AN APPROACH TO WIRELESS SCHEDULING CONSIDERING REVENUE AND USERS SATISFACTION

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1 The Medterranean Journal of Computers and Networks, Vol. 2, No. 1, AN APPROACH TO WIRELESS SCHEDULING CONSIDERING REVENUE AND USERS SATISFACTION L. Bada 1,*, M. Zorz 2 1 Department of Engneerng, Unversty of Ferrara, Ferrara, Italy 2 Department of Informaton Engneerng, Unversty of Padova, Padova, Italy ABSTRACT Recently, several proposals for wreless schedulng algorthms have been presented, usng allocaton models focused on users subjectve percepton of the servce. The goal of these nvestgatons s to desgn schedulng polces amed at satsfyng more drectly the users preference. In ths paper we extend ths approach, by studyng Rado Resource Management, and n partcular the scheduler, consderng an orgnal model to represent the behavor of multmeda users. We nclude chargng strateges and users reacton to prces, so that qualtatve and quanttatve economc consderatons are drectly ncluded. After a bref dscusson on how to nclude both perceved qualty and prcng, n order to acheve a user-centrc evaluaton of the QoS, we show how t s possble to schedule users by applyng ths model so as to obtan a more effcent resource usage, characterzed by both larger users apprecaton and hgher revenue for the servce provder. Keywords Schedulng, Communcaton system economcs, Resource management, Code dvson multaccess. 1. INTRODUCTION In current communcaton systems, many servces are accessble on the wreless channel, thanks to the dffuson of packet transmsson n Wdeband Code Dvson Multple Access (WCDMA) networks. However, n a WCDMA system t s necessary to consder the possble coexstence of several users nterferng wth each other, and the nherent unrelable nature of the rado channel. Moreover, n a wreless medum the errors are characterzed by varablty wth tme and locaton, as well as a consderably hgher rate and burstness. All these factors have a strong mpact on the system performance and the acheved Qualty of Servce (QoS). In partcular they usually prevent servce requests from beng satsfed wth rgorous guarantees and/or n an equal manner for all the users. *Correspondng author: E-mal: lbada@ng.unfe.t All Rghts Reserved. No part of ths work may be reproduced, stored n retreval system, or transmtted, n any form or by any means, electronc, mechancal, photocopyng, recordng, scannng or otherwse - except for personal and nternal use to the extent permtted by natonal copyrght law - wthout the permsson and/or a fee of the Publsher. Copyrght 2006 SoftMotor Ltd. ISSN: For these reasons, t becomes mpossble to apply on the wreless medum classc schedulng strateges desgned for the wrelne case. To solve ths problem, t s commonly exploted the fact that a scheduler can obtan an effcent usage of the system capacty by servng n a greedy way the users wth the best channel condtons. Ths leads to the development of Channel-State Dependent Schedulers[1]. However, to have a wde servce dffuson, t s necessary to provde a balanced resource supply, also servng users wth bad channel condtons. Henceforth, several contrbutons have dealt wth the problem of ncreasng farness among users [2, 3]. We are nterested n approachng the problem of ncreasng farness not only from the theoretcal pont of vew but also n terms of achevng a satsfactory servce accordng to the prce whch the users are wllng to pay, because users satsfacton s connected wth economc aspects, lke the provder s task of achevng an adequate revenue. For a real operator, n fact, the network mantenance s possble only f the costs of servce provsonng are compensated and overcome. Users apprecaton of the suppled QoS can be nvestgated wth an approach based on utlty functons, whch s a feld of research wdely explored n the recent lterature, n partcular for the Rado Resource Management (RRM) operatons [4, 5]. Several schedulng strateges can be regarded as applcatons of a utlty-based framework. Snce t s possble to see the schedulng problem as a prortzaton of users n a queue, ths can be done by defnng approprate weghts, as n the Weghted Far Queung (WFQ) [6] or WF 2 Q [7] schedulers. A detaled mathematcal formalzaton of the resource allocaton problem, whch nvolves utlty functons to represent the QoS requrements, can be found n [8]. By combnng these approaches, the schedulng can be seen as a strategy to maxmze the total system utlty. However, the system welfare s stll seen only from the users perspectve, wthout consderng the operator s economc counterpart. In ths paper we rather am at consderng also the provder s pont of vew, whch means to nclude consderatons about the earned revenue. To do so, t s necessary to extend the framework and consder the tarff of the servce, by ntroducng a prcng functon wth propertes smlar to utlty but wth a negatve mpact on users degree of satsfacton. Hence, we drectly nvestgate the trade-off between utlty and prce by applyng a mcro-economc framework, developed n [9], to the schedulng problem. Ths allows us to refer to economcs n two drectons, snce the allocaton effcency s eventually seen not only as the QoS provsonng but also through the money exchange between user and servce provder. In the prelmnary nvestgaton carred out n [9], we appled the model to dmenson the network and to gan nsght about the ponts of trade-off nvolved. The contrbuton of the

