Utilizing Call Admission Control to Derive Optimal Pricing of Multiple Service Classes in Wireless Cellular Networks

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1 Utilizing Call Admission Control to Derive Optimal Pricing of Multiple Service Classes in Wireless Cellular Networks Okan Yilmaz and Ing-Ray Cen Computer Science Department Virginia Tec {oyilmaz, Abstract We develop a ybrid partitioning-tresold call admission control algoritm to derive optimal pricing of multiple service classes in mobile wireless networks for revenue optimization wit quality of service (QoS) guarantees. Unlike traditional admission control algoritms wic make acceptance decisions to satisfy QoS constraints suc as te call blocking probability, te ybrid partitioning-tresold admission control algoritm is designed to maximize te revenue earned by te system wile satisfying QoS of multiple service classes. We utilize te ybrid call admission control algoritm to analyze a pricing sceme tat correlates service demand wit pricing, and to derive optimal pricing under wic te system revenue is maximized wile QoS requirements of multiple service classes are guaranteed.. Introduction Next generation wireless networks will provide diverse multimedia services to mobile users, including real-time services suc as video and audio streaming, and non-real-time services suc as image and text access. As tese multiple multimedia service classes ave distinct quality of service (QoS) requirements, it is important to design admission control algoritms tat admit roaming users of different service types to satisfy teir distinct QoS requirements wile maximizing te utilization of system resources. Te blocking probability of new calls and te dropping probability of andoff calls are two important QoS metrics. Mobile users in a cellular network establis a connection troug teir local base station. A base station as a fixed number of wireless cannels and can only support a limited number of connections (or calls) simultaneously due to bandwidt limitations. A andoff occurs wen a mobile user wit an ongoing connection leaves te current cell and enters anoter cell. Tus an ongoing, incoming connection may be dropped during a andoff if tere is insufficient bandwidt in te new cell to support it. We can reduce te andoff call drop probability by rejecting new connection requests. However, tis increases te new call blocking probability. Tus, tere is a tradeoff between te andoff and new call blocking probabilities. Call admission control for single-class network traffic, suc as voice, as been studied extensively [6, 7, 8, 4]. For multiple service classes, call admission algoritms offered in [5, 3, 6, 7] make acceptance decisions for new and andoff calls to satisfy QoS requirements in order to keep te dropping probability of andoff calls and te blocking probability of new calls below a specified tresold. All tese algoritms concern QoS requirements, not pricing or revenue issues of service classes. Cen et al. [3] first proposed te concept of maximizing te payoff of te system troug admission control in te context of multimedia services. Recently Cen et al. [4] developed a class of admission control algoritms integrated wit pricing wit QoS guarantees based on partitioning [3] and tresold-based [3] and a ybrid algoritm combining bot for revenue optimization in wireless networks. However, tese studies aimed at allocating system resources to maximize te revenue received given tat a fixed price as been assigned by te service provider. In tis paper, we address te issue of determining optimal pricing. We utilize admission control algoritms to derive optimal pricing of multiple service classes in mobile wireless networks for revenue optimization wit quality of service (QoS) guarantees. Te area of optimal pricing for service multiple classes in wireless networks is relatively unexplored. Hou et al. [9] proposed a dynamic pricing approac in response to canging call arrival rates to satisfy QoS requirements. We dispose dynamic pricing as a valid approac since canging pricing during call services is disturbing to callers. Aldebert et al. [] presented an empirical study tat reveals te relationsip between pricing and demand for residential telecommunication service. P. Rappoport, et al. [5] analyzed a consumer survey to estimate te demand for wireless internet access. Keon and Anandalingam [0] proposed an Proceedings of te 2t International Conference on Parallel and Distributed Systems (ICPADS'06) /06 $ IEEE

