RESOURCE CONTROL FOR HYBRID CODE AND TIME DIVISION SCHEDULING Vaslos A. Srs Insttute of Computer Scence (ICS), FORTH and Department of Computer Scence, Unversty of Crete P.O. Box 385, GR 7 Heraklon, Crete, Greece Emal: vsrs@cs.forth.gr Abstract - We present a model, based on economc theory, for effcent and robust resource control n hybrd code and tme dvson schedulng wreless systems. Based on ths model, we propose procedures for combned rate allocaton and tme slot allocaton to acheve effcent utlzaton of wreless resources, whle takng nto account user requrements. These procedures can be appled usng a class-based framework, whch allows smple mplementaton, and where users select a servce class reflectng ther valuaton for the average throughput and for the percentage of tme slots n whch they can transmt data. Keywords - resource management, utlty, economc effcency, servce dfferentaton I. INTRODUCTION Effcent spectrum and wreless resource utlzaton s one of the most mportant ssues n current and future wreless systems, due to the lmted capacty of such systems compared to wred networks. Many of these systems, such as Wdeband CDMA (Code Dvson Multple Access), wll support both code and tme dvson schedulng. Combnaton of these two schedulng schemes can be used to effcently utlze resources for both streamng applcatons, whch requre contnuous transmsson of data, and besteffort applcatons, whch generate bursty traffc and can tolerate delays. Tme dvson schedulng has the advantage of supportng hgher transfer rates for the same energy per transmtted bt, compared to code dvson schedulng, but requres tme synchronzaton between statons and has the dsadvantage of non-contnuous transmsson, whch results n bursty traffc. Indeed, [] shows that n a hybrd code and tme dvson schedulng system supportng real-tme (delay ntolerant) and non real-tme (delay tolerant) traffc, both wth fxed target bt-energy-to-nose-densty rato, the aggregate transmsson rate of non real-tme traffc s maxmzed f t s scheduled so that only one non real-tme source sends traffc n each tme slot. Unlke tme dvson multplexng, code dvson schedulng supports contnuous data transmsson, but has the dsadvantage of lower nstantaneous bt rates due to hgher nterference. The shared channels and the common packet channel (n the uplnk) of WCDMA typcally use both tme dvson and code dvson schedulng. In the downlnk, orthogonal codes are shared between many users n a tme dvson manner,.e. there may be many common packet channels per cell, each havng a dfferent bt rate, that are shared among many users n a tme dvson manner. On the other hand, dedcated channels typcally use code dvson schedulng, hence n the downlnk one orthogonal code s consumed for each user of a dedcated channel. Indeed, for dedcated channels the bt rate can change durng transmsson, but remans constant wthn a sngle frame that has a mnmum duraton of ms, and the orthogonal code must be allocated accordng to the hghest requested bt rate. In ths paper we present a model for effcent and robust resource control n hybrd code and tme dvson schedulng wreless systems, whch s based on economc theory and extends the work n [2], whch consdered pure code dvson multplexng. Based on ths model, we propose procedures for combned rate allocaton and tme slot allocaton to acheve effcent utlzaton of wreless resources, whle takng nto account user requrements; the latter are modelled usng utlty functons. The procedures can be appled usng a class-based framework, hence allow smple mplementaton, where users select a servce class reflectng ther valuaton for the average throughput and for the percentage of tme slots n whch they can transmt. Our work dffers from the work of [], whch also consders hybrd code and tme dvson schedulng systems, n that our model consders the jont control of the transmsson rate and the percentage of tme slots n whch users are allowed to send, n order to acheve effcent utlzaton of resources accordng to user requrements. Moreover our work dffers from other work that nvestgates the applcaton of economc theory to wreless systems, such as [3], [4], [2], [5], n that we consder systems wth smultaneous support for both code and tme dvson schedulng. The rest of the paper s organzed as follows. In Secton II we dscuss resource usage n the uplnk of hybrd code and tme dvson schedulng systems. In Secton III we present our model for the jont control of the transmsson rate and the percentage of tme slots n whch a user can transmt, and n Secton IV we dscuss the applcaton of our model usng a class-based servce dfferentaton framework. In Secton V we present numercal experments demonstratng the applcaton of the proposed model. Fnally, n Secton VI we conclude the paper.