2 58 AN APPROACH TO WIRELESS SCHEDULING CONSIDERING REVENUE AND USERS SATISFACTION present paper s to drectly utlze the user-centrc model of servce apprecaton as a concrete way to develop schedulng strateges n WCDMA system. In partcular, we nvestgate how an acceptable QoS for the users and together a satsfactory ncome for the provder can be obtaned. We evaluate exstng technques to enhance schedulng from the techncal pont-ofvew (.e., by maxmzng throughput), and dscuss ther performance wthn the above framework. Moreover, we study and quantfy possble margns of mprovement for both users satsfacton and provder s revenue, so to show that ntroducng servce-percepton awareness n the scheduler sgnfcantly ncreases the goodness of the allocaton. The remander of ths paper s organzed as follows: n Secton 2 we present the analytcal model for the users satsfacton, ncludng both prcng and utltes. In Secton 3 we dscuss dfferent schedulng strateges under the theoretcal pont-ofvew and we outlne how they can be modfed to take nto account the revenue mprovement aspect. Secton 4 presents smulaton results and Secton 5 concludes the work. 2. MODEL FOR USERS SATISFACTION In ths secton, we descrbe at frst the propertes of utlty and prcng functons whch wll be exploted n the followng analyss. Then, we consder a mcro-economc model whch quantfes the level of satsfacton for each of the users, determned by both the perceved QoS and the prce pad, so that ther trade-off can be explctly taken nto account. More detals about the model are avalable n [9]. Here, we smply gve a bref summary and then go drectly nto the applcaton of the model to the schedulng for wreless CDMA networks. Consder a set (network) of N users. In mcro-economcs [10], the concept of utlty functon s ntroduced to represent the evaluaton among the customers (users) of an assgned resource, whch we represent wth a generc non-negatve parameter r. For smplcty, we assume that r s a scalar, even though an extended analyss can be easly obtaned for a multdmensonal r by followng the same approach presented here. The allocaton of the resource r generates an assgnment vector r = ( r 1,, r N ), where r s the amount of resource allocated to user. The utlty of the th user s related to the amount of resource receved. An example of ths can be obtaned s shown n [11]. In other words, the element r s evaluated, from the perspectve of the th user, as mapped through the functon u ()., determnng a perceved utlty u (r ). When network management s studed, t s reasonable to assume that r represents the share of network resources allocated to user and the functon u (). s dfferent for each user, as t depends on the technology of the termnals and the subjectve percepton of the users. For what concerns the wreless schedulng, t s possble to dentfy r wth the assgned data rate. To correctly evaluate the utltes, r shall be averaged on the whole transmsson, to obtan meanngful results, snce subjectve percepton of the acheved data rate s possble only after a suffcently large tme wndow. A more complcated analyss whch re-evaluates the stuaton every gven tme nterval s possble, even though t s omtted here for the sake of smplcty. A detaled nvestgaton on how to derve proper utlty functons for dfferent specfc communcaton systems s beyond the scope of ths paper. Thus, we smply take standard assumptons performed n the lterature for the utlty-based RRM; f necessary, they can be specalzed n more detal. Usually, utltes are assumed for every knd of assgnment to be quas-concave non-decreasng functons,.e., u''(r)<0 for suffcently large r. We further ntroduce the assumpton of havng sgmod-shaped functons, as n [12]. In partcular, we adopt the followng expresson: = 1,2,..., N ( r / K ) u = 1+ ( r / ζ ζ K ) where the parameters K > 0 and ζ 2 depend on the ndex, so that dfferent users may be characterzed by dfferent utlty functons. In the smulatons, K and ζ are randomly generated wth unform dstrbuton wthn a gven nterval, whch can be connected n partcular wth the specfc type of servce requested by the users. These assumptons are qute common n the lterature, and they are also sutable for our purpose: for example, sgmod functons have also an upper-lmt, whch seems to be a reasonable descrpton of the performance of multmeda servces on wreless networks. In fact, accordng to the type of systems, n every case there s a maxmum rate r max allowed by the technologcal support and t s also realstc to assume that the hghest perceved QoS s close to u(r max ). Thus, t s possble to wrte: = 1, 2, K, N lm u ( r) = u ( r ) r The above assumptons for the utltes are however very general, snce the nternal parameters K and ζ can be tuned so as to determne very dfferent behavors for the users. An approprate way to choose them could be n connecton wth the user ntrnsc parameters. The above defnton consders only non-negatve values of the utltes, and the lowest utlty, whch s acheved when no servce at all s suppled, s u ( 0) = 0. Ths condton can also be changed f run-tme servce degradaton s consdered, as n ths case the utlty could even go below 0; n fact, t s commonly assumed preferable not to be admtted at all than to be dsconnected from the network whle recevng the servce. Thus, a lowest utlty equal to 0 corresponds to a condton of deal Admsson Control [13]. The aggregate of the utltes can be regarded as the total network welfare W(r), and a possble goal of the RRM can be consdered to be the welfare maxmzaton. If the utltes are addtve, W s smply ther sum. Ths leads to formulate the RRM task as an optmzaton problem [8]. A way to formalze t s: max W( r), W( r) = u( r) To have a properly defned optmzaton problem, one must also take nto account a capacty constrant of the network, represented by (4) n the above formulaton. Thus, C (r) s a gven functon of the allocaton vector r and C max descrbes the N = 1 s.t. C( r) C max max (1) (2) (3) (4)

