Comparative analysis of a randomized N-policy queue: An improved maximum entropy method

We analyze a single removable and unreliable server in an M/G/1 queueing system operating under the 〈p, N〉-policy. As soon as the system size is greater than N, turn the server on with probability p and leave the server off with probability (1 − p). All arriving customers demand the first essential service, where only some of them demand the second optional service. He needs a startup time before providing first essential service until there are no customers in the system. The server is subject to break down according to a Poisson process and his repair time obeys a general distribution. In this queueing system, the steady-state probabilities cannot be derived explicitly. Thus, we employ an improved maximum entropy method with several well-known constraints to estimate the probability distributions of system size and the expected waiting time in the system. By a comparative analysis between the exact and approximate results, we may demonstrate that the improved maximum entropy method is accurate enough for practical purpose, and it is a useful method for solving complex queueing systems.