A General Call Admission Policy for Next Generation WirelessNetworks

Hamid Beigy and M. R. Meybodi*

Soft Computing Laboratory

Computer Engineering and Information Technology Department

Amirkabir University of Technology

Tehran, Iran

{beigy, meybodi}~ce.aut.ac.ir

Abstract

In this paper, we consider the call admission prob-lem in ne}.."tgeneration wireless networks, whichmust handles multi-media traffics. We first intro-duce a multi-threshold guard channel policy. Thelimiting behavior of this policy. is analyzed un-der the stationary traffic. Then we give an algo-rithm, which finds the optimal number of guardchannels, which minimi?:esthe blocking probabil-ity calls with lowest level of QoS subject to thehard constraint on the blocking probabilities ofother calls.

Keywords

Next Generation Wireless Networks, Call Ad-mission Control, Guard Channel Policy, Multi-Threshold Guard Channels

1. Introduction

During the last decade, there has been a rapidgrowth of wireless communication technology. Thenext generation wireless networks are expected toeventually carry multi-media traffics. In order tosupport such wide range of traffics on a network,the network must be capable of satisfying variousquality of service (QoS) requirements. The satis-fying QoS means that the various traffics shouldget predictable service from the available resourcesin the network. Since wireless spectrum remainsas the prime limited resource in the next gener-ation networks, hence, it is necessary to developmechanisms that can provide effective bandwidthmanagement while satisfying the QoS requirementfor incoming calls. In order to satisfy the QoS re-quirements, call admission control is needed. The

*This work is partially supported by IranianTelecommunication Research Center (ITRC),Tehran, Iran.

call admission control policies determine whethera call should be either accepted or rejected at thebase station and assign the required channel(s) tothe admitted call. In order to satisfy the level ofQoS for each type of call, the call admission con-trol policies usually use the prioritized methods.This priority is usually implemented through allo-cation of more resources to calls with higher levelof QoS [1]. Several call admission control poli-cies have been proposed to reduce the droppingof voice calls in wireless networks [2, 3, 4, 5, 6].

Suppose that the given cell has C full duplexchannels. The guard channel (GC) policy reservesa subset of channels, called guard channels, allo-cated to the cell for sole use of hando££calls {sayC - T channels) [2]. ¥lhenever the channel oc-cupancy exceeds a certain threshold T, the GCpolicy rejects new calls until the channel occu-pancy goes below the threshold. The GC policyaccepts handoff calls as long as channels are avail-able. If only the dropping probability of handoffcalls is considered, the GC policy gives very goodperformance, but the blocking probability of newcalls is degraded to a great extent. In order tohave more control on both the dropping probabil-ity of handoff calls and the blocking probability ofnew calls, limited fractional guard channel policy(LFG) is proposed [4]. The LFG policy reservesnon-integral number of guard channels for handoffcalls. The limited fractional guard channel policyuses an additional parameter 1f and operates thesame as the guard channel policy except when Tchannels are occupied in the cell, in which casenew calls are accepted with probability ra. In [6],uniform fractional guard channel policy (UFG) isintroduced, which accepts new calls with proba-bility of 1rindependent of channel occupancy. Theuniform fractional guard channel policy performsbetter than guard channel policy in low handofftraffic conditions. In [7],two traffic classes of voiceand transactions are considered and static and

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lot'l Symposium 00 Telecommunications (IST2003 ), 16-18 August, 2003 Isfahao-Iran

dynamic guard channel schemes are proposed tomaintain the upper bound of dropping probabil-ity of handoff transaction calls. In this approach,(C - T) guard channels are reserved for handoiItransaction calls, but new calls and handoiI voicecalls have the same priority. Thus, this scheme failsto maintain the upper bound for dropping proba-bility of handoiI voice calls.

All of the above mentioned call admission con-trol policies consider only one threshold to de-cide for accepting/rejecting of new calls. Thesepolicies fail when there is several classes of traf-fics with different level of QoS. In such cases, weneed multi-threshold scheme, which provides dif-ferent thresholds for different classes. In [8], dual-threshold reservation (DTR) scheme is given forintegrated voice/data wireless networks. In thisscheme, three classes of calls in ascending order oflevel of QoS are considered which are data calls,new voice calls and handoiI voice calls. The ba-sic idea behind the DTR scheme is to use twothresholds, one for reserving channels for hand-oiI voice, while the other is used to block datatraffic into the network in order to preserve thevoice performance in terms of handoff droppingand call blocking probabilities. DTR assumes thatthe bandwidth requirement of voice and data arethe same. The equations for blocking probabilities'of DTR are derived but no algorithm for findingthe optimal number of guard channels is given. In[9], a two-threshold guard channel (TTGC) pol-icy, which uses two sets of guard channels, is in-troduced in which three classes of traffics in as-cending order of level of QoS are considered. Thelimiting behavior of TTGC policy is analyzed un-der stationary traffic and an algorithm for findingthe optimal number of guard channels is given.