3 AN APPROACH TO WIRELESS SCHEDULING CONSIDERING REVENUE AND USERS SATISFACTION 59 upper lmt allowed for C. Note that also ths constrant can be easly extended to a mult-dmensonal condton. For a generc communcaton system, the smplest possblty to model the capacty constrant s to consder a hard capacty system, where a fxed maxmum total rate C max can be allocated on aggregate. For wreless systems, ths holds for example for a Tme or Frequency Dvson Multple Access (TDMA, FDMA) where the capacty lmt s related to the number of avalable tme or frequency slots. Thus, the functon C (). s smply a sum, and the constrant becomes: N = 1 r C However, note that, even though ths knd of constrant s useful to understand what follows, t s not realstc for WCDMA networks. Code-dvson multplexng has n fact a smlar lmtaton n the maxmum number of codewords, but usually ths number s assumed to be very large for practcal purposes. Another constrant,.e., the nterference lmt, s usually more restrctve and wll be consdered n the followng [14]. The nterference lmt can be modeled by consderng the powers allocated to the users, mposng e.g., the Sgnal-to- Interference rato of each user to be known and the total power allocated to the users n the same cell to be lmted. Accordng to the lnk gan condtons, Sgnal-to-Interference Rato (SIR) requrements and allocated rates, an nterference condton can be wrtten for every user. Ths condton can be formalzed by ntroducng a vector of powers P = ( P 1,, P N ), where P s the power allocated to user. If for the sake of smplcty we consder a sngle-cell case, ths condton s: where Λ (). s a frst degree polynomal expresson. Ths can be connected wth the usual formulaton of the nterference condton for CDMA systems expressed as meetng an SIRtarget for user called g, as follows: BW γ r where BW s the spreadng bandwdth, g k s the power lnk gan for the kth user, 0 ζ j 1 s the normalzed cross-correlaton between and j at recever and the term h s due to background nose. Ths can be re-arranged so as to wrte, as n (5): In ths case, a vector r s sad to be feasble f these constrant are met. The feasblty condton can be complcated to nvestgate wth analytcal nstruments, but s easy to check wthn a smulator. For ths reason, n the present paper we adopt a smulaton-based approach. An extenson of the problem descrbed above can be gven consderng also the effect of prcng [15, 16]. Once the max Λ ( P) r P gp N ξ 1, j gp j j j + = η N η ( BW γ) ξ j 1, j jpj + r P = g (5) (6) (7) strateges to charge users for the offered servce are gven, t s possble to determne the generated revenue; t s also reasonable that, among allocatons that are almost equally satsfactory for the users, the operator chooses the one that determnes the hghest revenue, snce n ths way ts own satsfacton s ncreased. As long as ths can be done wthout decreasng too much the users welfare, ths mples ndeed a more effcent resource usage. On the other hand, prcng mpacts negatvely on users choce. As an mmedate consequence, by consderng that the servce does not come for free, t s possble to understand when an unnecessarly hgh amount of resource s provded to some users. Overassgnments are a trval way to allocate a hgh amount of resource, but they are possble only f the prce s neglected: n a more realstc case they are usually refused by users snce they mply hgher prces. Ths economc aspect enforces even more the ntrnsc property of nterference-lmted system, lke the CDMA envronment, of beng unable of provdng strct QoS guarantees, unless resource are severely over-provsoned. Henceforth, the best effort allocaton that can be commonly provded by such systems s not always consdered acceptable by the end users. Our clam s that ths decson s also strongly mpacted on by the tarff pad for the servce and the wllngness to pay of the users. More n general, wthout consderng the prcng mpact t s mpossble to understand whether the allocaton s not only techncally effcent, but also sensble from a mcro-economc perspectve, where users that do not get both adequate QoS and affordable prce are unsatsfed customers. It can be assumed that these users only pay a certan fracton of the tarff due, or alternatvely they leave the servce wth a certan probablty. Hence, the model presented n [9] proposes to defne the satsfacton A of the th user as a value nto the range [0,1]. Ths satsfacton value can be seen as a weght, or a probablty of servce acceptance, to evaluate all metrcs related to resource assgnment, so that only resource comng from satsfactory allocatons s effcently used. For example, the average revenue R earned by the provder s evaluated as where p s the prce pad by the th user. Smlar expressons can be used to evaluate other metrcs [13], for example the sum of the A s represents the fracton of satsfed customers,.e., the ones who keep payng for the servce wthout abandonng t or beng drven to other operators. However, the nterestng pont s that ths framework s not only useful for evaluatons, but also ndcates a possble approach to scan the solutons of the allocaton problem to mprove the schedulng strategy, as wll be outlned n next Secton. To map the trade-off between the offered QoS and the prce pad, we assocate A wth u and p. Hence, we wrte A = Au (, p ) for each, by assumng that every user n the network adopts the same crteron to decde whether the servce condtons are satsfactory or not. A possble expresson [9] for A (). s as follows: A N R = = A 1 p μ k ( u / ψ ) ( / (, ) = 1 p u p e φ ε ) (8) (9)

