Statistical inference on traffic intensity in an M / M / 1 queueing system

Abstract

Traffic intensity is perhaps the most important parameter of the M / M / 1 queueing system. This paper deals with the statistical inference of such a parameter. The maximum likelihood estimator of traffic intensity by observing the number of customers in the system at the departure epoch has been worked out. Confidence intervals and testing of hypotheses have been discussed. An approach to determining sample size has also been presented. While these aspects have been covered in the literature, the methods outlined are not without pitfalls. We propose a simple approach by exploiting a trick by which the M / M / 1 process is linked to the Bernoulli process.

Keywords:

• Classical inference
• confidence interval
• hypothesis testing
• M / M / 1 queue
• traffic intensity

JEL Classification:

• C10
• C12
• C13
• C15
• C18

Acknowledgements

The authors would like to thank the anonymous referees for their detailed, careful, and exhaustive comments. These have led to very substantial improvement of the paper.

Notes

No potential conflict of interest was reported by the authors.