Resource Control for Elastic Traffic in CDMA Networks

Transcription

1 Resource Control for Elastc Traffc n CDMA Networks Vaslos A. Srs Insttute of Computer Scence (ICS) Foundaton for Research and Technology - Hellas (FORTH) P.O. Box 1385, GR 711 1, Heraklon, Crete, Greece [email protected] ABSTRACT We present a framework for resource control n CDMA networks carryng elastc traffc, consderng both the uplnk and the downlnk drecton. The framework s based on mcroeconomcs and congeston prcng, and seeks to explot the jont control of the transmsson rate and the sgnal qualty n order to acheve effcent utlzaton of network resources, n a dstrbuted and decentralzed manner. An mportant feature of the framework s that t ncorporates both the congeston for shared resources n wreless and wred networks, and the cost of battery power at moble hosts. We prove that for elastc traffc, where users value only ther average throughput, the user s net utlty maxmzaton problem can be decomposed nto two smpler problems: one nvolvng the selecton of the optmal sgnal qualty, and one nvolvng the selecton of the optmal transmsson rate. Based on ths result, the selecton of sgnal qualty can be performed as done today usng outer loop power control, whle rate adaptaton can be ntegrated wth rate adaptaton at the transport layer. Categores and Subject Descrptors C.2.1 [Computer-Communcaton Networks]: Network Archtecture and Desgn wreless communcaton, network communcatons General Terms Algorthms, Desgn, Theory Keywords Congeston prcng, rado resource management, rate control, utlty functons, wreless/wred ntegraton Ths work was conducted whle the author was on a research fellowshp at BT (Brtsh Telecommuncatons) Research, Adastral Park, Ipswch, UK. Contnuaton of the work s funded by BT. Permsson to make dgtal or hard copes of all or part of ths work for personal or classroom use s granted wthout fee provded that copes are not made or dstrbuted for proft or commercal advantage and that copes bear ths notce and the full ctaton on the frst page. To copy otherwse, to republsh, to post on servers or to redstrbute to lsts, requres pror specfc permsson and/or a fee. MOBICOM 2, September 23 26, 22, Atlanta, Georga, USA. Copyrght 22 ACM X/2/9...$ INTRODUCTION Procedures for effcent control and management of wreless network resources are becomng ncreasngly mportant. Ths s due to two factors: Frst, compared to fxed networks, there s a lmted ablty for ncreasng the capacty of moble wreless networks. Second, emergng multmeda servces and applcatons wll ncrease the demand for bandwdth n wreless networks. Congeston prcng has been dentfed as a flexble framework for effcent and robust resource control n wred networks; e.g., see [8, 9, 2]. In ths paper we nvestgate the applcaton of mcroeconomc modellng and congeston prcng n Code Dvson Multple Access (CDMA) wreless networks. Although our approach s generally applcable to CDMA-based systems, ncludng systems utlzng a combnaton of code and tme-dvson schedulng, we focus our dscusson on Wdeband CDMA. WCDMA has emerged as the most wdely adopted thrd generaton (3G) ar nterface technology [6]. WCDMA s based on Drect Sequence CDMA (DS-CDMA), a spread spectrum technology where data bts are spread over the entre spectrum used for transmsson, and unque dgtal codes are used to separate the sgnals from dfferent mobles; such an approach enables smpler statstcal multplexng, wthout the need for complex tme or frequency schedulng. WCDMA supports varable bt rate transmsson wth the use of varable spreadng factors and multple codes; the former determnes how much a data bt s spread n tme. Fnally, all the cells n a WCDMA network use the same frequency spectrum; ths feature s behnd the soft-capacty property of WCDMA networks, whch results n the graceful degradaton of performance as the load ncreases. The goal of ths paper s to present and nvestgate a new framework for resource control n CDMA networks, based on mcroeconomcs and congeston prcng. The framework bulds on results for resource usage, n both the uplnk and the downlnk, and seeks to explot the jont control of the transmsson rate and sgnal qualty, the latter gven by the bt-energy-to-nose-densty rato, n order to acheve economcally effcent utlzaton of network resources, n a dstrbuted and decentralzed manner. An mportant feature of the framework s that t ncorporates the congeston for shared resources n both wreless and wred networks, as well as the cost of battery power at the moble hosts; hence, the framework can be the bass for the ntegraton of resource control mechansms n wreless and wred networks. We prove that for elastc traffc, where users value only ther average throughput, the user s net utlty maxmzaton problem can be decomposed nto two smpler problems:

2 one nvolvng the selecton of the optmal sgnal qualty, and one nvolvng the selecton of the optmal transmsson rate. Based on ths result, the selecton of sgnal qualty can be performed as done today usng outer loop power control, whle rate adaptaton can be ntegrated wth rate adaptaton at the transport layer. Our work dffers from other works, whch we brefly dscuss n Secton 6, n one or more of the followng ponts: Frst, our framework ncorporates the congeston for both wreless and wred resources, n addton to the cost of battery power at moble hosts. Second, our work consders the partcular resource constrants n the uplnk and downlnk drecton, dentfyng the dfferences n the resultng models. Thrd, n the uplnk our approach does not dfferentate moble users based on ther locaton. Fnally, our work consders the jont optmzaton of the transmsson rate and the sgnal qualty, n order to acheve effcent resource utlzaton. The paper s organzed as follows. In Secton 2 we summarze results concernng resource usage n CDMA networks. In Secton 3 we present a framework, based on mcroeconomcs and congeston prcng, for resource control n CDMA networks carryng elastc traffc. We begn wth a smple model for the uplnk and the downlnk, whch we then extend. In Secton 4 we dscuss the applcaton of the above framework, dentfyng a number of practcal ssues. In Secton 5 we present and dscuss numercal nvestgatons hghlghtng features of the proposed approach, ncludng the dfference of resource control n the uplnk and n the downlnk. In Secton 6 we present a bref overvew of related work, and n Secton 7 we conclude the paper, dentfyng a number of related research ssues we are currently nvestgatng. 