4 60 AN APPROACH TO WIRELESS SCHEDULING CONSIDERING REVENUE AND USERS SATISFACTION where k, μ, ε, ψ, φ are postve constants. The exponents μ and ε tune the senstvty to utlty and prce, respectvely, whereas ψ, φ and k are smply normalzaton constants (a reference utlty, a reference prce, and the opposte of the logarthm of a reference value for A, respectvely). Note that the above equaton s wrtten n ths form only to emphasze the trade-off, but actually both u and p depend on the allocated resource r. In fact, n ths work we always consder that u s follow (1), whereas p = pr ( ), wth p (). beng a non decreasng functon, whch s the same for all users (note that ths assumpton s made for farness reasons, snce n ths paper we consder only one servce class for all users). If there are dfferent servce classes, then a set of prcng functons should be consdered. However, t s realstc to assume that ths set s small; thus, an extenson to ths case s straghtforward). The defnton reported n (9) satsfes several propertes whch are expected to characterze A, lke monotoncty or boundary condtons (for detals see [9]). However, t s adopted here only for the sake of smplcty, but the conclusons drawn n the followng are stll vald for other choces of A(u,p). The total revenue of the provder, evaluated n (8) can be rewrtten as R(r). Ths opens up the formulaton of a dfferent optmzaton problem, n whch the goal functon s no longer the users welfare but the revenue. Note that ths goal, besdes beng an alternatve whch mght be nterestng for the provder, s not dsjont from welfare maxmzaton, snce generally the larger the utlty, the larger A and henceforth the revenue. Ths follows drectly from (8): however, A decreases wth ncreasng p. Wth a smlar formulaton of the problem (3)-(4) we wrte then: max R( r), R( r) = A( u( r), p( r)) p( r) = 1 where (10) s stll related to the WCDMA nterference management. The schedulng strateges derved n the followng wll be dentfed as approxmate solutons to ths problem. 3. ANALYSIS OF WIRELESS SCHEDULING WITHIN THE MODEL N s.t. C( r) C max (10) (11) Ths secton s dedcated to the applcaton of the above framework to schedulng strateges for WCDMA systems. In wreless systems, schedulng heavly mpacts on the performance and n partcular the scheduler must be aware of the rado condtons, because of the locaton-dependent and bursty errors. For example, a user n a fadng dp may experence a bad channel and may be unable to transmt. In ths respect, also tme varablty, whch s determned by fadng and users moblty, has to be consdered. For these reasons, we assume n the followng to have a wreless system wth mechansms to predct channel condtons. An example s the Hgh Speed Downlnk Packet Access (HSDPA) release of UMTS [17]. In HSDPA, the channel condtons mght be rapdly tracked to mprove the system throughput, thanks to the Medum Access Control features located n the node-b, to evaluate the rapd varatons of the wreless channel [18]. The knowledge of the channel state makes t possble to gve prorty to users that perceve a clean channel, whereas users wth a poor SIR wll be delayed. In ths way the scheduler tends to maxmze the total throughput because t mnmzes packet retransmssons, whle on the other hand farness s decreased. Conversely, farness s obtaned, e.g., wth a Round Robn (RR) approach, where resources are allocated to the communcaton lnk on a sequental bass. However, ths results also n the potental rsk of havng hgh number of corrupted packets and consequent retransmssons. Due to the poor performance of the pure RR scheduler, n the followng we wll not analyze ths strategy. To better guarantee the QoS requrements t s necessary to fnd a trade-off between a pure SIR-based heurstc and a round robn schedulng,.e., between maxmzng the throughput and allowng the hghest possble number of users to acheve a satsfactory QoS. In our analyss we consder frst of all a tradtonal SIR-based scheduler, called C/I, explotng a greedy assgnment of the avalable resources [19]; such a strategy obtans the maxmum sector throughput, but wth a hgh degree of unfarness. A possble soluton to cope wth ths problem was proposed n [3], where a smlar scheme called n the followng WCA C/I (short for Weghted Code Assgnment C/I) scheduler, was ntroduced. The WCA C/I scheduler adopts a utlty-functonbased assgnment, wth the goal of ncreasng farness. In other words, the allocaton procedure consders a weghted combnaton of exponental functons related to possble objectves of the scheduler and tres to heurstcally ncrease t wth respect to the pure channel-state dependent case. In partcular, the allocaton crteron of the WCA C/I scheduler consders the followng functon as a sortng value to prortze the allocaton of a packet to the requestng users: β e + β e + β e CS CQ CD S Q D (12) where S s the normalzed SIR of user n the consdered HSDPA Transmsson Tme-Interval (TTI), Q s ts buffer occupancy and D s the normalzed head packet deadlne. The term C smply refers to the possblty of managng dfferent classes of traffc (we dd not nvestgate ths here, so C can be equal to 1 for all the users). Fnally, the weghts β k, wth k { Q, S, D} are tunable weghts whch can be adjusted to change the behavor of the scheduler (only ther