the mathematcs of operatons research, Dekker, [9] D. P. Heyman, M. J. Sobel, Stochastc models n operatons research. Vol. 1 and Vol.2, McGraw-Hll, [10] J. Kelson, Markov chan models. Rarty and exponentalty. Sprnger-Verlag, New York, [11] S. Km, T. Kwon, Y. Cho, Call Admsson Control for Prortzed Adaptve Multmeda Servces n Wreless/Moble Networks, n IEEE VTC 2000 Sprng, Tokyo, [12] T. Kwong, Y. Cho, M. Nagshneh, Optmal Dstrbuted Call Admsson Control for Multmeda Servces n Moble Cellular Network n Proceedngs of 5th Inl. Workshop on Moble Multmeda Communvatons MoMuC 98, October 12-14, 1998 Berln. [13] B. L, C. Ln, S. T. Chanson, Analyss of a Hybrd Cutoff Prorty Scheme for Multple Classes of Traffc n Multmeda Wreless Networks, Wreless Networks, ACM Baltzer Scence Publshers, Vol. 4, No. 4, 1998, pp [14] S. Ross, Appled probablty models wth optmzaton applcatons, Holden-Day, [15] H. C. Tjms, Stochastc modelng and analyss. A computatonal approach, John Wley & Sons, References [1] A. S. Acampora, M Naghshneh, An archtecture and Methodology for Moble-Executed Handoff n Cellular ATM Networks, IEEE Journal on Selected Areas n Communcatons, Vol.12, No. 8, October 1994, pp [2] N. Bartoln, Handoff and Optmal Channel Assgnment n Wreless Networks Moble Networks and Applcatons, ACM/Kluwer Academc Publshers, Vol.6, No.6, November [3] A. T. Bharucha-Red, Elements of the theory of Markov processes and ther applcatons. McGraw- Hll, 1960.