In this paper, the idea given in [9] is gen-eralized to multi-class traffics. In the proposedmodel, there are N classes of traffics each of whichwith different level of QoS. Each class may con-tain either new calls or handoiI calls but havingthe same level of QoS. For example, class 1 cancontain new voice calls and class 2 can containhandoiI voice and new data calls. Our proposed:nodel, referred to as multi-threshold guard chan-nel (MTGC) scheme, builds upon guard channelscheme by using N - 1 thresholds in which eachthreshold is used to reserve channels for satisfyingthe specified level of QoS for that class. The limit-ing behavior of MTGC is analyzed under station-ary traffics using one dimensional Markov chain.Then we give an algorithm that finds the optimalnumber of guard channels.

The rest of this paper is organized as follows:Section 2. presents the limiting behavior of multi-

threshold guard channel scheme under stationarytraffics. Section 3. gives an algorithm to find theoptimal value of thresholds and section 4. con-cludes the paper.

Multi-Threshold Guard Chan-nel Scheme

In this section, we first introduce the multi-threshold guard channel policy and then give theblocking probabilities of multi-threshold guardchannel policy. These blocking probabilities arecomputed based on the following assumptions.

2.

1. There are N class of calls in the network. Eachclass can contain either new calls or hand-oiI calls but having the same level of QoS.For example, class 2 can contain handoff voiceand new data calls and class 1 can contain

new voice calls. Every call requests only onechannel. Class k (for k = 1,2..., N) hasa level of QoS, qk, which must be satisfied.Without loss of generality, it is assumed thatql ~ qz ~ . .. ~ qN.Thus,the priorityofcallsfor class k (for k = 1,2. . . ,N - 1) is lessthanthe priority of calls for class (k + 1).

2. The arrival process of calls for class k (for k =1,2..., N) is Poisson with rate Ak. Let Ak =I:~k+1 Aj and ak = t-.

3. The channel holding time of calls for classk (for k = 1,2..., N) is ex-ponentially dis-

tributed with mean 11.";;1.Let p-l = I:~1 pjtand p = 4a..JJ

4. The time interval between two calls from a mo-bile computer is much greater than the meancall holding time.

5. Only mobile to fixed calls are considered.6. The network is homogenous.

The assumptions 2 through 4 have been foundto be reasonable as long as the number of mo-bile computers in a cell is much greater than thenumber of channels allocated to that cell. Thefifth assumption makes our analysis easier and thesixth one let us to examine the performance ofa single network cell in isolation. Suppose thatthe given cell has a limited number of full du-plex channels, C, in its channel pool. We definethe state of a particular cell at time t to be thenumber of busy channels in that cell, which isdenoted by c(t). In order to provide the spec-ified level of QoS for calls of each class, chan-nels which are allocated to the given cell are par-titioned into (N) subsets. In order to partitionthe channel sets, (N -1) thresholds, Tt,..., TN-1(0 < Tt ::; Tz ::; ... ::; TN-d are defined.Forthe sake of simplicity, we use two additional fixed

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Int'l Symposium on Telecommunications (IST2003 ), 16-18August, 2003 Isfahan-Iran

-

Algorithm MinBlock1. setTo +- -1, Tl +- T2 +- ... TN +- C2. if BN(T) ::; qN then3. return T4. end if5. for k +- N downto 2 do6. while (Tk-l > 0 and Bk(T) > qk ) do7. if not MinBlockCheck(T, k + 1) then8. set T +- T - E~-l9. end if10. end while11. end for12. if at least one of constraints q2,..., qN

isn't satisfied then13. return Number of channels is too small.14. end ifend Algorithm

function MinBlockCheck (T, k)1. if k = N and Tk-l < Tk

and Bk(T + ek-d ::; qk thenset T +- T+ ek-lreturn true

end ifif k < N and not MinBlockCheck(T, k + 1)

and Tk-l < Tk and Bk(T + ek-l) ::; qk then6. set T +- T + ek-l7. return true8. end if9. return falseend function

2.3.4.5.

