Title: Variance reductions in simulation of a state-dependent queueing system using total hazard

Authors: Chi-Hyuck Jun, Sheldon M. Ross

Addresses: Department of Industrial Engineering, Pohang University of Science and Technology, Pohang, Korea. ' Department of Industrial Engineering and Operations Research, University of California, Berkeley, California 94720, USA

Abstract: A queueing system is considered where customers arrive according to a Poisson process. Each customer possesses a random workload which is processed by a single server using a state-dependent rate. Total hazards are derived and utilised as control variates for reducing the variance of the raw simulation estimator of the expected number of customers during a busy period. Simulation experiments are done for exponential and k-Erlang workload distributions. Performance of controlled estimators is measured in terms of the mean squared error, which is estimated by the bootstrap method. Simulation results show that hazard-controlled estimators outperform the raw simulation estimator and other controlled estimators based on workloads and inter-arrival times.

Keywords: queueing systems; simulation; total hazards; control variables; variance reduction; state-dependent queueing; Poisson process.

DOI: 10.1504/IJCEELL.1994.030291

International Journal of Continuing Engineering Education and Life-Long Learning, 1994 Vol.4 No.1/2, pp.69 - 79

Published online: 14 Dec 2009 *

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