Maximum Entropy Analysis to the N Policy M/G/1 Queue with Working Breakdowns

This paper deals with the N policy M/G/1 queue with working breakdowns. In this queueing system, the steady-state probabilities cannot be derived explicitly. Thus, we employ a maximum entropy approach with several constraints to develop the approximate formulae for the steady-state probability distributions of queue length and the expected waiting time in the queue. We perform a comparative analysis between the approximate results with established exact results for different service time distributions, such as exponential, two-stage Erlang, two-stage hyper-exponential, and deterministic. Numerical results demonstrate that the maximum entropy approach is quite accurate for practical purposes and is useful for complex queueing-systems solving.