2 optimal pricing approac in te context of wired networks considering a pricing sceme tat would carge customers for te use of a connection troug a sequence of switces based on a pricing-demand relationsip identified in [, 2] to optimize revenue. Our paper concerns optimal pricing for serviceoriented classes carged by te amount of time a call uses te service, rater tan being carged per connection. Te basic idea for finding optimal pricing is tat for eac cell we statistically determine a set of reference parameter values for eac service class, including te arrival/departure rates of new calls, te arrival/departure rates of andoff calls, and te current pricing, caracterizing te cell s current operating and workload conditions. Ten we apply a call admission control algoritm developed in te paper to allocate bandwidt resources to calls so as maximize te system revenue. Ten, by utilizing a pricing-demand relation function as suggested in [, 2], we adjust pricing relative to te reference pricing, tereby predicting te arrival/departure rates of eac service class relative to te service class s reference arrival/departure rates in eac cell. For eac price adjustment, a call admission control algoritm is applied to determine te maximum revenue obtainable. Te end product is a table generated periodically by eac cell listing all possible future pricing combinations considered by te service provider, and te associated local revenue obtainable as a result of executing an admission control algoritm cognizant of revenue optimization. Te tables from individual cells ten will be merged by te network service provider to determine global optimal pricing across all te cells in te system. Te goal of tis paper is to utilize admission control algoritms designed for revenue optimization wit QoS guarantees [4] to derive optimal pricing. A service provider typically adjusts pricing only periodically. Once a global optimal pricing sceme is derived, it would stay static for a period of time, allowing users to be carged wit te same rate wile roaming. We sow tat a ybrid admission control algoritm combining te benefits of partitioning and tresold-based call admission control would perform te best in terms of revenue earned wit QoS guarantees to service classes over a wide range of input parameters caracterizing te operating conditions. Te rest of te paper is organized as follows. Section 2 states te system model and gives assumptions used in caracterizing te operational environment of a wireless network. Section 3 presents our pricing sceme and metodology for finding optimal pricing. Section 4 describes a class of call admission control algoritm designed for revenue optimization wit QoS guarantees for mobile wireless networks. Section 5 demonstrates ow call admission control can be utilized to derive optimal pricing for multiple service classes. Numerical results are presented wit pysical interpretation given. Finally Section 6 discusses applicability, summarizes te paper, and outlines future researc areas. 2. System Model A cellular network consists of a number of cells, eac of wic as a base station at te center to provide network services to mobile osts witin te cell. We assume tere exists a number of distinct service classes, S, S 2,, S n, caracterized by service type attribute. A service type can be real-time or nonreal-time. Furtermore, tere are two call types: andoff and new. Of tese call types, andoff calls always ave iger priority tan new calls. Eac service type requires a number of bandwidt cannels to satisfy its intrinsic bandwidt QoS requirement. Eac combination of service type and call type may also impose a system-wide QoS requirement. For example, te andoff call drop probability of real-time service type being less tan 2% can be a QoS requirement. Assume tat for eac service class, say i, a QoS constraint exists on te andoff call blocking probability B i t and te new call blocking probability B i nt. From te perspective of a single cell, eac service class/call type combination is caracterized by its arrival rate, and departure rate. Let i n denote te arrival rate of new calls of service class i and μ i n be te corresponding departure rate. Similarly, let i denote te arrival rate of andoff calls of service class i, and μ i be te corresponding departure rate. Tese parameters can be determined by inspecting statistics collected by te base station in te cell and by consulting wit base stations of neigbor cells. Witout loss of generality we assume tat a