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O. Yilmaz et al.Author Proof425426427428429430431432433434435436437438439440441442443444Elapsed Time (sec)1 100 10000Partitioning Threshold Hybrid Spillover Fast SpilloverAlgorithm NameFig. 4 Notched-box plot for time spentTable 4 Average time spent to determine channel allocation for revenue optimization by CAC algorithmsAlgorithm name Partitioning Threshold-based Hybrid Spillover Fast spilloverAverage elapsed time (s) 0.32 29,572 27,595 2,202 151largest non-outlier observation. Notches around medians indicate the uncertainty about themedians obtained by the algorithm. We summarize the average elapsed time needed for eachalgorithm in Table 4.With less than a second to calculate the optimal partition allocation, the partitioningalgorithm performs the best in terms of execution time. This algorithm allocates fixed partitions,one for each service class. As each partition can be modeled as an M/M/n/n queue,closed-form analytical solutions can be pre-generated and looked up to calculate the blocking/droppingprobabilities and the reward obtainable. The second best algorithm is the fastspillover-partitioning algorithm with 151 seconds on the average. This algorithm performssignificantly better than other algorithms which do not have closed-form solutions. The nextbest algorithm is the pure spillover-partitioning algorithm with 2,202 s. This algorithm calculatesthe maximum channel allocation in less than 8% of the average time spent by thethreshold-based and the hybrid CAC algorithms. The heuristics applied improve the executiontime of this algorithm significantly, while not sacrificing the optimality of the solution.The next best algorithm is the partitioning-threshold hybrid CAC with 27,595 s. This algorithmhas fixed partitions, one for each service class. The remaining channels are allocatedto a share partition that accommodates all service classes based on threshold-based CAC.Finally, threshold-based CAC is the worst in execution time, with 29,572 s on the average.This algorithm is pure threshold-based, with each service class having a threshold. It iscomputationally expensive to determine optimal thresholds.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 Control4454.2 Performance Comparison in Solution QualityAuthor Proof446447448Figure 5 shows a notched-box plot diagram for the maximum reward generated with QoSguarantees by the optimal channel allocation of each CAC algorithm. Figure 6 shows anotched-box plot diagram for the revenue ratio relative to the upper bound revenue obtained,Reward Rate660 680 700 720 740 760 780Partitioning Threshold Hybrid Spillover Fast SpilloverFig. 5 Notched-box plot for revenue generatedRevenue Ratio0.975 0.980 0.985 0.990 0.995 1.000Algorithm Nameuncorrected proofPartitioning Threshold Hybrid Fast Spillover Pure SpilloverCAC Algorithm NameFig. 6 Notched-box plot for revenue ratio relative to the upper bound revenue123Journal: 11277 MS: WIRE823 CMS: 11277_2009_9673_Article TYPESET DISK LE CP Disp.:2009/2/19 Pages: 21 Layout: Small
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