Classical and Bayesian inference on traffic intensity of multiserver Markovian queuing system

Abstract

In this paper we consider multi-server single queue system in which inter-arrival and service times are exponentially distributed. When assessing the performance of such queuing model, information regarding the parameter traffic intensity (ρ), also called the utilization factor of the service station, is very essential. The unknown factor ρ is therefore our parameter of interest in the present work. Maximum likelihood (ML) and uniformly minimum variance unbiased (UMVU) estimators of ρ are proposed in the context of classical paradigm. A Bayes estimator of ρ is derived assuming that the prior density of ρ belongs to the family of Beta distributions. The performance of estimators is evaluated in terms of their relative efficiency. The proposed procedures are illustrated through a simulation study.

Keywords:

• Asymptotic expected deficiency
• Bayes estimator
• M/M/s queue
• predictive distribution
• relative efficiency

Acknowledgements

The authors would like to thank both of the anonymous reviewers for their valuable comments and suggestions to improve the quality of this manuscript.