cell as C cannels were C can vary depending on te amount of bandwidt available in te cell. Wen a call of service class i enters a andoff area from a neigboring cell, a andoff call request is generated. Eac call as its specific QoS bandwidt requirement dictated by its service traffic type attribute. Assume tat a service call of service class i requires k i cannels regardless of its call type. Anoter parameter tat is associated wit eac service class is service pricing wic determines te revenue tat te system receives wen te service is rendered. Te service provider would like to maximize te total revenue obtained by te system by means of optimal pricing for service classes and performing admission control functions subject to te bandwidt Proceedings of te 2t International Conference on Parallel and Distributed Systems (ICPADS'06) /06 $ IEEE

3 resources available in te system. Te system acieves total revenue maximization first in a distributed manner by maximizing eac cell s revenue for all service price combinations wit te consideration of QoS constraints and ten in a centralized manner by coosing te best price combination wic generates te maximum total revenue for te system. Tat is, for possible service price combinations, eac cell makes admission control decisions for new and andoff call requests in order to maximize te revenue received from servicing new and andoff calls in te cell. At te end, eac cell generates a pricing-revenue table to be used by a central entity to determine best pricing tat maximizes te total system revenue wile satisfying QoS. Te optimal pricing and te total revenue obtained by te system are inerently related to te pricing algoritm employed by te service provider. Wile many pricing algoritms exist [0], te most prevalent wit general public acceptance to date is te cargeby-time sceme by wic a user is carged by te amount of time in service. We assume tat suc a carge-by-time pricing sceme is adopted by te service provider suc tat a call of service class i as a carge-rate of v i per time unit. Tat is, if a call of service class i is admitted into a cell, and subsequently anded off to te next cell or terminated in te cell, a reward of v i multiplied wit te amount of time te service is rendered in te cell will be earned by te system. Tere is no distinction for andoff vs. new calls in pricing as long as te call is in te same service class. As suggested by empirical studies [, 2, 5] pricing canges of eac service class affect demands received for tese services. We assume tat QoS requirements are not affected by pricing cange as indicated in [2]. Tus, te determination of optimal pricing v i to eac service class is part of revenue optimization. Te performance model developed in te paper allows a service provider to calculate te revenue earned per unit time under an admission control algoritm by eac individual cell suc tat te revenue obtained by te system is maximized wile satisfying QoS constraints. 3. Metodology We consider a carge-by-time pricing sceme wit te goal to maximize te revenue obtainable by eac cell wile satisfying te QoS requirements. As suggested by empirical studies [, 2, 5] service pricing and demand for service type i are related by te following function: i i i i = a ( ν ) ε () were λ i and v i denote te arrival rate and pricing of service i wile a i and ε i are constants correlating λ i and v i. Te elasticity constant ε i determines te effect of pricing canges. A value greater tan predicts tat lower pricing would generate iger revenues, wile a value less tan predicts iger pricing would generate iger revenues. Te elasticity ε i value can be determined by analyzing statistical data collected. However, ε i sould be greater tan as suggested by [, 2, 5] reflecting te fact tat lower pricing would stimulate iger demand or iger arrival rates for te service provided, and consequently generate iger revenue. Te proportionality constant a i differs from cell to cell and can be calculated from Equation once te reference arrival rates (λ i ), te current price (v i ) and te elasticity constant ε i are known troug statistical data. Te total revenue R T generated by eac cell is te sum of te revenue generated from eac service class: R T = R + R n + R 2 + R 2 n (2) Here R represents revenue earned from servicing class andoff calls, R n represents revenue earned from servicing class new calls, and so on. Here we note tat pricing of a service class implicitly determines te arrival rate of tat service class based on Equation, wic