Fig. 2. Algorithm for finding the optimal parametersof multi-threshold guard channel scheme

Induction step:

Consider any N > 2 and assume that the in-duction hypothesis is true for all m traffic classes(1 ~ m ~ N). In order to prove the correctnessof MinBlock for N + 1 traffic classes, we considerfinding of Tk (for k = 1,..., N). The statementsin lines 6 through 10 of MinBlock algorithm usesa sequential search for finding the largest value ofTk. Since Bj (for 2 ~ j ~ N + 1) is an increasingfunction of Tk (k < j), thus decreasing Tk (k < j)also decreases Bj. This contradicts with the ob-jective of MinBlock which must find the largestvalue of Tk' This side effect is removed by us-ing MinBlockCheck function. Since in each iter-ation of the while-loop in line 6, MinBlockCheckis called and on each of its call at most one Tj(j > k) is increased, then the above side effect isremoved. Thus the while-loop in line 6 finds thelargest value of Tj (j > k) and hence the algo-rithm finds the largest value for Tl while satisfyingthe specified levels of QoS. From property 1, it is

concluded that the MinBlock algorithm minimi7.esBl' This completes the proof of this theorem.

3.1 A Numerical Example

In table 2, the usefulness of multi-threshold guardchannel policy is shown for four traffic classes(N = 4). This example assumes that the givencell has 20 full duplex channels (C = 20) and con-straints are q2 = 0.035, q3 =0.02 and q4 =O.Ol.The table 1 shows the normalized arrival rate Ak.The columns of table 2 show the optimal nwnberof guard channels and blocking probabilities fordifferent classes, respectively.

Table 1. The input traffic

Table 2. Results of the proposed algorithm for findingthe optimal number of guard channels

4. Conclusions

In this paper, we have studied the problem of calladmission control in the next generation cellularmobile networks, which supports multi-classes ofservices. We introduced a multi-threshold guardchannel policy and derived blocking probabilitiesof the network. We also studied their behaviorand compared analytical results with simulationresults. Then we gave an algorithm which findsthe optimal number of guard channels.

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Int'l Symposium on Telecommunications (IST2003 ), 16-18August, 2003 Isfahan-Iran

CaseAo At A2 k1 17 12 7 22 18 8 7 23 20 10 5 24 20 12 7 25 20 10 7 26 21 11 3 27 22 12 7 28 25 15 7 2

Case Tt T2 T3 T4 BI B2 B3 B41 18 18 18 20 0.015822 0.015822 0.015822 0.0014382 18 18 18 20 0.018911 0.018911 0.018911 0.0017193 15 17 18 20 0.267492 0.027544 0.002858 0.0002604 13 17 18 20 0.513851 0.031402 0.003259 0.0002965 14 17 18 20 0.346408 0.025677 0.002665 0.0002426 16 17 18 20 0.196272 0.030776 0.003194 0.0002907 13 17 18 20 0.540299 0.033018 0.003426 0.0003118 9 18 19 20 0.940582 0.034587 0.003144 0.003144

thresholds To = -1 and TN = C. The proce-dure for accepting calls in multi-threshold guardchannel scheme can be described as follows. A callfrom class k (for k = 1,..., N) will be acceptedwhen the number of busy channels is smaller thanTk' In the multi-threshold guard channel scheme,{c(t)lt ~ a} is a continuous-timeMarkov chain(birth-death process) with states a, 1,..., C. Thestate transition diagram of a particular cell inthe network, which has C full duplex channelsand uses multi-threshold guard channel scheme isshown in figure 1.

Fig. 1. Markov chain modf'J of Cf'Jl

Define the steady state probability Pn =limt~CX)Prob[c(t)= n], for n = a,l,...,TN. Pnis expressedby

(1)

for Tk < n ~ Tk+l and Po is obtained from equa-tion L:~=o Pn = 1 and is given by

Define T as [To,Tl"'" TN], ej as the unit ((N +1) xl) vector with 1 as the jth element and therest zero and E{ as L:{=i ek. Thus, the blockingprobability of class N is equal to

(3)

Similarly, the blocking probability of class k (K <N) is given by

c

L Pn,n=T.+l

(4)

Ek(') has interesting properties some of whichare listed below and proved in [la].

Property 1. For any given value of T, we haveBk(T) ~ BkH (T).

Property 2. For any given value of T, Bk(') is amonotonically decreasing function of Tk.

Property 3. For any given value of T, Bk(.) is amonotonically increasing function of Tj (j < k).

Property .4. For any given values of T, B k(.) is amonotonically increasing function of Tj (j > k).

