A maximum entropy approach for the 〈p,N〉〈p,N〉-policy M/G/1 queue with a removable and unreliable server

This paper analyzes a single removable and unreliable server in the 〈p,N〉〈p,N〉-policy M/G/1 queue in which the server breaks down according to a Poisson process and the repair time obeys an arbitrary distribution. We assume that when the number of customers in the system becomes N, turn the server on with probability p   and leave the server off with probability (1-p)(1-p). The use of maximum entropy approach is to develop the approximate formulae for the probability distributions of the number of customers and the expected waiting time in the system. We perform a comparative analysis between the derived approximate results with exact analytic results for three different service time and repair time distributions such as exponential, uniform, and gamma. It is shown from numerical results that the maximum entropy approach is sufficiently accurate for practical use.