in turn affects te revenue obtainable by te system. If we lowered pricing of a service class, te arrival rate of tat service class would increase. Since all service classes in a cell sare bandwidt cannels, if we lowered pricing of all service classes wit te intent to increase revenue, QoS requirements would be violated because of system overload. Tus, te searc for optimal prices to maximize te system revenue wile satisfying QoS is a combinatorial problem. Our approac is to calculate te maximum revenue obtainable as a result of applying a call admission control algoritm wen given 5 parameter values for eac service class i, namely, i n, μ i n i, μ i and v i, and use te revenue obtained as te objective function to guide te searc process. Since pricing canges under te carge-by-time sceme are often incremental so tere are not too many possibilities to searc for te optimal combination. Hence, our approac is to exaustively searc all possible combinations of [v i,min, v i,max ] for all service classes and look for te best combination of service class prices tat would maximize te system revenue wile satisfying QoS. Specifically for eac service class S i we obtain a 5- tuple reference parameter values ( i n, μ i n i, μ i, v i ) as te initial state. Ten we determine te pricing range [v i,min,v i,max ] for te service class suc tat v i,min and v i,max are determined as minimum and maximum Proceedings of te 2t International Conference on Parallel and Distributed Systems (ICPADS'06) /06 $ IEEE

4 pricing acceptable by te service provider and customer base. For eac service class S i were i {,, n}, we determine β i + prices wit δ i equal increments between v i,min and v i,max by using te following formula: i j i i v v j i { n} j { },,min = + δ 0,.., & 0,.., β i (3) were i i, min i, max i δ = ( v v ) β (4) Te number of possible combinations to searc for optimal pricing, denoted by η, is tus equal to: η = (β +) (β 2 +) (β n +) (5) Te predicted new call arrival rate of te j t price increment for S i is given by: i, j i i, j ε λ ( ) i n = a v (6) Here we note tat ε i remains te same wile a i differs from one cell to anoter. Te predicted andoff call arrival rate of te j t price increment for S i is given by: i, j i, j i λ = f λn (7) were ƒ i denotes te ratio between te statistically determined reference andoff call arrival rate and reference new call arrival rate for S i, given by: i, current i, current i f = λ λn (8) Note tat ƒ i is a constant because andoff requests coming into eac cell are modeled as te sum of te andoff requests coming into te reference cell from neigboring cells. Equation (7) olds as long as te arrival rate increase or decrease in neigboring cells generates proportional increase or decrease on te andoff rate coming into te reference cell from tese cells. For all possible combinations, eac of wic generates a new 5-tuple ( i,j n, μ i n i,j, μ i, v i,j ), we determine te revenue generated under a call admission control algoritm and store all te revenue values obtained in an n-dimensional revenue table were n denotes te number of service classes. Tis calculation procedure is done periodically by eac cell. Tables in all te cells are collected and merged to determine global optimal pricing tat would maximize te overall system revenue (sum of revenue from individual cells). Below we illustrate ow to build suc a table in individual cells based on tis metodology and describe a ybrid call admission control algoritm integrated wit pricing for revenue optimization. Later in Section 6, we discuss ow tese tables can be integrated to find global optimal pricing. 4. Admission Control Integrated wit Pricing for Revenue Optimization wit QoS Guarantees To make te paper self-contained, ere we give a brief overview of partitioning and tresold-based call admission control algoritms integrated wit pricing as well as a ybrid algoritm developed in [4] for revenue optimization wit QoS guarantees. We utilize tese algoritms to calculate system revenue obtainable and determine optimal pricing based on te metodology discussed in Section 3. For ease of presentation, we assume tat tere are two service types, class (igpriority) and class 2 (low-priority), distinguised primarily by teir traffic type, i.e., real-time vs. nonreal-time. Our metodology can be easily applied to te case in wic more tan two service classes exist. Te traffic input parameters to our algoritm are n, μ n, and μ for class and 2 n, μ 2 n, 2 and μ 2 for class 2. A call admission control