integration of pricing with call admission control

8/4/2019 Integration of Pricing With Call Admission Control

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Integration of Pricing with Call Admission Controlfor Wireless Networks

Jiongkuan Hou, Jie Yang and Symeon PapavassiliouNew Jersey Center for Wireless TelecommunicationsDepartmentof Electrical and Computer Engineering

New Jersey Institute of Technology, Newark, NJ 07102,[email protected], [email protected],[email protected]

Abmuct- Traditional CAC schemes that mainly focus on thetrade off between new call blocking probability and handoff callblocking probability can not solve the problem of congestion inwireless networks. In this paper we investigate the role of pricingas an additional dimension of the call admission control process inorder to efficiently and effectively control the use of wireless net-work resources. First we prove that for a given wireless networkthere exists a new call arrival rate which can maximize the totalutility of users. Based on this result and observation we proposean ntegrated pricing and call admission control scheme, where theprice is adjusted dynamically based on the current network condi-tions, n order to alleviate the problem of congestion. We comparethe performance of our approach with the corresponding results ofconventional systems where pricing is not taken into considerationin the call admission control process. These performance resultsverify the considerable improvement that can be achieved by theintegration of pricing in the call admission control process in cellu-lar networks.

Keywords-Call Admission Control, Pricing, Wireless Networks

1 IntroductionHE rising demand for mobile communication services isT ncreasing the importance of efficient use of the limited

bandwidth and frequency spectrum. In recent years considerableefforts have focused on the Channel Allocation and Call Ad-mission Control (CAC) problems and many schemes that rangefrom static to dynamic strategies have been proposed in liter-ature [3 , 61. Call Admission Control is a provisioning strategyused to limit the number of call connections into the networks inorder to reduce the network congestion and provide the desiredQuality of Service (QoS ) to users in service.

New call blocking probability and handoff call blocking prob-ability are two important connection level QoS parameters.Handoff calls are commonly given a higher priority since a callbeing forced to terminate during the service is more annoyingthan a call being blocked at its start. Various handoff priority-based CAC schemes have been proposed in literature includingGuard Channel Schemes, Queuing Priority Schemes and Chan-nel Borrowing Schemes. These research efforts have focusedon how to adjust the tradeoff between new call blocking prob-

ability and handoff call blocking probability. Within a certaindynamic range of call arrival rate, these schemes can improvethe system performance. However, we can observe from the re-sults presented by these research efforts that w ith the increase ofcall arrival rate, both the new call blocking probability and thehandoff call blocking probability increase. W hen the call arrivalrate is temporarily very high (for example in busy hours), nomatter how the parameters are adjusted, these schemes can notguarantee the Q oS to users.The m ain reason of degradation of QoS stems from the factthat resources in a wireless network, such as timeslots, codeand power, are shared by all the users. When on e user is ad-mitted into the network, it will cause QoS degradation to otherusers. In general we can observe that the most serious QoS vi-olation occurs when the system is congested. However, the cur-rent CAC schemes can not avoid congestion, because they donot provide incentives for users to use the channel resources ef-fectively. In broadband networks, pricing schemes are widelydiscussed as means for traffic management and congestion con-trol [ l ,41. Through pricing, the network can send signals to th eusers, providing incentives that influence their behavior. Thisprovides another dimension for the design of CAC schemes thatcan be used in wireless networks as well. In this paper we inte-grate pricing with CAC to address the problem of congestion.The remaining of this paper is organized as follows. Section 2provides the description of the proposed integrated pricing andcall admission control scheme, while section 3 includes the per-formance evaluation of our proposed approach and scheme.2 Integrating Pricing and Call Admission Con-

trolNetwork users act independently and sometimes selfishly,without considering the current network traffic conditions.

Hence system overload situations are unavoidable. If each userrequests the resources that maximize h ish er individual level ofsatisfaction, the total utility of the community will decrease, sothat there must be some mechanism to provide incentives forusers to behave in ways that improve overall utilization and per-formance. In commercial networks, this can be most effectivelyachieved through pricing.