2. RESOURCE USAGE IN CDMA Consder a sngle CDMA cell. Let W be the chp rate, whch s fxed and equal to 3.84 Mcps for WCDMA. The btenergy-to-nose-densty rato, E b /N, at a recever (ether moble host or base staton) s gven by [3, 22] ) ( Eb N = W r g p I + η, (1) where r s the transmsson rate, p s the transmsson power, g s the path gan between the base staton and moble, I s the power of the nterference, and η s the power of the background nose. The rato W/r s the spreadng factor or processng gan for moble. Due to the errors n the wreless network, the actual throughput (rate of successful data delvery) wll be smaller than r. The value of the bt-energy-to-nose-densty rato (E b /N ) corresponds to the sgnal qualty, snce t determnes the bt error rate, BER [3, 22]. Under the realstc assumpton of addtve whte Gaussan nose, BER s a non-decreasng functon of E b /N, whch depends on the multpath characterstcs, and the modulaton and forward error correcton (FEC) algorthms. Let γ be the target bt-energy-to-nosedensty rato requred to acheve a partcular BER, or equvalently a partcular frame error rate. Ths target s gven to fast closed-loop power control, whch adjusts the transmsson power n order to acheve t. If we assume perfect power control, then (E b /N ) = γ. When a sender does not send data contnuously, the average E b /N requrements wll be met, f the rght hand-sde of (1) s multpled by the percentage of tme the sender s on, actually transmttng data; ths percentage, called actvty factor, s.67 for voce. 2.1 Resource Usage n the Uplnk In the uplnk, the nterference I for moble s the sum of the power of the sgnals receved by the base staton from all other moble hosts,.e., I = j gjpj. Moreover, we can assume that the background nose at the base staton s the same for all mobles,.e., η = η. If γ s the target bt-energy-to-nose-densty rato, then under perfect power control (E b /N ) = γ, and (1) becomes γ = W r j g p gjpj + η. (2) Solvng the set of equatons gven by (2) for each moble, we get [22, 16] g p = where the load factor α UL α UL = ηα UL 1, (3) j αul j s gven by ( 1 ). (4) W r γ + 1 Note that the power levels gven by the set of equatons (3) for I, where I s the set of mobles, are the mnmum such that the target bt-energy-to-nose-densty ratos {γ } are met. Snce the power p can take only postve values, from (3) we get α UL < 1. (5) The last equaton llustrates that the uplnk s nterferencelmted: Even when they have no power constrants, moble hosts cannot ncrease ther power wthout bound, due to the ncreased nterference they would cause to the other mobles. If (5) s volated, then the target {γ } cannot be met for all mobles. Equaton (5) suggests that α UL s a measure of the resource usage, or the effectve usage, of a moble host n the uplnk drecton. From Equaton (4), we conclude that resource usage n the uplnk of CDMA networks s an ncreasng functon of the product of two parameters, whch can be controlled ndependently: the transmsson rate r and the sgnal qualty, expressed n terms of the target btenergy-to-nose-densty rato γ. If each moble uses a small porton of the wreless resource, whch s the case when there s a large number of moble W r γ users, then we have 1, hence α UL r γ and the W resource constrant gven by Equaton (5) can be approxmated by r γ < W. (6) The above results assumed that there are no constrants on a moble s maxmum transmsson power. They can be extended to nclude such constrants [16]. Moreover, the nterference from neghborng cells can be taken nto account by consderng the ntercell nterference coeffcent, whch gves the rato of the nterference from neghborng cells over the ntracell nterference [3].

3 2.2 Resource Usage n the Downlnk In the downlnk, the nterference for moble s I = θ g j pj, where θ represents the orthogonalty of the codes used n the downlnk. If γ s the target sgnal qualty for moble, and assumng as above that we have perfect power control, then (1) becomes γ = W r g p θ g j pj + η. (7) The orthogonalty factor θ depends on multpath effects, hence can be dfferent for dfferent moble hosts. Typcal values fall n the range [.1,.6], see [6, p. 163]. In the downlnk, unlke the uplnk, there s a lmt on the total transmsson power 1, say p, hence the downlnk s power-lmted. The correspondng resource constrant s p p. (8) The last equaton suggests that the transmsson power from the base staton characterzes resource usage n the downlnk drecton. 