algoritm adopted (among te tree) will be executed by eac individual cell to generate te system revenue obtainable wile satisfying QoS constraints expressed in terms of B t, B 2 t, B nt, and B 2 nt, wen given carge-by-time pricing of and 2 for classes and Partitioning Admission Control A partitioning call admission control policy divides te total number of cannels in a cell into several fixed partitions wit eac partition specifically reserved to serve a particular service class (real-time vs. non-real-time) and call type (new vs. andoff). In our system, te total number of cannels, C, is divided into C, C n, C 2, and C 2 n cannels for ig-priority andoff calls, ig-priority new calls, low-priority andoff calls, and low-priority new calls, respectively. Let (n, n n, n 2, n 2 n) be te numbers of calls corresponding to te four fixed partitions denoted by (C, C n, C 2, C 2 n). Ten n k = C, n nk = C n, n 2 k 2 = C 2, and n 2 nk 2 = C 2 n suc tat C + C n + C 2 + C 2 n = C. Te optimization problem for te partitioning algoritm is to identify te best partition (C, C n, C 2, C 2 n) tat would maximize te cell s revenue wile satisfying te imposed QoS constraints defined by: B < B t, B n < B nt, B 2 < B 2 t, B 2 n < B 2 nt (9) A partitioning solution is legitimate if Condition (9) is satisfied. Since no saring is allowed among partitions, te system beaves as if it is managing four concurrent subsystems, eac of wic beaves like an M/M/n/n queue. Te call dropping probabilities for andoff calls for various service classes (i.e., B and B 2 ) and te blocking probability for new calls for various service classes (i.e., B n and B 2 n) can be determined easily by calculating te probability of te partition allocated to serve te specific calls being full. We can calculate te revenue generated per unit time by te partition reserved to serve only ig-priority andoff calls by associating a reward of i * v for state Proceedings of te 2t International Conference on Parallel and Distributed Systems (ICPADS'06) /06 $ IEEE

5 i in te M/M/n /n queue. Te same way applies to oter partitions. Specifically, we can compute te revenue per unit time to te cell by PR(C,, n, 2, 2 n) = PR + PR n+ PR 2 + PR 2 n were te notation PR(C,, n, 2, 2 n) is used to stand for te revenue earned by te partitioning algoritm as a function of C,, n, 2, 2 n (wit oter parameters not listed), wile PR, PR n, PR 2, and PR 2 n stand for te revenues generated per unit time due to ig-priority andoff calls, ig-priority new calls, low-priority andoff calls, and low-priority new calls, respectively, as given by (only PR is sown below since expressions for oters are similar): PR = n i= λ i! μ iv j n λ + j= j! μ 4.2 Tresold-Based Admission Control i (0) In te tresold-based admission control algoritm, we select a tresold C T to separate class from class 2 based on te service type, i.e., real-time vs. non-real time. Te meaning of te tresold is tat wen te number of cannels used in te cell exceeds C T ten new or andoff calls from service class 2 (lowpriority) will not be admitted. Witin eac service class, we furter create tresolds to differentiate andoff from new calls suc tat C T is te tresold for class ig-priority andoff calls; C nt is te tresold for class ig-priority new calls; C 2 T is te tresold for class 2 low-priority andoff calls; and C 2 nt is te tresold for class 2 low-priority new calls. Since we give andoff calls a iger priority tan new calls, te following additional conditions must also be satisfied, C nt C T, C T C T, C 2 nt C T, and C 2 T C T. A tresold-based admission control integrated wit pricing for revenue optimization wit QoS guarantees tus aims to find te optimal set (C T, C nt, C 2 T, C 2 nt) satisfying te above conditions tat would yield te igest revenue wit QoS guarantees. We ave analyzed te tresold-based admission control algoritm by using an SPN model [4] to compute B i and B i n of class i. A legitimate solution from a tresold admission control algoritm must generate B n, B, B 2 n, and B 2 to satisfy te QoS constraints specified by Condition (9). We compute te revenue generated per unit time from te tresoldbased admission control algoritm to te cell by: TR(C,, n, 2, 2 n) = TR +TR n+tr 2 +TR 2 n. Here TR, TR n, TR 2, and TR 2 n stand for te revenues generated per unit time due to ig-priority andoff calls, ig-priority new calls, low-priority andoff calls, and low-priority new calls, respectively, given by: TR i = (- B i ) i v i / μ i, and TR i n = (- B i n) i n v i / μ i n. 4.3 Hybrid