relatve ratos are relevant). Note for example that lettng β s 0 and β Q = β D = 0 corresponds to adoptng a pure C/I scheduler. In the followng we set the weghts so that β S = β Q = β D, whch corresponds to a scheduler tryng to combne several objectves at the same tme and n a smlar manner. Wthn ths approach, users utlty can account for more parameters lke SIR, buffer state, deadlne of the packets, whch can be mxed n a more effcent manner than n the C/I case. Henceforth, the dependence on the utlty permts to obtan not only a better degree of farness, but also a generally better allocaton. An optmzaton of the schedulng weghts, whch would be surely possble, s beyond the goal of the present paper. Note, however, that the results shown n the followng hold n a qualtatvely smlar manner for other choces of β s, β Q, and β D. Wth the mcro-economc framework s possble to compare for example the pure C/I strategy and the WCA C/I one. The mert of the framework outlned n Secton 2 s n ths case to show that t s possble to compare the polces of schedulng

5 AN APPROACH TO WIRELESS SCHEDULING CONSIDERING REVENUE AND USERS SATISFACTION 61 algorthms n terms of economc metrcs. For example, t s mmedate to thnk that a better matchng of users utltes can also determne a hgher revenue. Table 1. Local search algorthm polcy can be seen also as a measure of the number of admtted users. Instead, the revenue n the lnear prcng case equals the unt prce tmes the throughput; thus, n ths case a weghted verson of the throughput s consdered. In general, t s at the same tme true that a real prcng polcy s lkely to be somethng hybrd between these two polces [15], but also the nterest for the provder n havng a satsfactory revenue s connected to havng both hgh throughput and a large fracton of satsfed users. For these reasons, we clam that ths choce of prcng polces s nterestng, as t allows to separate these two opposte goals, among whch a trade-off can be cut. In the next we wll consder the behavor of the C/I schedulng polces n the classc [1, 19] and modfed [3] verson aganst our proposal ntroduced to mprove the revenue. The polces wll be compared by means of smulaton n terms of generated revenue n order to hghlght the consequences on the provder sde. Table 2. Lst of Parameters of Smulaton Scenaro However, we can also thnk to address the problem of the users servce apprecaton and revenue generaton more drectly. Thus, we propose an orgnal contrbuton n whch the soluton presented n [3] s taken as an ntal condton, but the assgnment s modfed teratvely by means of a localsearch algorthm, obtanng a locally optmum soluton. A possblty s to use the algorthm reported n Table 1. Here, the schedulng process starts from a soluton obtaned wth a greedy heurstc and modfes ths assgnment by gvng more resources to the user wth the hghest margnal utlty, n order to mprove the total sector utlty. Resources are subtracted to users wth the lowest margnal utlty, to obtan a varaton of the total utlty as small as possble. The algorthm ends when the goal functon reaches a local maxmum. The revenue wll also depend on the prcng strategy. Thus, the choce of the functon p(r) should be ndcated to clarfy the above defnton of revenue, as gven n (8). In the lterature [16], dfferent prcng strateges have been proposed, and obvously the prcng strategy choce heavly affects the value of the total revenue. In ths work we wll consder two knds of prcng polces, manly for ther conceptual smplcty. The frst one s a flat prce strategy,.e., the prce s fxed for any value of the assgned rate. The second polcy represents a smple usage-based prcng wth lnear prce. Ths means that p(r)=kr s lnearly related to r through a gven constant k. It s nterestng to observe that n (8) there s expressed a double dependence of the revenue on the prcng, as also A s a functon of the prce. These two metrcs are also representatve of other values of nterest from the techncal pont of vew. Snce a flat prce polcy assgns the same prce to all users, the revenue s drectly proportonal to the number of users acceptng the servce. Hence, the revenue for the flat prce 4. RESULTS In ths Secton we wll present the results obtaned wth a HSDPA UMTS smulator developed at the Unversty of Ferrara. A cellular cluster s smulated wth a 3x3 hexagonal cell structure and wrapped onto tself n order to avod border effects. In rado channel propagaton, path loss, fast fadng and shadowng have been ncluded. To consder the envronment moblty, a non-zero Doppler frequency s assgned, even though statonary users are consdered. All these effects are ncluded n the Power Control module, so that the spreadng gan (whch determnes the rate) and the transmtted power are tuned to allocate a vector r whch s feasble wth the nterference constrants. Ths apples (11) to our case. Table 2 reports the parameters for the smulaton scenaro and the Acceptance-probablty model. In Fg. 1-6 we compare dfferent schedulng strateges, by evaluatng the earned revenue for the cases of flat and lnear prce. In partcular we compare the classc C/I C/I and WCA C/I respectvely. Also, we consder mproved versons for both strateges n whch the Local Search (LS) procedure ntroduced n the prevous Secton s mplemented. These strateges wll be referred to as LS wth C/I and LS wth WCA C/I respectvely. Note that the strategy LS wth C/I s not reported n all graphs, namely where t obtans smlar results to the basc C/I. Hence, sometmes we choose not to plot t to avod unnecessary confuson n the graphs.