3. Number GuardofOptimalChannels

In this section, we consider problem of finding theoptimal values of thresholds Tl,' . . ,TN-1, whichcan be described as: Given C channels allocatedto a cell, the objective is to find T* that mini-mizes BI (.) with constraints Bk(.) ~ qk for k =2, . . . ,N. Thus, we have the following nonlinearprogramming problem.

Problem 1. Minimize BI (T) subject to the hardconstraint Bk(T) ~ qk, where qk is the level ofQoS to be satisfied for calls of class k = 2,.. .,N.

We now present an algorithm called MinBlock,which is shown in figure 2, for solving problem1. The MinBlock algoritlun uses a function calledMinBlockCheck. Function MinBlockCheck (T, k)increments Tj (j > k) by one if the specified levelof QoS for class j is satisfied and returns true; oth-erwise it returns false, where j (k -1 ~ j ~ N - 1)is the largest possible value which satisfies thespecified level of QoS.

Theorem 1. Algorithm MinBlock minimizesBl (.) while satisfying constraints Bk(.) ~ qk fork=2,...,N.

Proof. Since Bk (for k = 1,..., N) is a decreasingfunction of Tk (property 2), it is sufficient to showthat the MinBlock algorithm maximizes TI whilesatisfying the specified levels of QoS. The proof isby induction on the number of traffic classes, N.We shall show that if the MinBlock algorithm min-imizes BI (.) for N classes, then it still minimizesEl (.) for N + 1 classes and when the algorithmstops, T gives the optimal solution to problem 1.

Basis:

When we have 2 traffic classes (N = 2.),the Min-BlockCheck function always return false. Hence,the statements in lines 6 through 10 performs alinear search and finds the largest value of TI sat-isfying level of QoS, Q2.Since El is a decreasingfunction of Tl, thus the MinBlock algorithm min-imizes Bl'

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Int'l Symposium on Telecommunications (IST2003 ), 16-18August, 2003 Isfahan-Iran

References

[1] Y. B. Lin, S. Mohan, and A. Noer-pel, "Queueing Priority Channel AssignmentAtrategies for PCS Handoff and Initial Ac-cess," IEEE 1hmsactions on Vehicular Tech-nology, vo!. 43, pp. 704-712, Aug. 1994.

[2] D. Hong and S. Rappaport, "Traffic Mod-elling and Performance Analysis for CellularMobile Radio Telephone Systems with Pri-otrized and Nonpriotorized Handoffs Proce-dure," IEEE TI-ansactions on Vehicular Tech-nology, vo!. 35, pp. 77-92, Aug. 1986.

[3] S. Oh and D. Tcha, "Priotrized Channel As-signment in a Cellular Radio Network," IEEETI-ansactions on Communications, vo!. 40,pp. 1259-1269, July 1992.

[4] R. Ramjee, D. Towsley, and R. Nagarajan,"On Optimal Call Admission Control in Cel-hilar Networks," Wireless Networks, vo!. 3,pp. 29-41, 1997.

[5] G. Haring, R. Marie, R. Puigjaner, andK. Trivedi, "Loss Formulas and Their Ap-plication to Optimi7.ation for Cellular Net-works," IEEE TI-ansactions on VehicularTechnology,vo!. 50, pp. 664-673, May 200l.

[6] H. Beigy and M. R. Meybodi, "Uniform Frac-tional Guard Channel," in Proceedings ofSixth World Multiconference on Systemmics,Cybernetics and Informatics, Orlando, USA,July 2002.

[7] G. C. Chen and S. Y. Lee, "Modeling ofStatic and Dynamic Guard Channel Schemesfor Mobile Transactions," IEICE TI-ansac-tions on Information and Systems, vo!. E84-D, pp. 87-99, Jan. 2001.

[8] L. Yin, B. Li, Z. Zhang, and Y. Lin, "Perfor-mance analysis of a dual-threshold reserva-tion (DTR) scheme for voice/data integratedmobile wireless networks ," in Proceedings ofthe IEEE Wireless Communications and Net-working Confernce, WCNC. 2000, pp. 258-262, Sept. 2000.

[9] H. Beigy and M. R. Meybodi, "Two-Thresholds Guard Channel Scheme ," Tech.Rep. TR-CE-2002-005, Computer Engineer-ing Department, Amirkabir University ofTechnology,Tehran, Iran, 2002.

[10] H. . Beigy and M. R. Meybodi, "A Gen-eral Call Admission Policy for Next Gener-ation Wireless Networks," Tech. Rep. TR-CE-2003-003,Computer Engineering Depart-ment, Amirkabir University of Technology,Tehran, Iran, 2003.

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