Partitioning-Tresold Admission Control Te ybrid partitioning-tresold admission control algoritm takes advantage of bot partitioning and tresold-based. Te ybrid algoritm divides te cannels into fixed partitions te same way as te partitioning algoritm does. However, to take advantage of multiplexing, a sared partition is reserved to allow calls of all service classes/types to compete for its usage in accordance wit te tresold algoritm. Te sared partition is available for use by a service class/type only if te partition reserved for tat service class/type is used-up. Let n s, n ns, n 2 s, n 2 ns be te numbers of ig-priority andoff calls, igpriority new calls, low-priority andoff calls, and low priority new calls, respectively, in te sared partition. Let C s be te number of cannels allocated to te sared partition under te ybrid algoritm. Ten, te number of calls of various service classes and types admitted into te sared partition are limited by C s cannels allocated to te sared partition, tat is, n sk + n nsk + n 2 sk 2 + n 2 nsk 2 C s subject to te constraint tat C + C n + C 2 + C 2 n + C s = C. Te QoS constraints are specified by Condition (9). Note tat te ybrid algoritm encompasses te partitioning algoritm as a special case in wic C s = 0 and also te tresold-based algoritm as anoter special case in wic C, C n, C 2, and C 2 n are all zero. Te performance model for te ybrid algoritm is composed of two sub-models: one for te partitioning algoritm wit te four fixed partitions C, C n, C 2, and C 2 n and one for te tresold-based algoritm for wic C = C s. Since te fixed partitions are modeled as M/M/n/n queues, te arrival rates into te sared partition from ig-priority andoff calls ( s), igpriority new calls ( ns), low-priority andoff calls ( 2 s), and low priority new calls ( 2 ns) are simply te spill-over rates from teir respective M/M/n/n queues, e.g., n λ n! μ () λ = λ s j n λ + j = j! μ Here only s is sown since expressions for ns, 2 s, and 2 ns are similar. From te perspective of te sared partition, te arrival rates are tus s, ns, 2 s, and 2 ns and te total number of cannels available is C s wit all oter Proceedings of te 2t International Conference on Parallel and Distributed Systems (ICPADS'06) /06 $ IEEE

6 parameters remained te same. Hence we compute te revenue generated per unit time from te ybrid admission control algoritm to te cell by te sum of revenue earned from te fixed partitions plus tat from te sared partition, i.e., HR(C,, n, 2, 2 n) = PR(C-C s,, n, 2, 2 n) + TR(C s, s, ns, 2 s, 2 ns). Te optimization problem for te ybrid algoritm is to identify te best partition (C, C n, C 2, C 2 n, C s ) tat would maximize te cell s revenue subject to te imposed QoS constraints defined by Condition (9). 5. Numeric Data and Analysis We present numerical data for η=6x8=48 possible future pricing combinations by applying te revenue formulas derived for partitioning, tresold-based and ybrid admission control algoritms. Tese possible future pricing combinations are relative to current pricing suc tat te price increment/decrement is considered acceptable to te service provider. We compare performance caracteristics of tese admission control algoritms wit QoS guarantees wit pysical interpretations given. Te analysis considers two classes. Class (real-time) demands more resources wit iger QoS constraints tan class 2 (non-real-time). Tus, class as more stringent call blocking probabilities tan class 2, as well as iger pricing. Te input parameters are C,, μ, n, μ n, 2, μ 2, 2 n, μ 2 n,, 2, a, a 2, ε, ε 2, k, k 2, B t, B 2 t, B nt, and B 2 nt. We set C=80, k =4 and k 2 = for a typical cell in mobile wireless networks to service real-time and non-real-time traffic suc tat tere are 80 cannels in te cell wit a class call (real-time) consuming 4 cannels and a class 2 call (non-real-time) consuming cannel. We assume tat te statistical data collected for te reference cell would provide =5.0, μ =.0, n=2.0, μ n=.0, 2 =4.4, μ 2 =.0, 2 n=4.4, μ 2 n=.0, and te current pricing is =80, 2 =2. Similarly, we set elasticity constants to values greater tan, ε =.3 and ε 2 =.7 for class and class 2 calls, respectively. We apply Equation (6) to calculate proportionality constants a =600 and a 2 =300 for class and class 2 calls, respectively for our reference cell. We vary service prices in te range [50, 00] for and [6, 20] for 2 and te resulting call arrival rates are calculated by using Equations 6 and 7. Figure, Figure 2, and Figure 3 sow te maximum revenue