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O. Yilmaz et al.E 1 hP4UC 1 hP4S 1 hP4Author ProofE 1 nP4E 2 hP4E 2 nP4Fig. 3 SPN model for the fourth partitionUC 1 nP4UC 2 hP4UC 2 nP4261 Similarly, we develop an SPN model shown in Fig. 3 to model P 4 as well as to compute262 B i h and Bi n of class i in P 4. The SPN model for P 4 is very similar to the SPN model for P 3263 except that this model includes one more SPN subnet for modeling class 2 new calls. It canbe shown that the blocking/dropping probabilities B 1 n , B1 h , B2 n ,andB2 hcan be calculated by:()λ 1Bh 1 = hP 4− rate(EhP 1 4)265λ 1 (9)hP(4)λ 1Bn 1 = nP 4− rate(EnP 1 4)266λ 1 (10)nP(4)λ 2Bh 2 = hP 4− rate(EhP 2 4)267λ 2 (11)hP(4)λ 2Bn 2 = n − rate(E2 nP 4)268(12)The revenue earned per unit time, R 1 269 n , R1 h , R2 n ,andR2 hin Eq. 1, can be calculated from the270 four performance models developed for P 1 , P 2 , P 3 ,andP 4 . Specifically, since class 2 newcalls can only be in the 4th partition, R 2 271 n is calculated as:Rn 2 = ( 1 − Bn2 )λ2n · v 2 272(13)Class 2 handoff calls can only be in the last two partitions. Hence R 2 273 his calculated by summing274 the revenue earned from the last two partitions as follows:275λ 2 nS 1 nP4S 2 hP4S 2 nP4R 2 h = rate(E2 hP 3) · v 2 + ( 1 − B 2 h)λ2hP4 · v 2 (14)276 Class 1 new calls can be in the last three partitions. Hence, R 1 n is calculated as:277Rn 1 = (λ1 n − λ1 nP 3) · v 1 + rate(EnP 1 3) · v 1 + ( 1 − Bn1 )λ1nP4 · v 1 (15)Finally, class 1 handoff calls can be in any of the four partitions. Hence R 1 278 his calculated by279 the revenue earned in all four partitions as follows:Rh 1 = (λ1 h − λ1 hP 2) · v 1 + (λ 1 hP 2− λ 1 hP 3) · v 1 + rate(EhP 1 3) · v 1 + ( 1 − Bh1 )λ1hP4 · v 1280281(16)uncorrected proof123Journal: 11277 MS: WIRE823 CMS: 11277_2009_9673_Article TYPESET DISK LE CP Disp.:2009/2/19 Pages: 21 Layout: Small
Performance Analysis of Spillover-Partitioning Call Admission ControlTable 1 Pure spillover-partitioning CACAuthor Proof2822832842852862872882892902912922932942952962972982993003013023033.1 Search for Optimal Partitioning that Generates Maximal Revenuewith QoS GuaranteesWe consider two variations of spillover-partitioning. The pure spillover-partitioning algorithmfinds the optimal partition allocation that would maximize the revenue earned per unittime while satisfying QoS constraints specified in (2). The method essentially is exhaustivesearch with heuristics being applied to improve search performance by eliminating combinationsthat would not generate a feasible solution. A second variation is the fast spilloverpartitioningalgorithm that applies a greedy heuristic search method to find a near optimalsolution fast at the expense of search quality. It should be noted that a solution found bythe pure or fast spillover-partitioning algorithm will be evaluated by the analytical modeldeveloped. As we shall see, the solution found by the fast spillover-partitioning algorithm isvery close to that found by the pure spillover-partitioning algorithm but the search efficiencyis greatly improved.3.1.1 Pure Spillover-PartitioningTable 1 shows a pseudo code listing the pure spillover-partitioning algorithm utilizing exhaustivesearch for finding optimal resource allocation. Pure spillover-partitioning CAC first eliminatesall channel combinations that cannot even satisfy the QoS constraint of class 2 newcalls. The logic behind the elimination of these channel combinations is that these combinationscould not possibly lead to a feasible solution that could satisfy QoS constraints of allservice classes. Exhaustive search is then performed to find the best reward rate achievable.Specifically, this algorithm first determines the minimum number of channels needed tosatisfy the QoS constraints of new/handoff calls. This is done by modeling the call admissionuncorrected proof123Journal: 11277 MS: WIRE823 CMS: 11277_2009_9673_Article TYPESET DISK LE CP Disp.:2009/2/19 Pages: 21 Layout: Small
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