6 62 AN APPROACH TO WIRELESS SCHEDULING CONSIDERING REVENUE AND USERS SATISFACTION From all the results reported, t s clear that the classc C/I schedulng obtans worse revenue performance wth respect to the weghted verson. Ths s reasonable, snce the C/I method has the problem of assgnng the resource to the best users, wthout consderng ther utlty. In fact, a gven user mght be already satsfed and not requre a larger assgnment, even though hs channel condtons are good and a C/I scheduler would assgn hm more resource. In other words, the C/I scheduler mght ntroduce over assgnments, whch are avoded wth the WCA verson. Note that we are ntroducng here two knds of contrbutons: frst of all, we evaluate the performance of the scheduler n terms of economc quanttes, whch reflect also effcency metrcs, as dscussed before. Moreover, we are able to go further by ntroducng the LS algorthm, where the mcroeconomc concepts of users satsfacton are employed also to drve the scheduler. Ths strategy s more revenue-aware, and therefore s able to mprove the performance, wth respect not only to the pure C/I scheduler, whch s clearly outperformed, but also to the weghted assgnment. amount of resource C, the revenue s dentcal (t s equal to the unt prce tmes C). Thus, to mprove the revenue n the lnear case, the scheduler must also ncrease the total throughput. Ths s more dffcult to do when the system s saturated,.e., the rate request s hgher than the resources avalable for allocaton, snce the total rate allocated s supposed to be hgh anyway. However, n WCDMA systems t becomes possble thanks to a better nterference management, snce the total allocated rate s not fxed, but depends on the nterference constrants, as dscussed n Secton 2. A Local Search amed at mprovng revenue s therefore able to ncrease the assgnment where t s more effcent,.e., for users whch cause less nterference to the system. Fgure 2. Provder revenue for flat prce, 180 users, as a functon of the prce Fgure 1. Provder revenue for flat prce, 120 users, as a functon of the prce There are two types of mprovement that the LS solutons present: the frst one s a general ncrease n the curves, whch means that the revenue that the provder can acheve s ncreased. Secondly, the LS curves present a wder range of prces for whch a gven reference revenue s overtaken, whch means an ncreased robustness. In fact, one mght expect that the prce can not always be set up optmally by the provder. Thus, the LS strategy s also able to ncrease even more sgnfcantly the revenues gven by suboptmal prces, whch mples a hgher robustness of the system performance. Fnally, an mportant comment whch dstngushes between the flat and lnear prcng s as follows: for the flat prcng a revenue mprovement means that the resource s better allocated snce satsfacton s acheved by a hgher number of users. For the lnear prcng, thngs are more complcated. If the number of users s suffcently large, a revenue ncrease can not be acheved only by ncreasng the number of satsfed users, snce f two assgnment vectors allocate the same global Fgure 3. Provder revenue for flat prce, 300 users, as a functon of the prce

7 AN APPROACH TO WIRELESS SCHEDULING CONSIDERING REVENUE AND USERS SATISFACTION 63 smple C/I strategy s not reported here (nether n the orgnal nor n the LS verson) due to the poor performance exhbted. The reasons for the falure of the standard C/I polcy when we adopt a lnear prcng are n the hgher neffcency of over provsonng. In ths case n fact, not only over assgnments are a waste, but they also decrease the users apprecaton of the servce, snce they mply a hgher cost. Another phenomenon that should be observed s that the gan of the LS strategy s slghtly lower than wth flat prcng (ts average s around 10%), even though t s not always decreasng wth the number of users. However, as prevously dscussed, ths s ndeed the result of a strong mprovement n the assgnment effcency, snce t corresponds to a throughput ncrease. Fgure 4. Provder revenue for lnear prce p(r)=kr, 120 users, as a functon of k We now dscuss the results n more detal. Fg. 1 to 3 refer to the case of flat prcng polcy. As dscussed before, here the revenue s drectly related to the number of admtted users, as the tarff pad by each user s the same, regardless of the qualty, as long as the servce s satsfactory. In ths case t can be shown that there s a margn for ncreasng the number of satsfed users wth respect to the C/I strateges. Ths happens because the LS allocaton scheme avods unnecessary over assgnments, whch waste resources wthout mprovng users satsfacton. For the flat prcng polcy, we plotted results also for the orgnal C/I strategy snce t s comparable wth WCA (even though the general performance s poorer). In Fg. 1 and 2 we consdered also the LS wth C/I, wthout weghted code assgnment. It s emphaszed here that the LS strategy, beng only drected toward a local optmum, heavly reles on the frst soluton. However, there s anyway a sgnfcant gan n usng the Local Search: the revenue ncrease acheved by the mproved allocaton scheme s between 15 and 20 percent for the cases wth low load ( users). For hgher loads, ths gan decreases f we consder the peaks of the curves only. Two remarks should be made, though. Frst of all, the gan n applyng the LS to heavly loaded networks s lower snce the larger the number of users, the hgher the revenues n general, snce t s lkely that the capacty s fully allocated even by an neffcent scheme. On the