3. RESOURCE CONTROL BASED ON CON- GESTION PRICING In ths secton we frst propose a utlty functon that s approprate for elastc traffc n wreless networks; utlty functons are wdely used for capturng user and applcaton requrements, and gve the level of satsfacton for a gven level of servce. Then, based on the results for resource usage of the prevous secton, we present and nvestgate congeston prcng models for the uplnk and the downlnk n CDMA networks. We consder the case of elastc (best-effort) traffc, where users value only the average throughput of successful data transmsson. Ths throughput s the product of the transmsson rate and the probablty of successful packet transmsson. The latter s a functon of the bt error rate BER, whch as dscussed n Secton 2 s a functon of the target bt-energy-to-nose-densty rato γ. Hence, the probablty of successful packet transmsson can be wrtten as P s(γ), n whch case the average throughput s rp s(γ) [13, 4]. Thus, the utlty for elastc traffc where users value only ther average throughput has the form U (rp s(γ)). If the moble user does not have mnmum rate requrements, then hs utlty s typcally concave. On the other hand, f the user has mnmum rate requrements, equvalently maxmum delay requrements, then hs utlty has a sgmod shape. Let c(r, γ, p ) be the charge ncurred by user wth rate r, target bt-energy-to-nose-densty rato γ, and transmsson power p. The user s net utlty maxmzaton problem has the followng general form (for smplcty, we assume that all users have the same packet success probablty): maxmze U (r P s(γ )) c(r, γ, p ) (9) over r, γ, 1 p refers to the total power the base staton can transmt mnus the power used for the downlnk control channels. where the varables r, γ, p are related through Equaton (2) or (7), for the uplnk or the downlnk drecton respectvely. The charge c(r, γ, p ) can nclude both the congeston charge for shared resources n the wreless network and, as we dscuss n Secton 3.2, the congeston charge for resources n the wred network and the cost of battery power at the moble host. Specfc formulatons for the uplnk and downlnk, based on the results of the prevous secton regardng resource usage n each drecton, wll be dscussed n the followng subsectons. The optmzaton n (9) nvolves two parameters: the transmsson rate r and the target bt-energy-to-nose-densty rato γ. An mportant result that we prove n Secton 3.1 for the uplnk, but whch also holds for more general forms of the charge functon c( ), s that the user s net utlty maxmzaton problem can be decomposed nto two subproblems: one nvolvng the selecton of the optmal γ, whch depends only on the packet success probablty P s(γ), and one nvolvng the selecton of the optmal rate r, whch depends on the user s utlty and charge. 3.1 Congeston Prcng for the Uplnk In ths secton we consder the uplnk, and frst assume there s a large number of mobles, each usng a small porton of the wreless resource. Note, however, that the results for ths smple case also hold for the more general case. The wreless resource constrant s gven by (6) r γ < W. To provde the rght ncentves for effcent use of network resources, user s charge should be proporton to hs resource usage, whch s gven by r γ. Hence, n the uplnk the user optmzaton problem (9) becomes maxmze U (r P s(γ )) λr γ (1) over r, γ, where λ s the shadow prce for resource r γ. In the above model, prces are ndependent of the moble s poston. Ths s because the uplnk s nterference-lmted, and nterference depends on the receved power at the base staton. In ths respect our approach dffers from the work of [4, 17, 21], where charges depend on the transmtted power; such a dependence results n moble users that are far from the base staton to ncur a hgher charge, for the same rate and sgnal qualty, compared to users close to the base staton. On the other hand, as we dscuss n Secton 3.3, n the downlnk a moble s poston nfluences the charge, snce resource usage n ths case s determned by the transmtted power from the base staton Propertes of the optmal soluton An mportant property whch greatly smplfes the applcaton of (1) s that the optmal γ of the target bt-energyto-nose-densty rato s ndependent of both the prce λ and the user s utlty. Ths allows the decouplng of the two problems of selectng the optmal γ and the optmal transmsson rate r. Ths property s stated and proved n the followng proposton. 2 2 We nclude only the proof for the frst Proposton. The other proofs can be found n [18].

4 Proposton 1. Let U (x ) and P s(γ ) be contnuously dfferentable functons of the throughput x = r P s(γ ) and the target bt-energy-to-nose-densty rato γ, respectvely. Also assume that U (x ) > for all x. If there exsts r > and γ > that acheve the maxmum of (1), then γ s ndependent of the prce λ and the utlty, and satsfes P s(γ ) = P s(γ )γ. (11) Proof. At the optmal, the partal dervatves of (1) wth respect to r and γ are zero, hence and ϑu (r P s(γ )) ϑr = λγ U (x ) ϑ(rps(γ )) ϑr = λγ U (x )P s(γ ) = λγ (12) ϑu (r P s(γ )) ϑγ = λr U (x ) ϑ(r P s(γ )) = λr r > ϑγ From (12) and (13) we get (11). U (x )P s(γ ) = λ (13) Proposton 1 can be proved for the more general case where the charge has the form c(rγ) or c(rp s(γ)). Interestngly, the extensons to the basc model gven by (1) that we dscuss n Secton 3.2, and the net utlty maxmzaton problem for the downlnk that we dscuss n Secton 3.3, are of ths form. An nterestng observaton s that the optmal γ, n the case γ >, that satsfes (11) also maxmzes the number of bts successfully receved per unt of energy [4]: r P s(γ ) max, γ > p snce substtutng (2) n the last equaton gves max γ > W P s(γ ), I + η γ whch s maxmzed for γ satsfyng (11). Ths last observaton ndcates that the optmal γ that maxmzes the net utlty n (1), also maxmzes the number of bts successfully receved per unt of energy. Moreover, under the assumptons of Proposton 1, ths result s ndependent of the user s utlty and the congeston prce, and can be acheved n a decentralzed manner va prcng. Fnally, we note that (11) also holds when the objectve s to maxmze the total throughput [13]. The next proposton s related to the exstence of a γ >. For smplcty we drop the