II. RESOURCE USAGE MODEL Consder the uplnk of a sngle CDMA cell. Note, however, that the results can be extended to the multple cell case by consderng the nter-cell nterference coeffcent [6]. Let W be the chp rate. The bt-energy-to-nose-densty rato at the base staton s gven by [6], [7] ( Eb N ) = W r g p j g jp j + η, () where r s the transmsson rate, p s the transmsson power, g s the path gan between the base staton and moble, and η s the power of the background nose at the base staton. The rato W/r s the spreadng factor or processng gan for moble. 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 [6], [7]. Under the assumpton of addtve whte Gaussan nose, BER s a non-decreasng functon of E b /N, that depends on the multpath characterstcs, and the modulaton and forward error correcton (FEC) algorthms. Let γ be the target bt-energy-to-nose-densty rato requred to acheve a target BER. Ths target s gven to closed-loop power control, whch adjusts the transmsson power n order to acheve t. If we assume perfect power control, n whch case (E b /N ) = γ, and solve the set of equatons gven by () for each moble, we get [7], [8] ηα g p = j α, (2) j where the load factor α s gven by α = ( ). W r γ + The power levels gven by the set of equatons (2) 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 (2) we get α <. (3) The last equaton llustrates that the uplnk s nterferencelmted: Even when they have no power constrants, moble hosts cannot ncrease ther power wth no bound, due to the ncreased nterference they would cause to the other mobles. If (3) s volated, then the target {γ } cannot be met for all mobles. For hybrd code and tme dvson multplexng, the constrant on resource usage n the uplnk becomes α <, (4) where α = rγ W+r γ s the resource usage for the uplnk n pure code dvson multplexng systems, and s the percentage of tme slots n whch user sends traffc. The constrant (4) can be extended to take nto account the case of lmted transmsson power at moble hosts, mperfect power control, and nter-cell nterference; ths s done by consderng an nterference margn I margn [9], whch lmts the maxmum utlzaton ρ that can be acheved. In ths case, (4) becomes α < ρ, where ρ = I margn I margn. (5) III. RESOURCE CONTROL MODEL In ths secton we frst propose a utlty model for elastc users that value both the average throughput wth whch they can transmt and the percentage of tme slots n whch they can transmt; note that the two are not dentcal, snce the user can transmt a dfferent amount of data,.e. have a dfferent transmsson rate, n dfferent tme slots. Utlty functons are wdely used for capturng user and applcaton requrements, and gve the level of satsfacton for a gven level of servce. Then, consderng the results for resource usage dscussed n the prevous secton, we present our model for effcent resource control n hybrd code and tme dvson schedulng systems. The average throughput for user s gven by the product r P (γ ), where s percentage of tme slots n whch user can send data, r s hs average transmsson rate n each slot, and P (γ ) s the probablty of successful packet transmsson. Hence, user s valuaton for the average throughput can be wrtten as U ( r P (γ )). The factor encodng user s valuaton for the percentage of tme slots he s allowed to transmt can be expressed as V ( ), where s percentage of tme slots n whch user can transmt. Note that ths factor captures solely the average percentage of tme slots a user can transmt, and s ndependent of ther dstrbuton. Based on the above, the overall utlty for a user that values both the average throughput and the percentage of tme slots n whch he can transmt data can be expressed as U ( r P (γ )) + V ( ), where the frst factor U encodes user s valuaton for the average throughput and the second factor V encodes user s valuaton for the percentage of tme slots n whch he can transmt. The above model assumes an addtve relatonshp between the two factors; another alternatve s to have a multplcatve relatonshp between the two factors; the conclusons obtaned consderng such a multplcatve model are qualtatvely the same as those obtaned for the addtve model that we consder n ths paper.
