Bayesian inference and prediction in single server M/M/1 queuing model based on queue length

Abstract

This paper is concerned with the problem of estimating traffic intensity, ρ for single server queuing model in which inter-arrival and service times are exponentially distributed (Markovian) using data on queue size (number of customers present in the queue) observed at any random point of time. Here, it is assumed that q is unknown but random quantity. Bayes estimator of ρ are derived under squared error loss function assuming two forms of prior information on ρ. The performance of the proposed Bayes estimators is compared with that of the corresponding classical version estimator based on maximum likelihood principle. The model comparison criterion based on Bayes factor is used to select a suitable prior for Bayesian analysis.

Keywords:

• M/M/1 queue
• Bayesian estimation
• Predictive distribution
• Bayes factor

Acknowledgments

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