subscrpt, snce the optmal target bt-energy-to-nose-densty rato wll be the same for mobles wth the same dependence of the packet success probablty on γ. Proposton 2. Assume that P s(γ) s contnuously dfferentable, and s strctly convex for γ < γ and strctly concave for γ > γ 1. Also assume that P s() =. Then there exsts γ > that satsfes (11). Moreover, f γ = γ 1, then γ s unque. In practse, we can have P s() >,.e., the packet success probablty does not tend to zero as γ tends to zero; γ =, hence p =, corresponds to the case where the recever s guessng what the bts transmtted by the sender are [4]. However, as we see next, P s() wll typcally be very small, and γ satsfyng (11) wll exst. In the case of addtve whte Gaussan nose and a nonfadng channel, the bt error rate for DPSK (Dfferental Phase Shft Keyng) modulaton s [15] BER(γ) =.5e γ. From the last equaton, observe that BER() >. If there s no error correcton, and bt errors are ndependent and are all detected, then the packet success probablty P s(γ) s gven by P s(γ) = (1 BER(γ)) L, (14) where L s the number of bts n one packet. For L = 6 bts, the last equaton gves P s() = When up to k bt errors are correctable, the packet success probablty can be approxmated by P s(γ) = ( ) k L BER(γ) j (1 BER(γ)) L j. (15) j j= Fgure 1(a) shows the packet success probablty wth no error correcton, whch s computed from Equaton (14). Observe that P s(γ) has a sgmod shape, and a unque γ satsfyng (11) exsts. Indeed, γ corresponds to the tangent of the lne passng through the orgn wth the curve P s(γ). Fgure 1(b) shows that n the presence of forward error correcton (FEC), n whch case the packet success probablty s computed from Equaton (15), a unque γ agan exsts; moreover, γ n the presence of FEC s smaller than when there s no FEC; γ s also smaller n the case of BPSK and QPSK modulaton, n whch case the bt error rate s [15] BER(γ) =.5erfc( γ), where erfc s the complementary error functon. The optmalty of γ s stated n the followng two propostons. The proof for the latter uses Propostons 1, 3, and Theorem 1 n [8]. Proposton 3. Let γ be the unque value satsfyng (11), and assume P s (γ ) <. If the utlty U (x ) n (1) s dfferentable and strctly concave and U (x ) >, x >, where x = r P s(γ ), then there exsts a r, that along wth γ acheves the maxmum n (1). Proposton 4. Under the condtons stated n Propostons 1 and 3, and f U (x ) s ncreasng and strctly concave n x = r P s(γ ), then there exsts a prce λ such that the allocatons {(r, γ )} formed from the unque solutons (r, γ ) to (1) maxmze the network revenue maxmze λr γ over r, γ subject to r γ < W,

5 Sfrag replacements Sfrag replacements Ps(γ) Ps(γ) DPSK, no FEC γ (a) DPSK modulaton DPSK, no FEC DPSK, FEC k=3 BPSK,QPSK γ (b) DPSK wth FEC and BPSK/QPSK Fgure 1: Packet success rate for DPSK modulaton wth 6 bts long packets, wth and wthout error correcton, and for BPSK/QPSK modulaton. The optmal γ ( 5) satsfes (11), and s the value of γ at whch the lne passng through the orgn s tangent to P s(γ). and the socal welfare maxmze U (r P s(γ )) over r, γ subject to r γ < W. Due to Propostons 1 and 3, the user optmzaton problem n (1) can be reduced to maxmze U (r P s(γ )) λr γ (16) over r, wth γ satsfyng (11). In the case of a strctly concave utlty, the optmal r s gven by ( ) r 1 = P s(γ ) U 1 λγ. (17) P s(γ ) Assume now that the utlty s not a strctly concave functon of the rate, but has a sgmod shape and s bounded by the lne ξr, whch s tangent to the utlty U (r P s(γ )) at rate r, after whch the utlty s strctly concave. In ths case, the optmal rate r s gven by (17) f and only f r r. If ths nequalty does not hold, then the optmal rate s zero. In ths case, γ can take any value, snce both the utlty and the charge s zero (Equaton (11) need not hold n ths case). 3.2 Extensons In ths secton we consder extensons to the basc model correspondng to (1). For all extensons, Propostons 1-3 hold, hence the correspondng user optmzaton problems can be reduced to a form smlar to (16) and (11) Small number of moble hosts If the number of moble hosts s not large, then the resource constrant s gven by (5) rather than ts approxmaton (6), and the user optmzaton problem becomes wth α UL gven by (4). maxmze U (r P s(γ )) λα UL over r, γ, Includng the cost of battery power The cost of battery power can be ncluded by addng an approprate term to (1). For example, f the battery cost s lnear to the power, we have maxmze U (r P s(γ )) λr γ ν p over r, γ, where p s the transmtted power and ν s the cost per unt of battery power, whch can be dfferent for dfferent users Integraton wth transport layer congeston control The congeston cost assocated wth the fxed network can be taken nto account by modfyng (1) to maxmze U (r P s(γ )) λr γ µr P s(γ ) (18) over r, γ, where µ s the congeston prce for resources n the fxed network. Observe that the congeston charge for the fxed network s proportonal to the rate of successful data transfer over the wreless network,.e., r P s(γ ). Equaton (18) can be the bass for ntegrated rate control over wreless and wred resources. We wll dscuss n Secton 4.1 one possble approach for usng the same sgnallng mechansm for conveyng congeston nformaton n both networks Bound on the total nterference produced by elastc traffc The network mght wsh to lmt the total nterference that elastc traffc causes to other types of traffc, such as realtme traffc, to be p max. In ths case, the target functon n the user problem (1) remans the same, but the constrant (6) changes to g jp j p max. j 3.3 Congeston Prcng for the Downlnk The capacty constrant n the downlnk s n terms of the maxmum power p that the base staton can transmt (8): p p.

