Performance and sensitivity analysis of an M/G/1 queue with retrial customers due to server vacation

Abstract

This paper treats an M/G/1 queue with retrial customers due to server vacation, which can be used to model a hospital service system. When an arriving customer finds the server on vacation at his arrival epoch, he either enters the retrial group with probability p or leaves the system with probability 1-p. Otherwise, the new arriving customer begins his service immediately if the server is idle upon his arrival or joins the original queue with infinite capacity under FCFS if the sever is busy at his arrival epoch. First, we develop the steady-state analysis by the supplementary variable method and the generating function approach, and give some important performance measures. Moreover, we obtain the Laplace-Stieltjes transform of the sojourn time in the system of an arbitrary customer and prove that the Little’s law still holds in our model. Finally, sensitivity analysis and optimal joining policy are given for illustrative purpose.