A comparison of variance reduction techniques in the simulation of a retrial M/M/1/K queue

Abstract

Retrial queueing systems play a significant role in the modeling and performance evaluation of various dynamic stochastic systems, such as computer networks, airlines, communication and financial systems. This article presents a comprehensive assessment on the applicability of three popular variance reduction techniques (VRTs) in the performance evaluation of an M/M/1/K retrial queue based on shortest job first served (SJFS) retrial policy. The M/M/1/K retrial queue with SJFS retrial policy is not currently analytically tractable. Therefore, the credibility of such queueing systems is heavily dependent on simulations and accurate output data analysis. We seek to identify the best possible VRT so that a system performance evaluator can focus on optimizing the accuracy of relevant performance metrics under study. A comparative applicability analysis of three VRTs, i.e., antithetic variates, importance sampling, and control variates, on the retrial M/M/1/K queueing model has been presented. Our analysis showed a significant level of reduction in terms of variance and confidence interval size of the final estimates for the control variates technique. Furthermore, it has been found that unlike the other VRTs, the control variates technique shows a consistent trend in variance reductions as the number of retrials increases.