obtained by partitioning, tresoldbased and ybrid admission control algoritms. Class and class 2 pricings are sown on y and x axis, respectively. Te revenues obtained for only te legitimate solutions are sown on z axis. Figure indicates tat te revenue obtainable increases as te anticipated arrival rate increases as a result of lowering te prices, as long as te QoS constraints can still be satisfied. Neverteless, as and n increase to 2.4 and 6.0 for v =70.0, te partitioning admission control algoritm fails to yield a legitimate solution because te workload is too eavy to satisfy te imposed QoS constraints. Likewise as 2 and 2 n increase to 8.7 wen v 2 =8.0, te algoritm fails to yield a legitimate solution. Te maximum revenue is establised at v =80.0 and v 2 =0.0 as tese prices result in te igest arrival rate tat can be andled wit QoS guarantees. Te best partition reserved to andle te traffic generated for (v =80.0, v 2 =0.0) is (C =0, C n=5, C 2 =, C 2 n=9) wile te best partition reserved to andle te traffic generated in te current system for (v =80.0, v 2 =2.0) is (C =0, C n=5, C 2 =0, C 2 n=0). As te arrival rate of class 2 becomes iger due to te price cut of v 2 from 2.0 to 0.0, partitioning admission control in tis case reduces C 2 n and increases C 2 to satisfy te iger QoS requirement of class 2 andoff calls V V Revenue Rate Figure : Maximum Revenue obtained by Partitioning Admission Control Algoritm V V Revenue Rate Figure 2: Maximum Revenue Rate obtained by Tresold Admission Control Algoritm. Figure 2 sows tat te igest revenue is acieved wen v =80.0 and v 2 =6.0. To satisfy QoS requirements of class calls, te system applies tresolds C nt=80, C T=80, C 2 nt=76, C 2 T=76 to andle iger class 2 traffic generated for (v =80.0, Proceedings of te 2t International Conference on Parallel and Distributed Systems (ICPADS'06) /06 $ IEEE

7 v 2 =6.0), as opposed to all tresolds being set to 80 for te current system wit (v =80.0, v 2 =2.0). By saring resources among service classes and controlling te effect of iger class 2 arrival rates by applying lower tresold values, tresold-based admission control performs better tan partitioning admission control. Figure 3 illustrates te maximum revenues obtainable wit ybrid admission control wit QoS guarantees as a function of v and v 2. Hybrid admission control reserves (C =7, C n=3, C 2 =, C 2 n=, C s =38) to andle te traffic generated for te current system wit (v =80.0, v 2 =2.0). To andle iger class and class 2 arrival rates due to optimal pricing at (v =60 and v 2 =8), it reserves (C =6, C n=, C 2 =, C 2 n=0, C s =5) and applies a lower tresold to class 2 calls in te common partition. In response to a iger class and class 2 arrival rates, ybrid admission control tends to increase te size of C s partition V V Revenue Rate Figure 3: Maximum Revenue obtained by Hybrid Admission Control Algoritm. Comparing Figure 3 wit Figures and 2, it is clearly seen tat te ybrid admission control algoritm outperforms bot partitioning and tresold based algoritms. Te multiplexing power of te sared partition is clearly demonstrated by te fact tat ybrid always significantly outperforms partitioning in terms of revenue obtainable over a wide range of class and class 2 service call arrival values, wile being able to sustain a iger workload and provide QoS guarantees. We observe tat te performance of tresold-based admission control is comparable to ybrid admission control until bot class and class 2 arrivals become very ig ( =7.3, n=2.9, 2 =8.7, 2 n=8.7 anticipated wen v =60 and v 2 =8). At tese ig arrival rates, tresold-based admission control fails to yield a legitimate solution compared wit ybrid admission control. We attribute te superiority of ybrid admission control over partitioning and tresold-based admission control to te ability to optimally reserve dedicated resources for ig-priority classes troug fixed partitioning to reduce interference from low-priority classes, and to optimally allocate resources to te sared partition in accordance wit tresold-based admission control to exploit te multiplexing power for all classes. We conclude tat te cannel allocation made by te ybrid admission control algoritm represents te best possible way to andle iger arrival rates and to allow a wider ranger of pricing for revenue optimization. Also ybrid admission control generates maximum revenue obtainable wile satisfying QoS requirements for te example cell. In order to optimize te total system revenue, eac cell first follows te