The user s net utlty maxmzaton problem s maxmze U ( r P (γ )) + V ( ) λα (6) over r,γ,, where λ s the shadow prce for the wreless resource constrant (5). Although the general form of the above user utlty can have a complex non-concave structure, hence the global problem of maxmzng the sum of all utltes (socal welfare) can have a non-trval structure for whch the Lagrangan method for fndng the maxmum cannot be appled, through expermentaton wth a range of user utlty expressons we have found that for a wde range of user utltes the Lagrangan method can ndeed be appled. In ths case, the socal welfare can be acheved n a decentralzed manner, by teratvely adjustng the shadow prce λ and ndependently solvng each user problem (6). The teratve adjustment of λ can nvolve decreasng the value of λ when the constrant n (5) s not tght,.e. when the demand for resources s less than the supply, and ncreasng ts value when the constrant s volated,.e. when the demand for resource s greater than the supply. Moreover, as we dscuss n Secton IV, the above model can be appled usng a class-based servce dfferentaton framework, where users select a partcular class for ther valuaton of the average throughput and for the percentage of tme slots n whch they can transmt data, and the network controls the transmsson rate and tme slot allocaton based on the network traffc load; such an approach has the advantage of not requrng the mplementaton of complex mechansms at the moble hosts. Based on the frst order condtons of (6), f we take the partal dervatves wth respect to r, γ, of the objectve functon n (6) and equatng them wth zero we get Wγ U ( r P (γ ))P (γ (W + r, γ )2 (7) U ( r P (γ ))P (γ W (W + r, γ )2 (8) r γ U ( r P (γ ))r P (γ ) + V ( W + r, (9) γ From (7) and (8) we fnd that the optmal γ s ndependent of the prce λ and the user utlty, and satsfes P (γ ) = P (γ )γ. () The last expresson shows that the selecton of the optmal sgnal qualty s ndependent of both the user s utlty and the prce, and depends only on the dependence of the packet success rato on the target sgnal qualty. Ths result s smlar to the case of best-effort traffc where users value only the average throughput [2], and allows us to decompose the utlty maxmzaton problem (6) nto two smpler problems: one problem nvolvng the selecton of the optmal sgnal qualty γ, and one problem nvolvng the selecton of the optmal transmsson rate r and the optmal percentage of tme slots n whch a user can transmt data. The frst problem s dentcal to the one dscussed n [2], hence n the remander of the paper we focus on the second problem. From (9) and (7) we have Wr γ r γ λ (W + r + V γ )2 ( W + r γ V From (7) and () we have U ( r P (γ )) P (γ )r 2 γ W (r γ )2 ( (W + r. () γ )2 = V ( ). (2) The last equaton gves the tradeoff between the optmal transmsson rate r and the optmal percentage of tme slots that user can transmt data. Note that ths tradeoff depends solely on the utlty factors U,V, and s ndependent of the network traffc load; however, the partcular par whch s optmal for a gven traffc scenaro wll depend on the network traffc load through the shadow prce λ, and wll satsfy (). IV. APPLICATION The model presented n the prevous secton suggests how to optmally set the three control varables n hybrd code and tme dvson multplexng systems: the target bt-energyto-nose-densty rato based on (), and the transmsson rate and percentage of tme slots n whch a user can transmt data, based on () and (2). The frst procedure for adjustng the target bt-energy-to-nose-densty rato s performed by outer-loop power control, and s dentcal to the correspondng procedure n the pure code dvson multplexng case dscussed n [2]. The adjustment of the other two varables can be acheved n a class-based framework where the network supports a lmted set of classes, each correspondng to a partcular valuaton for the average throughput and a partcular valuaton for the percentage of tme slots a user can transmt data. As a specfc example, consder the followng expresson for the throughput valuaton factor U (x ) = e ux, (3) where x s the average throughput, and the followng expresson for the valuaton factor related to the percentage of tme slots a user can transmt data V ( ) = e v. (4) A network provder can offer a small set of possble values for u, each correspondng to a dfferent throughput class, and v, each correspondng to a dfferent class related to the percentage of tme slots a user can transmt data. Each user selects, at the subscrpton or the connecton setup phase, a partcular class, whch corresponds to partcular values
BS RNC.9.8.7.6 u=. u=.2 u, v.5.4.3 (r, ) = F(u, v, traffc load) Fg. Class-based mplementaton of the proposed model. Each user selects a class correspondng to partcular values for u, v. Based on ths selecton, and takng nto account the network load, the RNC computes the optmal transmsson rate and percentage of tme slots the user can transmt..2. 2 4 6 8 Fg. 2 Throughput utlty factor gven by (3), for u =.,.2..9 v= v=2 of the parameters u,v, Fg.. The network, through the Rado Network Controller (RNC) n the case of 3G wreless systems based on WCDMA, and based on the traffc load, selects for each user the transmsson rate and the percentage of tme slots he can transmt, accordng to () and (2). V. NUMERICAL INVESTIGATIONS In ths secton we present numercal nvestgatons demonstratng the model proposed n the prevous sectons. We assume that users have a utlty functon that s the sum of the two factors gven by (3) and (4). Fg. 2 shows the throughput factor for the two values of parameter u n (3) that we consder. Fg. 3 shows the factor related to the percentage of tme slots a user s allowed to transmt, for the two values of parameter v n (4) that we consder. In the case of addtve whte Gaussan nose and a nonfadng channel, the bt error rate for DPSK (Dfferental Phase Shft Keyng) modulaton s [] BER(γ) =.5e γ. If there s no error correcton, and bt errors are ndependent and are all detected, then the packet success probablty P(γ), whch we assume to be the same for all mobles, s gven by P(γ) = ( BER(γ)) L, where L s the number of bts n one packet. The values of the other parameters are shown n Table. Fgure 4 shows the tradeoff between the transmsson rate r and the percentage of tme slots a user s allowed to transmt; ths tradeoff s computed from (2), and s ndependent of the network traffc load. Observe that for both small and large values of the transmsson rate, the percentage of tme slots a user should be allowed to send.8.7.6.5.4.3.2..2.4.6.8 percentage of tme slots, Fg. 3 Utlty factor related to the percentage of tme slots gven by (3), for v =, 2. s close to one. The former behavour, for small values of the transmsson rate, s due to the rght-hand sde of () obtanng small values, hence the dervatve V should be small, whch s the case for large values of due to the concavty of V, Fg. 3. The latter behavour, for large values of the transmsson rate, s due to the left-hand sde of (2) obtanng small values due to the concavty of the throughput factor U, Fg. 2, hence as before the dervatve V should be small, whch s the case for large values of. Fg. 5 shows the optmal transmsson rate for dfferent traffc loads, expressed as the number of users. As expected, a hgher load results n a smaller transmsson rate for each user. From ths fgure, also observe that the optmal transmsson rate depends on the user preferences, expressed through the utlty functon. In the class-based approach descrbed n Secton IV, a network provder would determne the optmal transmsson rate, based on the number and type of users, from Fg. 5, and then the optmal percentage of tme slots a user s allowed to transmt, from Fg. 4.