other hand, even though the peaks of the curves are approxmately the same, whch means that the maxmum achevable revenue s only slghtly ncreased by the LS strategy, as remarked before the prce setup s more robust because of the general ncrease by the whole curve. In partcular, the range of prces achevng a generally hgh revenue s wder. Smlar conclusons can be drawn also for the case of lnear prcng polcy, analyzed n Fg.s 4-6. For ths prcng strategy, the revenue can be equvalently seen as a measure of the total assgned throughput,.e., how much the provder succeeds n assgnng as much resource as possble to the users. We have a gan of the same order of magntude as n the prevous case, and ths shows that even wth a completely dfferent prcng strategy our proposal s stll able to sgnfcantly mprove the assgnment. However, note the followng: frst of all, the Fgure 5. Provder revenue for lnear prce p(r)=kr, 180 users, as a functon of k Fgure 6. Provder revenue for lnear prce p(r)=kr, 300 users, as a functon of k To sum up, for all the cases reported n Fg. 1-6 the Local Search strategy outperforms sgnfcantly the C/I (or WCA C/I) algorthm taken as the ntal soluton. The prce for such mprovements s n the ncreased computatonal complexty

8 64 AN APPROACH TO WIRELESS SCHEDULING CONSIDERING REVENUE AND USERS SATISFACTION requred by the LS procedure. Fortunately, for the examned cases ths s not very hgh, snce the number of teratons s usually low (10 teratons at most, but usually 4-5); thus, n ths case a smple varaton from the ntal soluton allows to greatly mprove the earned revenue. Ths remark can be extended to make the scheme even more tunable, snce further research can be done n the drecton of applyng dfferent local search heurstcs so to explore the solutons space n more depth. Fgure 9. Prce maxmzng revenue for flat prce, as a functon of the load Fgure 7. Normalzed provder revenue for flat prce equal to 0.8, as a functon of the load We also reported a lnear nterpolaton of the collected prces. These results can serve as a practcal gudelne n prce settng. In partcular, the most nterestng concluson whch can be drawn from these results s that flat prcng s very senstve to the number of users (and hence the optmal prce settng s more crtcal), whereas lnear prcng s almost nsenstve on the number of users, whch confrms the prevous dscusson about ts sutablty for the purpose of tarff collecton. Fgure 10. Prce maxmzng revenue for lnear prce, as a functon of the load Fgure 8. Normalzed provder revenue for flat prce equal to 0.8, as a functon of the load To better study the dependence on the network load (.e., the number of users), and to gan nsght on the prce settng ssue, we mght consder the collecton of the revenues acheved by the same scheduler for dfferent load condtons for a gven prcng polcy setup. For example, n Fg. 7-8 ths s reported for flat (wth prce p(r) = 0.8) and lnear (p(r) = 0.3r) prcng, respectvely. Other choces of flat or lnear prces, respectvely, exhbt completely smlar results, so that these choce are more or less representatve of the entre class. From these Fgures, one can see that the gan n usng the LS strategy s present for dfferent load condtons. However, ths holds f the prce s kept constant and not adaptvely set. Hence, t could be also nterestng to collect all the prce values maxmzng the provder revenue, to understand how the prce settng s senstve to the load. The result of ths operaton s represented n Fg. 9 and 10, for flat and lnear prcng, respectvely. Nose s present n these Fgures, because the

9 AN APPROACH TO WIRELESS SCHEDULING CONSIDERING REVENUE AND USERS SATISFACTION 65 granularty of the results s not always accurate, snce only certan prce values are smulated. Fnally, we remark that we also tested rather dfferent choces for the local search polcy, and the results obtaned are more or less equvalent to those shown n ths secton. In general, t s emphaszed that the real gan comes from the schedulng strategy beng drven by a utlty- and prce-aware model, whch makes t capable of better allocatng the constraned resource. 5. CONCLUSIONS We analyzed the schedulng from the provder s pont-of-vew, by ncludng also revenue maxmzaton among the goal of the scheduler. Ths s made possble by the ntroducton of the Acceptance-probablty model, whch accounts for the jont effect of user utlty and prce, and ncludes economc consderatons nto the analyss. The results show nterestng possbltes of mprovng the network management. In partcular, the applcaton of a classcal effcent strategy, lke the C/I scheduler, by neglectng the economc counterpart of the allocaton, can lead to unsatsfactory results for the operator, snce the maxmzed throughput provded by the C/I strategy mght not be what users want. On the other hand, a smple strategy that locally searches for hgher values of the revenue s able to greatly mprove the proft and the economc effcency of the resource management, by keepng the users satsfacton level almost constant, f not ncreased. Thus, the usefulness of the economc consderatons s hghlghted. Several further observatons can be made on the strategy used for optmzaton. The heurstc strateges dscussed here offer the advantages of smplcty and fast evaluaton; however, more detaled procedures can mprove even further the performance and/or the convergence rate. It could be also possble to develop, wthn the gven framework, a theoretcal analyss of the schedulng, n whch the optmzaton problem (10) (11) for revenue maxmzaton s explored analytcally. Ths study, that can allow better understandng of the RRM ssues, s left for future research. REFERENCES [1] C. Fragoul, V. Svaraman, & M. Srvastava, Controllng multmeda wreless lnk va enhanced class-based queueng wth channel state dependent packet schedulng, Proc. INFOCOM, San Francsco, CA, USA, 1998, Vol. 2, pp [2] X. Lu, E. K.