procedure described above to calculate te local maximum revenue obtainable wit QoS guarantees for eac possible future pricing combination (e.g., v =80.0, v 2 =0.0) under consideration compared to current reference pricing (e.g., v =80.0, v 2 =2.0). A table is generated by eac cell tat lists te local maximum revenue obtainable for eac future pricing tat yields a legitimate solution (i.e., te QoS requirements are satisfied). Ten a merging process is used to merge tables generated by individual cells to determine global optimal pricing and te associated maximum revenue obtainable by te system. Tis process first eliminates any future pricing combination tat fails to yield a legitimate solution for any of te cells. Ten for oter future pricing combinations for wic a legitimate solution exists for eac cell, te maximum revenue obtainable by te system is calculated by summing all local maximum revenues earned by all te cells. Te future pricing combination tat yields te maximum aggregate revenue is declared as global optimal pricing among all suc future pricing combinations. 6. Applicability and Summary In tis paper we proposed and analyzed a metodology to determine optimal pricing for revenue optimization wit QoS guarantees in wireless mobile networks, utilizing admission control algoritms integrated wit pricing. Our metodology is based on te idea tat te maximum revenue generated by a cell wile satisfying QoS depends on bot te admission control algoritm cosen by te system and pricing applied to eac service class. To determine optimal pricing, we first applied an empirical function tat relates pricing wit demand so as to predict te cange to te arrival rate of a service class wen its price canges. Ten we tested a range of future pricing for eac of te multiple service classes, eac combination of wic generates a new set of demand arrival rates as Proceedings of te 2t International Conference on Parallel and Distributed Systems (ICPADS'06) /06 $ IEEE

8 input to feed into a call admission control algoritm to calculate te revenue generated wit QoS guarantees as te objective function. We discovered tat a ybrid sceme combining te benefits of bot partitioning and tresold-based performs te best in terms of revenue maximization wit QoS guarantees and optimal pricing tat maximizes te revenue earned. To apply te results obtained in te paper, eac cell would independently collect statistical data periodically to estimate a set of reference arrival and departure rates of new/andoff calls of various service classes based on statistical analysis [4]. Eac cell ten determines te proportionality constant a i for eac service class by applying Equation based on current pricing, te arrival rate and elasticity constant of eac service class. Later eac cell determines new/andoff call arrival rates for a range of pricing for eac service class. Finally, for eac price combination, eac cell calculates optimal (C, C n, C 2, C 2 n, C s ) based on ybrid admission control for revenue optimization wit QoS guarantees, and reports te results in a table to a central entity wic collects and analyzes revenue tables from all te cells in te system. To guarantee QoS, te future pricing combination tat satisfies QoS constraints in all of te cells wile maximizing te aggregate revenue would be cosen as te winner for optimal pricing. Tis work is only a beginning of te design concept of utilizing admission control algoritms cognizing revenue optimization wit QoS guarantees to determine optimal pricing in wireless networks. Possible future researc directions extending from tis work include (a) extending te matematical analysis to te case in wic cells are eterogeneous and formalizing global pricing in tis case; (b) considering oter pricing scemes (flat rate or carge by connection) and investigating optimal resource allocation settings under wic ybrid admission control can yield te igest revenue wit QoS guarantees; (c) considering oter revenue collection model, e.g., revenue is collected on call termination or revenue is lost wen a call is terminated prematurely. References [] M. Aldebert, M. Ivaldi, and C. Roucolle, Telecommunications demand and pricing structure: An economic analysis, 7 t Conf. Telecommunications Systems: Modeling and Analysis, Nasville, TN, 999, pp [2] A. Bouc and M.A. Sasse, Wy value is everyting: A user centric approac to internet quality of service and pricing, IWQoS, Karlsrue, Germany, June 200. [3] I.R. Cen and C.M. 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