Comparison of Confidence Interval Based on Bootstrap Method for the Mean Response time in a Simulation Study

Document Type : Original Paper

Authors

Department of Mathematics, Maku Branch, Islamic Azad University

Abstract

The mean response time plays an important role in the analyzing and optimizing the queuing system which determines the number and type of giving service. In this paper, new confidence intervals of mean response time for an M/G/1 FCFS queuing system is contrasted based on the nonparametric delta method and five bootstrap methods. These methods include: nonparametric delta method confidence interval based on the influence function, standard bootstrap confidence interval, percentile bootstrap confidence interval, bootstrap-t confidence interval, bias corrected and acceleration bootstrap confidence interval and bootstrap pivotal confidence interval. In a simulation study, these six methods are compared and evaluated the accuracy and performance of the confidence intervals for three different M/G/1 FCFS queuing systems based on the coverage percentage and the average length of confidence intervals.

Keywords

Main Subjects


[1] Clarke, A.B. (1957). Maximum likelihood estimates in a simple queue, Annals of Mathematical Statistics, 28, 1036–1040. [2] Lilliefors, H.W. (1966). Some confidence intervals for queues, Opeartions Research, 14, 723–727. [3] Basawa, I.V. and Prabhu,
N.U. (1981). Estimation in single server queues, Naval Research Logistics Quarterly, 28, 475–487. [4] Dave, U. and Shah, Y.K. (1980). Maximum likelihood estimates in an M/M/2 queue with heterogeneous servers, Journal of the Operational Research
Society, 31. [5] Jain, S. and Templeton, J.G.C. (1991). Confidence interval for M/M/2 queue with heterogeneous servers, Operations Research Letters, 10, 99– 101. [6] Rubin, G. and Robson, D.S.A. (1990). single server queue with random rrrivals and balking: confidence interval estimation, Queueing Systems Theory and Applications, 7, 283–306. [7] Jain, S. (1991). Estimation
in M/Ek/1 queueing systems, Communications in Statistics-Theory and Methods, 20, 1871–1879. [8] Abou-E1-Ata, M.O. and Hariri, A.M.A. (1995). Point estimation and confidence intervals of the M/M/2/N queue with balking and heterogeneity, American
Journal of Mathematical and Management Sciences, 15, 35–55. [9] Basawa, I.V., Bhat, U.N. and Lund, R. (1996). Maximum
likelihood estimation for single server queues from waiting time data, Queueing Systems-Theory and Applications, 24, 155–167. [10] Efron, B. (1979). Bootstrap methods: another look at the jackknife, Annals of Statistics, 7, 1-26.
  • Receive Date: 13 January 2014
  • Revise Date: 14 September 2014
  • Accept Date: 24 September 2014
  • First Publish Date: 24 September 2014