Mean response time for a G/ G/1 queueing system: Simulated computation

Abstract

Mean response time, denoted by r, plays an important role of system characteristics in queueing models. In this paper we developed a data-based recursion relation to compute a sequence of response times, and the sample mean from these response times, denoted by r ˆ , was used to estimate mean response time r of an FCFS G/ G/1 queueing system. We further construct new confidence intervals of r for a G/ G/1 queueing system, which are based on four bootstrap methods; standard bootstrap (SB) confidence interval, percentile bootstrap (PB) confidence interval, bias-corrected percentile bootstrap (BCPB) confidence interval, and bias-corrected and accelerated (BCa) confidence interval. A numerical simulation study is conducted in order to demonstrate performance of the proposed estimator r ˆ and bootstrap confidence intervals of r. From the simulation results, we show that r ˆ is a consistent estimator of r. In addition, we also investigate the accuracy of the four bootstrap confidence intervals by calculating the coverage percentage, the average length, and the relative average length of confidence intervals. Detailed discussions of simulation results for seven various queueing models are presented.