Confidence Intervals of Performance Measures for an M/G/1 Queueing System

Abstract

In this article, we discuss constructing confidence intervals (CIs) of performance measures for an M/G/1 queueing system. Fiducial empirical distribution is applied to estimate the service time distribution. We construct fiducial empirical quantities (FEQs) for the performance measures. The relationship between generalized pivotal quantity and fiducial empirical quantity is illustrated. We also present numerical examples to show that the FEQs can yield new CIs dominate the bootstrap CIs in relative coverage (defined as the ratio of coverage probability to average length of CI) for performance measures of an M/G/1 queueing system in most of the cases.

Keywords:

• Confidence intervals
• Fiducial empirical quantity

Mathematics Subject Classification:

• 62G15
• 60K25

Acknowledgments

We wish to thank two anonymous referees and the Associate Editor for useful comments.

This work was supported by NNSF of China 10771015.

Notes

^aIndicate the largest coverage probability, the shortest average length, and the largest relative coverage among the three confidence intervals.

^aIndicates the largest coverage probability, shortest average length, and largest relative coverage among the three confidence intervals.

^aIndicates the largest coverage probability, shortest average length, and largest relative coverage among the three confidence intervals.

^aIndicates the largest coverage probability, shortest average length, and largest relative coverage among the three confidence intervals.

^aIndicates the largest coverage probability, shortest average length, and largest relative coverage among the three confidence intervals.

^aIndicates the largest coverage probability, shortest average length, and largest relative coverage among the three confidence intervals.

^aIndicates the largest coverage probability, shortest average length, and largest relative coverage among the three confidence intervals.