-P. Chong, & N. B. Shroff, Transmsson Schedulng for Effcent Wreless Utlzaton, Proc. INFOCOM, Anchorage, AK, USA, 2001, Vol. 2, pp [3] M. Boaretto, D. Angeln, & M. Zorz, Fast schedulng polces usng WCDMA hgh-speed downlnk packet access, Proc. VTC Fall, 2003, Vol. 4, pp [4] V. Srs, Resource control for elastc traffc n CDMA networks, n Proc. ACM MobCom, Atlanta, GA, 2002, pp [5] M. Xao, N.B. Shroff, & E.K.-P. Chong, A Utlty-based Power-control scheme n Wreless Cellular Systems, IEEE/ACM Transactons on Networkng, Vol. 11, No. 2, 2003, pp [6] A. Demers, S. Keshav, & S. Shenker, Analyss and smulaton of a far queung algorthm, Proc. ACM SIGCOMM, Vancouver, BC, Canada, 1998, pp [7] J.C.R. Benner & H. Zhang, WF2Q: worst case far weghted far queung, Proc. INFOCOM, San Francsco, CA, USA, 1996, pp [8] F.P. Kelly, A. Maulloo, & D. Tan, Rate control n communcaton networks: shadow prces, proportonal farness and stablty, Journal of the Operatonal Research Socety, Vol. 49, 1998, pp [9] L. Bada, M. Lndstr, J. Zander, & M. Zorz, An Economc Model for the Rado Resource Management n Multmeda Wreless Systems, Elsever s Computer Communcatons, Vol. 27, 2004, pp [10] H. R. Varan, Intermedate Mcroeconomcs: A Modern Approach. Norton, New York, [11] G. Banch, A. T. Campbell, & R. R.-F. Lao, On utlty-far adaptve servces n wreless networks, Proceedngs of IWQoS, Napa, CA, USA, 1998, pp [12] D. Famolar, N. Mandayam, D. Goodman, & V. Shah, A New Framework for Power Control n Wreless Data Networks: Games, Utlty and Prcng, n R. Ganesh, K. Pahlavan, & Z. Zvonar, Wreless Multmeda Network Technologes, Kluwer Academc Publshers, 1999, chapter 1, pp [13] L. Bada & M. Zorz, On Utlty-based Rado Resource Management wth and wthout Servce Guarantees, Proc. ACM/IEEE MSWM 04, Vence, Italy, 2004, pp [14] F. Berggren, S.-L. Km, R. Jäntt & J. Zander, Jont power control and ntra-cell schedulng of DS-CDMA non-real tme data, IEEE JSAC, Vol. 19, No. 10, 2001, pp [15] H. Jang & S. Jordan, A Prcng Model for Hgh Speed Networks wth guaranteed qualty of servce, Proc. INFOCOM, San Francsco, CA, USA, 1996, Vol. 2, pp [16] C. Courcoubets, F.P. Kelly, V.A. Srs, & R. Weber, A study of smple usage-based chargng schemes for broadband networks, Telecommuncatons Systems, Vol. 15, 2000, pp [17] 3rd Generaton Partnershp Project, TR V 4.0.0, UTRA Hgh Speed Downlnk Packet Access, [18] H-Y. We & R. Izmalov, Channel-aware soft bandwdth guarantee schedulng for wreless packet access, IEEE WCNC, Atlanta, GA, USA, 2004, Vol. 2, pp [19] T.J. Moulsley, Throughput of HSDPA for UMTS, Proc. 2nd Int. Conference on 3G Moble Communcaton Technologes, London, UK, 2001, pp

10 66 AN APPROACH TO WIRELESS SCHEDULING CONSIDERING REVENUE AND USERS SATISFACTION Bographes Leonardo Bada was born n Ferrara, Italy, n He receved the Laurea Degree (MS) n Electrcal Engneerng and the Ph.D. n Informaton Engneerng from the Unversty of Ferrara, Italy, n 2000 and 2004, respectvely. In 2001 he joned the Department of Engneerng of the Unversty of Ferrara, where he s a currently a Post-Doc Researcher. Durng 2002 and 2003 he was on leave at the Royal Insttute of Technology of Stockholm, Sweden. Hs research nterests nclude energy effcent Ad Hoc Networks, transmsson protocol modellng, Admsson Control and economc modellng of Rado Resource Management for Wreless Networks.receved hs Ph.D. degree n 1989 from Oregon State Unversty, USA. Currently he s a faculty member wth the department of Informaton and Computer Scence at KFUPM, Dhahran, SA. He has vared research nterests and publcatons n the felds of dstrbuted computng and web publshng. Mchele Zorz was born n Vence, Italy, n He receved the Laurea Degree and the Ph.D. n Electrcal Engneerng from the Unversty of Padova, Italy, n 1990 and 1994, respectvely. Durng the Academc Year 1992/93, he was on leave at the Unversty of Calforna, San Dego (UCSD), attendng graduate courses and dong research on multple access n moble rado networks. In 1993, he joned the faculty of the Dpartmento d Elettronca e Informazone, Poltecnco d Mlano, Italy. After spendng three years wth the Center for Wreless Communcatons at UCSD, n 1998 he joned the School of Engneerng of the Unverstà d Ferrara, Italy, where he became a Professor n Snce November 2003, he has been on the faculty at the Informaton Engneerng Department of the Unversty of Padova. Hs present research nterests nclude performance evaluaton n moble communcatons systems, random access n moble rado networks, ad hoc and sensor networks, and energy constraned communcatons protocols. Dr. Zorz currently serves on the Edtoral Boards of the IEEE Transactons on Communcatons, the IEEE Transactons on Wreless Communcatons, the IEEE Transactons on Moble Computng, the Wley Journal of Wreless Communcatons and Moble Computng and the ACM/URSI/Kluwer Journal of Wreless Networks. He was also the Edtor-In-Chef of the IEEE Wreless Communcatons Magazne and guest edtor for specal ssues n the IEEE Personal Communcatons Magazne, Energy Management n Personal Communcatons Systems and the IEEE Journal on Selected Areas n Communcatons (Mult-meda Network Rados).