6 Hence, t s approprate for the network to charge user n proporton to hs power p. In ths case, the user optmzaton problem becomes maxmze U (r (P s(γ ))) λp (19) over r, γ, where λ s the prce per unt of power, andpsfrag the varables replacements r, γ, and p are related through (7). Propostons 1-3 also hold for the downlnk. On the w other hand, note that Proposton 4 does not hold. Due to r = 1 w γ Propostons 1 and 3 the user optmzaton problem n (19), W j w j combned wth (7), can be reduced to maxmze U (r P s(γ )) λ rγ (I + η ) W g (2) over r, wth γ satsfyng (11), and I = θ g j pj. In the case of a strctly concave utlty, the optmal r s gven by ( ) r 1 = P s(γ ) U 1 λγ (I + η ). (21) W g P s(γ ) In the above model, unlke the case for the uplnk, moble users that are far from the base staton ncur a hgher charge, for the same rate and target bt-energy-to-nose-densty rato. As a result, for the same utlty, users far from the base staton wll send at a lower transmsson rate, compared to users close to the base staton; related nvestgatons are presented n Secton 5. In the downlnk, the dependence of charges on a moble s dstance results n more effcent utlzaton of the base staton s power, snce t leads to hgher aggregate utlty. 4. APPLICATION OF THE FRAMEWORK In ths secton we dscuss the applcaton of the framework presented n the prevous secton, hghlghtng some mportant practcal consderatons. In partcular, we dscuss two alternatves for applyng the proposed framework: The frst nvolves drect communcaton of prces from the base staton/rado network controller (BS/RNC) to the moble hosts (MHs), whch respond by selectng the transmsson rate that maxmzes ther net utlty. The second nvolves communcaton of wllngness-to-pay or weght values from the moble users to the RNC, whch allocates rates accordng to these values. The above two alternatves are smlar to the two decompostons of the model for rate control of elastc traffc n fxed networks that s nvestgated n [8]. 4.1 Procedure wth explct communcaton of prces Uplnk We frst descrbe the procedure for applyng the congeston prcng model for the uplnk, presented n Secton 3.1, when there s drect communcaton of prces from the base staton/rado network controller (BS/RNC) to the moble hosts (MHs), Fgure 2(a). The procedure nvolves the followng steps: 1. For each MH, the RNC selects the optmal γ based on (11). 2. The RNC announces the prce per unt of wreless resource λ. r BS RNC PSfrag replacements feedback (charge) (a) drect prce feedback r w r = 1 γ BS RNC w j w j W (b) wllngness-to-pay Fgure 2: Wth drect prce communcaton (left fgure), a moble responds to prce feedback by adjustng ts transmsson rate. On the other hand, wth the wllngness-to-pay approach (rght fgure), the wllngness-to-pay can be adjusted over longer tmescales. The frst approach results n more effcent behavor, but requres more complex functonalty n the moble compared to the second approach. 3. Each MH selects ts rate r based on (16). 4. The RNC charges MH by λr γ. 5. The RNC adjusts prce λ based on the load, and goes to Step 2. In WCDMA, the procedure for selectng γ (target E b /N ) s performed at the RNC, durng outer loop power control: The BS measures the bt error rate BER (or the frame error rate FER), and sends the measurement to the RNC, whch adjusts γ to acheve a partcular BER; γ s then used as the target for fast closed-loop power control, whch operates between the base staton and the mobles. Hence, t s approprate to perform the selecton of the optmal γ n Step 1 at the RNC, effectvely replacng the normal outer loop power control procedure. Moreover, γ wll change whenever the dependence of the packet success probablty on γ changes, e.g., when the multpath characterstcs change. Assumng all mobles have the same packet success rate, they wll have the same optmal γ that satsfes (11). Gven the sgmod shape 3 of P s(γ) n Fgure 1, γ can be found by gradually ncreasng γ whle the dervatve P s(γ) s larger than P s(γ)/γ, and decreasng t when the dervatve s smaller. The above procedure s smlar to the typcal procedure used for outer loop power control today [6, p ], hence the latter would requre small modfcatons n order to select the target bt-energy-to-nose-densty rato based on (11). On the other hand, f the packet success rate s dfferent for dfferent mobles, then the optmal γ would be dfferent for dfferent mobles; note that n all cases γ would satsfy (11). As noted above, γ s the target for fast closed-loop power control between the base staton and the moble hosts; ths power control loop operates on a much faster tmescale compared to the tmescale over whch the transmsson rate s adjusted. Indeed, n WCDMA fast closed-loop power control operates at a frequency of 15 Hz, resultng n one 3 The fact that P s() > wll not be a problem n practse snce, as our numercal results show, P s() wll typcally be very small.

7 power update approxmately every.67 mllseconds. On the other hand, the rate remans constant wthn a sngle frame, whose mnmum duraton s 1 mllseconds. Hence, the rate control procedure n Step 3 works on slower tmescales compared to the tmescales of fast closed-loop power control. Moreover, observe from Equaton (2) that a change n the transmsson rate would requre adjustng the transmsson power n order to mantan the same γ. In Step 4, charges are proportonal to the product r γ. The BS/RNC, assumng perfect error detecton, can estmate the transmsson rate r from the receved rate. Also, the BS/RNC knows γ. Hence, there s no parameter that the moble user can falsely declare n order to reduce hs charge, wthout reducng hs level of servce. Step 5 nvolves adjustng the prce λ based on some estmate of the level of congeston of wreless network resources. The specfc procedure for adjustng the prce s related to how prces are communcated to the moble users. One alternatve s to have the RNC drectly announce prces; ths requres a new control channel from the RNC to the MHs. The prce functon s of the form λ(ρ) : [, 1] [, ]. The functon that we consder n our numercal nvestgatons s λ(ρ) = φ 1 ρ, (22) where φ can be adjusted to acheve a target utlzaton, f a rough estmate of the demand (number of users and ther utltes) s known. Another opton s to consder the same sgnallng channel to convey congeston nformaton for both wreless and wred network resources; the correspondng model s gven by (18). An nterestng approach s to have the congeston sgnals for both types of networks communcated usng Explct Congeston Notfcaton (ECN) [14], whch has been approved as an IETF proposed standard. The possble use of ECN markng n wreless networks has been proposed by other researchers, e.g., see [11], but wth the objectve of mprovng the performance of TCP over wreless lnks. ECN markng for conveyng congeston nformaton related to the wreless network can be performed at the RNC, whereas n the wred network routers are responsble for packet markng. Indeed, the RNC would be responsble for packet markng n both the uplnk and the downlnk, based on the level of congeston n each drecton. Such a selecton s approprate, snce the RNC s responsble for managng rado resources, and performs admsson control and transmsson schedulng. One challengng ssue s that n the uplnk there s no shared buffer, hence queue-dependent markng schemes, such as Random Early Detecton (RED), cannot be appled. Instead, markng can depend solely on the average load of the wreless channel. Both the above two alternatves requre estmaton of the load ρ. One approach for measurng the load nvolves drect applcaton of αul, wth α UL gven by (4). A more effcent method s to use aggregate measurements of the total nterference I total (whch ncludes the nose), and the nose η, from whch the total load can be estmated from the followng equaton, whch can be derved by summng (3) for all mobles (ths sum s called uplnk load factor, [6, p ]): j α UL j = I total η I total. (23) Advantages of usng the last equaton are that only aggregate