M/PH/1 queueing model with re-servicing

Abstract

In this paper, we analyze an M/PH/1 queuing system with optional re-service. In this queueing system the interarrival time distribution is exponential with mean service time and re-service time distribution follows continuous time phase-type distribution and each customer will be re-serviced with probability ‘p’. We have obtained the expressions of various system performance measures and maximum likelihood method using E-M algorithm and Bayesian procedure based on MCMC method were proposed to estimate system parameters. Numerical illustration of various special cases of the queueing system was carried out using simulated data sets.