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Network pricing has recently been embraced by researchers inthe multi-service broadband networks [1,4] ot only as an eco-nomic issue and element, covering the infrastructure expensesand operational expenses through charging the end users, butalso as a resource m anagement issue. T he aggregate traffic loadon a wireless network is the result of many users' individual de-cisions about whether and how to use the network, and thesedecisions are affected by the incentives these users encounterwhen using the resources of a wireless network. These incen-tives can take many form s; one of the most important incentivesis the monetary incentive [11-raising unit price that could makesome of the users request less resources.2.1 OptimalNew Call Arrival Rate

If we consider the wireless network resources as a publicgood, the best policy to shar e this goo d is the one that can max-imize the total user utility [4]. n terms of economics, utilityfunctions describe users' level of satisfaction with the perceivedQuality of Service [l , 41; he higher the utility, the more sat-isfied the users. In general, utility function characterizes howsensitive users are to the changes in QoS. It is sometimes use-ful to view the utility functions as of m oney a user is w illing topay for certain QoS. Som e utility function s have been suggestedin literature in order to model customer behavior and evaluatepricing policies. For example, in [I], Cocchi e t ul. proposedutility function for Email applications to be a decreasing func-tion of both average delay and the percentage of messages notdelivered within a delay bound of five minutes. In this paper wedefine utility function a s function of call blocking probabilities,which represent the main QoS metrics in cellular networksIn this section, we prove that there exists a new call arrivalrate where the total user utility is maximized and therefore thenetwork resources are optimally utilized. We consider a wire-less network that carries out Guard Channel CAC scheme; thearrival process of new calls is assumed to be Poisson and thechannel holding time is assumed to have negative exponentialdistributions. The parameters of the syste m are given, includ-ing the total number of channels, the number of guard channels,the average new call channel holding time an d average handoffcall channel holding time, so that the performance of the sys-tem depends on the new call arrival rate (A and handoff callarrival rate (Ah) [3] .Lin er al . also proved in [6 ] hat handoffcall arrival rate is a function of new call arrival rate and othersystem parameters. Therefore, in the following we study howthe total utility changes with the change of new call arrival rate.Our analysis is based on the following definitions, observationsand assumptions.Definition 1. We define the average number of admitted users( N ) as a function of new call arrival rate, i.e. N = f(A,).f A is a differentiable and m onotonically increasing concavefunction of A [5]. herefore:

Definition 2. We define the Quality of Service metric Pb as aweighted sum of new ca ll blocking probability ( p nb ) and hand-

off call blocking probability (Phb):pb = f f p n b k PPhb ( 2 )

where a and p are constan ts that denote the penalty associatedwith rejecting new calls and handoff c alls respectively, with /3 >a to reflect the higher cost to block a handoff call. Because bothP,b and Phb are monotonically increasing convex functions ofA [ 5 ] ,Pb is also a monotonically increasing convex function ofA

Pb = g(A,) with (3)g ( M > 0; d ( A , ) > 0; g"(A,) > 0 (4)

In the following, we describ e the general properties and charac-teristics of the user utility function. As m entioned before, utilityfunction models network users' preference. We argue that whenPb increases, users w ill suffer more call blockings and the levelof user satisfaction decreases. We also note that when Pb issmall, the satisfaction degradation cau sed by the increase of Pbis not significant; as Pb becomes large, the satisfaction degra-dation will be substantial. There fore, throughout this paper wemake the following assumption:Assumption 1. The utility function of a single user ( U , ) is adifferentiable and m onotonically decreasin g concave function ofthe QoS parameter Pb.That is:

U , = h(Pb) with ( 5 )/&(Pa) 0; h'(%) < 0; h"(Pb)< 0 ( 6 )

Note that U , achieves maximum value at Pb = 0, whichmeans that if the blocking probability is 0% the user has thehighest level of satisfaction. Mor eover, although different ap-plications may have different QoS requirements and thereforedifferent utility function s, without loss of generality we can as-sume that there exists a ,Tax such that U,(%) = 0 for allPb 2 PbmaZ. his means that when call blocking probabilityis very high, the user satisfaction is zero. In a realistic wirelesssystem P r a x epresents the threshold value (maximum) of Pbthat can be tolerated so that the Qu ality of Serv ice is consideredacceptable. Based on the abov e definitions and assumptions wecan prove the follow ing theorem:Theorem1For a given wireless network, th ere exists an optimalnew call arrival rate that maximizes the total utility U , where Uis defined as:

U = N x U , = ma)x h[g (A , ) ] (7)Pro05 (i)

V(A, = 0) = 0 (8)This is the case that no user is in the system, i.e. N = 0, hencethe total utility is zero;

(ii)U(A , = = 0 (9)

where Araxs the new call arrival rate that satisfies g(Arax)=Ppaz , t which point single user's utility becomes zero. This

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corresponds to the case that the netw ork is congested becausea large number of users are competing for the limited channelresources and as a result no user is satisfied with the QoS.(iii) From the above definitions and assumption, we have- OdAZ,

which means that U is a concav e function of new call arrival rateAn.From (i) (ii); and by Rolle Theorem we conclude that:

Combining this result with equation (lo), we can sufficiently0

It should be noted here that maximum total user utility alsomeans that channel resources are most efficiently utilized. WhenA, < A i , users can get a better quality than their QoS require-ments, but some channel resources are wasted and from the per-spective of the serv ice provider, this means less revenue. On theother hand, when A, > A a large number of users are blockedwhen trying to initiate their calls or w hen trying to handoff toanother cell in the middle of a call, which means that the QoSdegrades and may becom e unacceptable. In this case, althoughon average, more channels are used, because of the increasinghandoff failures, it is hard for a user to finish hish er call suc-cessfully and as a result the effective utilization of channelresources is low. Therefore, we can say that A, = A i s a pointwhere the number of satisfied users is maximized and channelresources are most efficiently used. When A, > A i , both thetotal user utility and the QoS decrease with any further increaseof A, and we may say that the cell enters the congestion state.From the view point of QoS guaran tee, it is ideal for a system tooperate at the optimal traffic load (Ah ) or below.

ensure a maximum of U at A, = A

2.2 SystemModelIn current wireless networks users are charged w ith fixed rate

or based on the time of the day. The m ajor advantage of theseschemes is that the billing and accounting processes are simple.However, the price is independent of the current state of the net-work. Such systems can not provide enough incentives for usersto avoid congestion, and furtherm ore can not react effectively tothe dynamic and sometimes unpredictable variation of the net-work usage and conditions. Th is paper proposes a new schemewhich integrates the congestion pricing with call admission con-trol to address this problem. Figure 1provides a schematic rep-resentation of the proposed approach and m odel.The system is composed of two functional blocks: Pricingblock and CAC block. H ere we use a guard channel scheme atthe CAC block. The pricing block works as follows: when thetraffic load is less than the optimal value, A, < A i , a normalprice is charged to each user. The no rmal price is the price that isacceptable to every user. When the traffic load increases beyondthe optimal value, dynamic pea k hour price will be charged tousers who want to place their calls at this time. It should be

Handoff Callphb t Blmkine

Figure 1. Integration of pricing scheme with calladmission control

noted here that according to our scheme the decision about thepeak hour fee is based on the network conditions. T his meansthat the price is continuously and dynam ically adjusted accord-ing to the changes in the system condition as the system evolves.During the period that dynam ic peak hour price is charged tousers, if some users are not w illing to accept the extra charge,they will choose not to place their calls at this time. T hese userscan make their calls later when the network conditions changeand the price decreases. This generates another traffic stream tothe pricing block-the retry traffic, whose arrival rate is denotedby A, in figure 1.2.3 Setting Price According to TrafficLoad

We define the system function of pricing block ( H ( t ) ) s thepercentage of the incoming users that will accept the price att im et , i . e.(12)

where Ai,(t) is the rate of inp ut traffic to CACblock. The con-gestion pricing block should be designed in such a way that byadjusting H ( t ) according to current traffic condition, A a ( t ) al-ways meets the following requirement:

( A n ( t )+ A r ( t ) ) H ( t )= Ain( t )

A i , ( t ) L A: (13)where A is the optimal new call arrival rate we obtained insection 2.1. This requirement guarantees that the cell will notbe congested and therefore the quality of service of the callersin service can be guaranteed.As m entioned before, m onetary incentive can influence theway that users use resources and is usually characterized bydemand functions. Dem and function describes the reaction ofusers to the change of price. Different demand functions havebeen proposed in literature. In this paper we use the followingdemand function [2].

D b ( t ) ]= e- ($+I2 P ( t ) 1 o (14)where po is the normal price, p ( t ) s the price charged to users attime t which is the sum of norm al price and extra peak hour price(if applicable). D[p( t ) ] enotes the per centage of users that willaccept this price. The control function of H ( t ) is realized byusers reaction to the current price, therefore we have:

H ( t )= Db(t)l (15)

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Combining equations (12) through (15) we have

004-

&P5, OO Ja%"":02too15.2 0 0 1 -

0 0 0 5 -

0

This is the price that should be set at time t in order to obtain thedesired QoS.

--

4 8 18 242

3 Performance AnalysisIn this section we evaluate the performance of the proposedintegrated pricing and call admission control in te? of con -gestion prevention. We observe that our proposed integratedscheme achieves to alleviate the system congestion occurrences

and meet the QoS requirements of the users in service, whileother conventionalCAC schemes fail to do so.In section 3.1 we describe in detail the basic assumptionsabout the system under consideration. In section 3.2 we com-pare the results of conventional guard channel scheme and theproposed integrated scheme.