power measurements are requred and the nterference of neghborng cells s mplctly handled Downlnk The procedure for applyng the congeston prcng model for the downlnk, presented n Secton 3.3, nvolves smlar steps as those n the uplnk, wth the modfcatons that we descrbe next. The selecton of the optmal bt-energy-to-nose-densty rato γ, as n the uplnk, s based on (11), but s performed at the moble hosts. The selecton of the rate r n Step 3 s based on (2). Note that the path gan and nterference n ths equaton can change on a fast tmescale. Snce, as dscussed n the prevous subsecton, our rate control procedure operates on slower tmescales, the values of I and g that appear n (2) can be taken to be averages. Moreover, the nterference and the nose can be drectly measured at the moble host, whereas the path gan can be estmated usng the receved power of the downlnk plot channel [6]. The charge n Step 4 s proportonal to the average transmsson power p. Fnally, the prce adjustment n Step 5 can follow a smlar functon as (22), wth the dfference that now the load s gven by p, p snce the resource constrant n the downlnk, Equaton (8), s n terms of the total transmsson power at the base staton. 4.2 Allocaton of rates by RNC accordng to wllngness-to-pay An alternatve to the approach dscussed n the prevous subsecton, that nvolves communcaton of prces from the base staton to the moble hosts and rate adaptaton by the moble hosts, s to add more ntellgence to the RNC, to allocate rates accordng to the users declared wllngnessto-pay or weght values, Fgure 2(b). Indeed, ths approach s smlar to the class-based qualty of servce framework presented n [5]. The above approach s attractve for the followng reasons: ) WCDMA supports negotaton of bearer servce propertes both at call setup, and durng a call [6, p. 1]; ) the RNC already has ntellgence for supportng flexble packet schedulng and load control; ) cellular rado networks are sngle hop networks 4, hence the approach we descrbe satsfes desrable farness propertes, namely proportonal farness [8]; and v) the approach s less demandng for moble hosts, whch do not need to adjust ther rate n the (relatvely fast) tmescale over whch the congeston prce changes, but rather adjust ther wllngness-to-pay on a slower tmescale. Due to all the above, rate allocaton accordng to wllngness-to-pay values requre fewer modfcatons to exstng procedures n WCDMA systems, compared to the explct prce communcaton approach descrbed n the prevous subsecton, hence s easer to mplement. On the other hand, the explct prce communcaton approach places more ntellgence and control at the moble user, and 4 Achevng smlar farness objectves n a multple hop network, wth rate allocaton done by the routers, s more complcated.

8 can support the ntegraton of congeston control n wreless and wred networks; support of such ntegraton wth a wllngness-to-pay lke scheme s not straghtforward Uplnk The scheme for the uplnk works as follows: Moble users communcate ther wllngness-to-pay to the RNC, whch then allocates rates n proporton to the declared wllngnessto-pay values. In partcular, the rate for user s gven by r = 1 γ w j wj W, (24) where w s the wllngness-to-pay for user and γ satsfes (11). Observe from the last equaton that a user s rate s nversely proportonal to hs target bt-energy-to-nose-densty rato γ. Also note that n ths approach the rate r needs to be sgnaled from the RNC to the moble. The approach for rate allocaton based on wllngness-topay values corresponds to the case where users have a logarthmc utlty U (r P s(γ )) = w log(r P s(γ )). Substtutng ths utlty n Equaton (1), and takng the dervatve wth respect to r, we fnd that a user s net utlty s maxmzed for w = λr γ, where as before γ satsfes (11); hence w represents a prce per unt of tme, whch justfes the term wllngness-to-pay. From the above we see that user s resource usage r γ s proportonal to hs wllngness-to-pay, whch leads to the proportonal allocaton of resources n Equaton (24). For a general form of the utlty functon, and f updates of the wllngness-to-pay can occur n ntervals of fxed duraton τ, then the user can vary hs wllngness-to-pay accordng to w (t) = ˆλ(t)γ r (t), where r (t) and γ are gven by (17) and (11) respectvely, and ˆλ(t) s an estmate of the prce; e.g., ˆλ(t) = w (t τ) r (t τ)γ, where r (t τ) s the rate allocated to user at tme t τ Downlnk In the downlnk, smlar to the uplnk, users declare ther wllngness-to-pay to the RNC. Based on these declaratons, the average power allocated to moble s p = w j wj p. From p, and usng (7), the RNC allocates to moble the rate r = W g w p, γ I + η j wj where smlar to the uplnk, γ s determned from (11). Hence, the above approach requres the RNC to have knowledge of the average path gan, the average nterference, the nose, and the target bt-energy-to-nose-densty rato. Although WCDMA supports the reportng of such parameters to the RNC [6], care must be taken to ensure truthful declaraton from the moble hosts; for example, truthful declaraton can be ensured f the software runnng n the moble hosts, whch s responsble for reportng the above parameters, cannot be modfed by users. 5. NUMERICAL INVESTIGATIONS In ths secton we present numercal nvestgatons that demonstrate the applcaton of our framework and how varables such as the rate, the sgnal qualty, and the charge n Table 1: Parameters for the numercal nvestgatons. d s dstance n Km. parameter value total BS power, p 16.7 Watt load 6% nose, η 1 13 Watt path gan, g(d) kd u, u = 3.52, k = downlnk orthogonalty, θ.1 BER(γ) (DPSK).5e γ bts per pkt, L 6 γ, from (11) & Fg. 1(a) 5 utlty, concave 1 e bx, b =.4 utlty, sgmod 1 e b(x x), x 5.6P s(γ ) 1 e bx, x < 5.6P s(γ ) b =.4, x = 2 the steady state depend on a moble s dstance and the wreless network s load; moreover, we dentfy and explan the dfferences between the uplnk and the downlnk resource control models. The rate for the uplnk s computed from (1) and for the downlnk from (19). In both cases, γ s determned from (11). We consder two types of utlty curves: concave and sgmod. The parameters for the partcular functons, along wth the propagaton model and other system parameters are shown n Table 1. Fgure 3(a) shows that n the uplnk, the rate s ndependent of a moble s dstance from the base staton. Ths s expected, snce congeston charges are also ndependent of the dstance, and depend only on the transmsson rate and the target bt-energy-to-nose-densty rato. On the other hand, n the downlnk, the optmal rate that maxmzes a user s net utlty decreases wth the dstance. Ths s due to the dependence of charges on the transmtted power from the base staton, whch results n the rate dependng on the path gan, as evdent from Equaton (21). Fgure 3(b) s for the case where users have a sgmod utlty. The results for the uplnk reman the same. On the other hand, the results for the downlnk are dfferent. In partcular, there s a dstance where the optmal rate drops abruptly to zero; ths s the dstance after whch the net utlty becomes negatve for any postve rate, hence the user benefts most by not sendng data. Fgure 4(a) shows the correspondng power requrements for the uplnk and the downlnk, n the case of a concave utlty. In the uplnk, charges are ndependent of the moble s poston and ts transmsson power, hence the power contnuously ncreases wth the dstance n order to mantan a constant sgnal qualty. In the downlnk, the power ntally ncreases wth the dstance, snce dong so ncreases the net utlty; at some dstance, the power decreases wth the dstance, snce the path loss ncreases fast wth the dstance, hence the necessary power and the correspondng charge, whch s proportonal to the power, ncrease fast. Fgure 4(b) shows the results for a sgmod utlty. There s a dfference only for the downlnk, where the power drops to zero after some dstance, when the net utlty s negatve for any postve rate, hence the net utlty s maxmzed, and equals zero, for zero rate and power.

