Hypothesis Testing and Confidence Regions for the Mean Sojourn Time of an M/M/1 Queueing System

Abstract

This article discusses testing hypotheses and confidence regions with correct levels for the mean sojourn time of an M/M/1 queueing system. The uniformly most powerful unbiased tests for three usual hypothesis testing problems are obtained and the corresponding p values are provided. Based on the duality between hypothesis tests and confidence sets, the uniformly most accurate confidence bounds are derived. A confidence interval with correct level is proposed.

Keywords:

• Confidence interval
• M/M/1 queueing system
• Mean sojourn time
• p value
• Uniformly most accurate confidence bounds
• Uniformly most powerful tests

Mathematics Subject Classification:

• 60K25
• 62F03

Acknowledgments

The authors are deeply indebted to the reviewer for his valuable comments and suggestion. This work was supported by NNSF of China 10771015.

Notes

This experiment is also considered in Ausín et al. (2004) and Chu and Ke (2007)