Table Parameters for the numercal nvestgatons. parameter value chp rate, W 3.84 Mcps load, ρ 6% BER(γ) (DPSK).5e γ bts per pkt, L 6 γ, from () 5 throughput factor U(x) = e ux, u =.,.2 tme slot factor V ( ) = e u, v =, 2 8 6 4 2 8 6 4 u=., v= u=., v=2 percentage of tme slots,.8.6.4.2 u=.2, v= u=., v= u=., v=2 5 5 2 25 Fg. 4 Tradeoff between transmsson rate and percentage of tme slots a user can transmt. VI. CONCLUSION We have presented a model for effcent resource control n hybrd code and tme dvson schedulng systems. Our approach s based on economc theory and utlty functons for capturng user preferences, and addresses the ssue of how the transmsson rate and the percentage of tme slots that users can transmt should be jontly controlled n order to acheve effcent utlzaton of network resources. Fnally, our approach can be appled usng a class-based servce dfferentaton framework, where users select a throughput class reflectng how much they value ther average throughput, and a class related to the percentage of tme slots they are allowed to transmt. Possble further work ncludes evaluatng our proposal n the case of fadng channels that are dfferent for each user, extendng the model to the downlnk, and consderng utlty functons where users value, n addton to the average throughput, the packet loss probablty; work related to the latter s presented n []. ACKNOWLEDGEMENTS Ths work has been supported n part by Brtsh Telecommuncatons (BT), UK. REFERENCES [] S. Ramakrshna and J. M. Holtzman, A scheme for throughput maxmzaton n a dual-class CDMA sys- 2 2 3 4 5 6 7 8 9 number of users, N Fg. 5 Optmal transmsson rate for a dfferent number of users. tem, IEEE J. Select. Areas Commun., vol. 6, no. 6, pp. 83 844, August 998. [2] V. A. Srs, Resource control for elastc traffc n CDMA networks, n Proc. of ACM MOBICOM 2, 22. [3] D. J. Goodman and N. B. Mandayam, Power control for wreless data, IEEE Personal Commun., vol. 7, pp. 48 54, Aprl 2. [4] M. Xao, N. B. Shroff, and E. K. P. Chong, Utltybased power control n cellular wreless systems, n Proc. of IEEE INFOCOM, Aprl 2. [5] T. Alpcan, T. Basar, R. Srkant, and E. Altman, CDMA uplnk power control as a noncooperatve game, Wreless Networks, vol. 8, no. 6, pp. 659 67, November 22. [6] K. S. Glhousen, I. M. Jacobs, R. Padovan, A. J. Vterb, L. A. Weaver, and C. E. W. III, On the capacty of a cellular CDMA system, IEEE Trans. on Vehcular Technology, vol. 4, no. 2, pp. 33 32, May 99. [7] L. C. Yun and D. G. Messerschmtt, Power control for varable QoS on a CDMA channel, n Proc. of IEEE MILCOM 94, October 994. [8] A. Sampath, P. S. Kumar, and J. M. Holtzman, Power control and resource management for a multmeda CDMA wreless system, n Proc. of IEEE Int. Symp. on Personal, Indoor, Moble Rado Commun. (PIMRC), September 995. [9] H. Holma and A. Toskala, WCDMA for UMTS. New York: Wley, 2. [] J. M. Rulnck and N. Bambos, Moble power management for wreless communcatons networks, ACM/Baltzer Wreless Networks Journal, vol. 3, pp. 3 4, 997. [] V. A. Srs and C. Courcoubets, Resource control for loss-senstve traffc n CDMA networks, n Proc. of IEEE INFOCOM 4, March 24.