9 3 25 uplnk downlnk 1.8 uplnk downlnk rate (Kbps) power (Watts).6.4 Sfrag replacements d (Km) (a) Concave utlty uplnk downlnk PSfrag replacements d (Km) (a) Concave utlty uplnk downlnk rate (Kbps) power (Watts).6.4 Sfrag replacements d (Km) (b) Sgmod utlty PSfrag replacements d (Km) (b) Sgmod utlty Fgure 3: In the uplnk, the optmal rate s ndependent of the dstance, and n the downlnk t decreases wth the dstance. For a sgmod utlty, n the downlnk the rate drops to zero after some dstance, when the net utlty s negatve for any postve rate. Fgures 5(a) and 5(b) show the dependence of the charge on the dstance. As expected, for the uplnk the charge s ndependent of the dstance. On the other hand, for the downlnk, the dependence of the charge on the dstance s smlar to the dependence of the power on the dstance, snce n the downlnk the charge s proportonal to the power. The dependence of the rate and the power on the load, for a concave utlty, and for the uplnk and downlnk are shown n Fgures 6(a) and 6(b). For the uplnk, the load s taken to be j αul j j rjγj/w, and for the downlnk j pj/ p. Fgure 6(a) shows that the rate decreases faster wth the load n the downlnk. The reason for ths behavor s that the rate n the downlnk, as (21) shows, depends on the load both through the congeston prce and through the nterference. Fgure 6(b) shows that n the uplnk the power ncreases wth the load. On the other hand, n the downlnk the power ntally ncreases and then decreases. Ths dfference s due to the followng: The power depends on both the rate and the nterference, Equaton (1). The dependence of the rate on the load s shown n Fgure 6(a). In the uplnk the nterference ncreases fast wth the load, snce from (23) we have I + η I total = η/(1 ρ). On the other hand, n the downlnk the nterference has an almost lnear dependence on the load, snce I +η = θ g j pj +η θgρ p+η. Both the Fgure 4: In the uplnk, the power ncreases wth the dstance, to mantan a constant sgnal qualty. In the downlnk, the power ntally ncreases, and then decreases. For a sgmod utlty, n the downlnk the rate drops to zero after some dstance, when the net utlty s negatve for any postve rate. above two approxmatons are for the case of a large number of moble users, each contrbutng a small percentage to the total nterference. 6. RELATED WORK Next we present a bref overvew of related work; ths s not an exhaustve survey of the area, and has the goal to dentfy the man dfferences between other research and the work presented n ths paper. The authors of [4] consder a utlty that s dfferent from the utlty that we consder, and s nterpreted as the number of nformaton bts transmtted per unt of energy. It s shown that the non-cooperatve game, where mobles adjust ther power to maxmze ther utlty, has a unque Nash equlbrum, whch however s neffcent. Wth the ntroducton of prces [17], Pareto mprovements are acheved, but not the socal welfare optmal. On the other hand, the resource control model we have presented for the uplnk, under some assumptons regardng the utlty functons, acheves the socal welfare maxmum. The authors of [2] consder a utlty that s a functon of the transmsson rate, and nvestgate the problem of maxmzng the sum of all utltes n the forward lnk (downlnk), under constrants on the total transmsson power at the

10 Sfrag replacements Sfrag replacements charge charge uplnk downlnk d (Km) (a) Concave utlty uplnk downlnk d (Km) (b) Sgmod utlty PSfrag replacements power (Watts) PSfrag replacements rate (Kbps) rate (Kbps) power (Watts) uplnk downlnk load (a) Rate uplnk downlnk load (b) Power Fgure 5: In the uplnk, the charge s ndependent of the dstance. In the downlnk, the charge follows a shape smlar to the power, Fgure 4, snce t s proportonal to the power. Fgure 6: The rate depends on the load more for the downlnk than for the uplnk. The power n the downlnk ntally ncreases, and then decreases. The moble dstance from the base staton s d =.5 Km. base staton, and constrants on the maxmum error rate for each user. The allocaton of rates s done centrally at the base staton. The approach proposed n Secton 3.3, and gven by (19), consders a smlar objectve, but wth the utlty beng a functon of the actual throughput (transmsson rate multpled by the success probablty), rather than the transmtted rate. Moreover, our approach uses a decentralzed scheme, based on prces, to acheve the objectve. The authors of [21] consder a utlty that s a functon of the bt-energy-to-nose-densty rato, whch can have a sgmod shape, and formulate a utlty-based dstrbuted power control algorthm where each user seeks the maxmze hs net utlty, and charges are proportonal to the power. For a constant prce per unt of power, t s proved that the power update algorthm converges. The authors of [1] consder downlnk resource allocaton n CDMA networks based on prcng. The user utlty s a step functon of the bt-energyto-nose-densty rato, and a moble s charge contans a constant term (prce per code) and a term lnear n the transmtted power from the base staton. The authors of [7] consder a utlty that s a monotoncally ncreasng concave functon of the bt-energy-to-nose-densty rato and a monotoncally decreasng concave functon of the moble s power. Our work dffers from the above n that t consders the jont optmzaton of the sgnal qualty and transmsson rate, and takes nto account the partcular resource con- strants n both the downlnk and uplnk, dentfyng the dfferences of the two correspondng models; also, our framework takes nto account the congeston for both wreless and wred network resources, n addton to the cost of moble battery