Bayesian Inference and Prediction in an M/G/1 with Optional Second Service

Abstract

In this article, we exploit the Bayesian inference and prediction for an M/G/1 queuing model with optional second re-service. In this model, a service unit attends customers arriving following a Poisson process and demanding service according to a general distribution and some of customers need to re-service with probability “p”. First, we introduce a mixture of truncated Normal distributions on interval (− ∞, 0) to approximate the service and re-service time densities. Then, given observations of the system, we propose a Bayesian procedure based on birth-death MCMC methodology to estimate some performance measures. Finally, we apply the theories in practice by providing a numerical example based on real data which have been obtained from a hospital.

Keywords:

• Birth-death MCMC
• M/G/1 queue
• Optional service
• Truncated normal mixture

Mathematics Subject Classification:

• 62F15
• 60K25

Acknowledgments

We wish to thank Dr. N. Nematolahi for helpful discussions and comments on this work, and Prof. G. Gholami for discussing Bayesian approaches. We would like to thank three anonymous referees for their valuable comments and suggestions.

Notes

First Come First Service.

Laplace Stieltjes Transform.