Optimal Control of the D-Policy M/G/1 Queueing System with Server Breakdowns

This study deals with a single server in the D-policy M/G/1 queueing system in which the server is turned off at the end of each complete period and is activated again only when the cumulative completion times of the customers in the system exceeds a given level D. While the server is working, he is subject to breakdowns according to a Poisson process. When the server breaks down, he requires repair at a repair facility, where the repair time obeys a general distribution. We have demonstrated that the probability that the server is busy in the steady-state is equal to the traffic intensity. The total expected cost function per customer per unit time is constructed to determine the optimal operating D-policy at a minimum cost. We use the steady-state analytic results and apply an efficient Matlab computer program to calculate the optimal value of D. Based on three different service distributions: exponential, 3-stage Erlang and deterministic, we provide extensive numerical computation for illustration purpose. Sensitivity analysis is also investigated.