power. Moreover, the above approaches are geared towards mechansms for power control; on the other hand, our work deals wth control mechansms that operate on a slower tmescale, hence on top of fast closed-loop power control. Fnally, n the model we have proposed for the uplnk, there s no dfferentaton of moble users based on ther poston. On the other hand, n the approaches of [4, 17, 21], moble users far from the base staton that encounter hgh path loss are charged more and receve less resources, compared to users close to the base staton; ths s termed nearfar unfarness n [21]. Investgaton of the above schemes, and comparson wth a resource control scheme based on mcroeconomcs, smlar to the one presented n ths paper, but for traffc wth fxed-rate requrements, appears n [19]. The concept of utlty n wreless local area networks s consdered n [1, 12]. In partcular, the work of [1] uses utlty curves for modellng applcaton requrements, and based on ths, for buldng adaptve QoS support n the MAC layer. The work of [12] uses the utlty concept for defnng far contenton resoluton algorthms, takng nto account unque characterstcs of ad hoc wreless networks, such as locaton-dependent contenton and decentralzed control.

11 7. CONCLUDING REMARKS We have presented a framework, based on mcroeconomcs and congeston prcng, for resource control n CDMA, and Wdeband CDMA n partcular, networks carryng elastc traffc. An mportant property of the framework s that t ncorporates the congeston for shared resources n both wreless and wred networks, as well as the cost of power consumpton. Hence, t can be used as the bass for ntegraton of control mechansms n wreless and wred networks. We have dentfed a number of practcal ssues regardng the applcaton of the framework, and have presented a seres of numercal nvestgatons dentfyng ts key features, and how varous parameters such as a moble s poston and the wreless network s load, nfluence resource sharng. Regardng the applcaton of the proposed framework, dfferent aspects of the framework have a dfferent complexty. For example, currently the selecton of the frame error rate for non-real-tme servces s fxed, equal to some (arbtrary) value n the range 1-2% [6, p. 198]. Typcal outer loop power control procedures ncrease or decrease the target btenergy-to-nose-densty rato n order to acheve ths fxed frame error rate. On the other hand, we have seen that n order to acheve effcency, the optmal target bt-energyto-nose-densty rato should depend on the packet success probablty as a functon of the bt-energy-to-nose-densty rato, and n partcular for best-effort traffc should satsfy (11). Moreover, as dscussed n Secton 4.1, the procedure for selectng the optmal bt-energy-to-nose-densty rato can take advantage of the sgmod shape of the packet success probablty, hence can be mplemented wth small modfcatons to the typcal procedures used for outer loop power control. Also, the allocaton of rates by the rado network controller (RNC) accordng to the wllngness-to-pay values declared by all moble users can be mplemented as part of the load control functonalty of the RNC, n a class-based framework where a dfferent class corresponds to a dfferent wllngness-to-pay value. Based on the above dscusson, the wllngness-to-pay approach appears to requre fewer modfcatons to exstng procedures compared to the explct prce communcaton approach, snce the latter places more ntellgence n the moble hosts; on the other hand, the explct prce communcaton approach places more control, hence flexblty, n the moble hosts, and can be the bass for supportng the ntegraton of congeston control n wreless and wred networks. Issues we are currently nvestgatng nclude the extenson of the proposed framework for bursty traffc, for whch a hybrd code and tme dvson multplexng scheme mght be more approprate [6], and for loss senstve traffc, whose utlty depends on the packet loss rate n addton to the average throughput. Another ssue of practcal nature s the fact that we have assumed that rates obtan contnuous values, whereas rates n WCDMA can obtan dscrete values, wth the use of dscrete spreadng factors. In ths paper we ntroduced the dea of usng ECN as the common sgnallng mechansm for conveyng congeston nformaton n wreless and wred networks, n order to support seamless congeston control over both network technologes. An area for further nvestgaton s the necessary mechansms to support the above. In partcular, an mportant ssue s that there s no shared buffer n the uplnk drecton, hence queue-based markng schemes such as Random Early Detecton (RED) cannot be appled. Fnally, we are nvestgatng the applcaton of mcroeconomc models for wreless network dmensonng, and for resource control n wreless LANs based on IEEE The overall goal of the above work s to further the research on the applcaton of mcroeconomc models for developng effcent, flexble, and robust mechansms for resource control n wreless networks; ths ncludes both modellng work that takes nto account the partcular characterstcs of wreless networks, and more practcal engneerng nvestgatons on how to modfy and enhance exstng mechansms n order to mplement these models. 8. ACKNOWLEDGMENTS The author would lke to thank Bob Brscoe and Dave Songhurst of BT Research, and Costas Courcoubets of the Athens Unversty of Economcs and Busness, for stmulatng and nsghtful dscussons, and the anonymous revewers for provdng helpful comments. 9. REFERENCES [1] G. Banch and A. T. Cambell. A programmable MAC framework for utlty-based adaptve qualty of servce support. IEEE J. Select. 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