3.1 Model and AssumptionsThe parameters used throughout our performance evaluation

are as follows:(1). Each cell is assigned C = 40 channels, and 2 of them are

used as guard channels.(2). Each call requires only one channel for service.(3). The arrival of new calls initiating in each cell forms a Pois-son process with rate An( t ) . The variation of new call

arrival rate during a 24-hour period used through out ourstudy is shown in figure 2.(4). For both new calls and handoff calls, the call duration times

are exponentially distributed with mean 240 seconds, andthe cell dwell times are also exponentially distributed withmean 120 seconds.(5). Parameters a nd p in equation (2) are set to be 5 and 2respectively, which m eans that we treat handoff calls twicemore impo rtant than new calls.(6). In the following numerical study, we use the following util-ity function

The optimal new call arrival rate for this system is A =0.12 calYsec and at this point the QoS metric is Pb = 1%Based on the an alysis in section 2.1, this is the optimal op-eration point of the system in the sense that at this point,the total user utility can be maximized given that the QoSrequirement (e. g. Pb 5 0.01) is met.

0 8

0 4 -

Figure 2. Input new call arrival rate as function oftime

- 1 I

Figure3.Call blocking probabilityof conventionalsystem

3.2 Numerical Results and DiscussionFigur e 3 shows the results of conventional system that do notuse pricing in the call admission control process to control thetraffic. From this figure, we can find that when traffic load is

heavy (e. g. in noon hours), Pb can be as high as 4.2%. Thisvalues is far beyond users' minimum QoS requirement 1%, ndtherefore we can conclude that cells are seriously congested dur-ing this period.The corresponding results of the proposed scheme are shownin figures 4through 6. Figure 4shows how the price is adjustedaccording to the change of offered traffic load. F or the given newcall arrival variation, when the offered traffic load into the pric-ing block is more than the optimal new call arrival rate (6:30AMto 11:OOPM in figure 4(a) ), the ratio p ( t ) / p obecomes more than1,which means that the pricing mechanism comes into effectand the peak hour prices are charged to users. The heavier thetraffic load, the higher the price, so that the less the percentageof users that would like to access the network, as suggested byequation (16). In o ur scheme, there is no central control mecha-nism to determ ine which user can access the channel resources.

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2.5..... -3q7- . .- ,&re _ - - - - _6 -

a

4 I2 16 20 24M o l h g Y lFigure4. Set price according to traffic condition

Each b ase station just sets the price according to current traf-fic load of the cell, and it is the individual users decision onwhether to accept this price or not that controls the input traf-fic load to the system at this time. This implicitly implementsa distributed user-based prioritization schem e where the priorityis set by users reaction to current price.Figure 5 shows the traffic rates at different points of the sys-tem.From this figure we observ e that the inputs to theCACblockare always lower than the optimal rate, i. e. Xin(t) < A i , whichmeans that the cell is not congested. The reason is that we adjustthe price based on th e user dem and function and current trafficload (equation (16)) so that the price is always set to the ap-propriate value to guarantee that the traffic rate going throughthe pricing block is less than the optimal value. This resultis justified by figure 6. From this figure we observe that theweighted call blocking probabilities are always lower than 1%,which means the Qo S of the users who accept current price canbe guaranteed. Comparing figure 5with figure2we ob serve thatour pricing block works like a traffic shaper, which can movepart of the peak hour (630AM o 6:OOPM infigure 5(a)) trafficto relative ly idle hours tha t follow th e peak (6:OOPM to 11:OOPMin figure 5a)). Th e traffic being m oved is composed of usersthat will not accept peak hour price.

rmr0llhedartFigure 5. Traffic rates at different points

References[l]R.Cocchi, S. Shenker, D. Estrin and L . Zhang, Pricing inComputer Networks: Motivation, Formulation and Exam-ple, IEEDAC M Transactions on Networking, Vol. 1,No. 6,December 1993.[2]P.C. ishbum and A. M. Odlyzko, Dy namic Behavior ofDifferential Pricing and Quality of Service Options for th eInternet,ICE98, pp. 128-139[3] J. Hou and Y. Fang, Mobility-based Channel Reservation

Scheme for Wireless Mobile Networks, Proceedings ofZEEE WCNC 2000, Chicago, September 2000.[4]H. i, J. Y. Hui and E. Karasan, GoS-Based Pricing andResource Allocation for Multimedia Broadband N etworks,Proceedings of IEEE INFOCO M 1996,pp . 1020-1027.[5 ] K. R. Krishnan, The Convexity of Loss Rate in an Erlang

Loss System and Sojourn in an Erlang Delay System withRespect to Arrival rate and Service Rate, ZEEE Transac-tions on Communications, Vol. 38, No. 9, September 1990.[6]Y. B. Lin, S . Mohan and A. Noerepel, Queueing PriorityChannel Assignment Strategies for PCS Hand-Off and Ini-tial Access, IEEE Transactions on Vehicular Technology,Vol. 43,No . 3,August 1994.

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Figure 6. Call blocking probability for proposedscheme

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integration of pricing with call admission control

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