Maximum entropy analysis to the T policy M/G/1 queue with server breakdowns and startup times

This paper uses the maximum entropy approach to solve the steady-state probabilities of the T policy M/G/1 queue with server breakdowns and general startup time. Besides the constraints of normalizing condition and the probability of the various server status, the maximum entropy solutions are used to derive the queue length distributions using the first moment and second moment of the number of customers in the system, respectively. We derive the approximate formulas for the steady-state probability distributions of the queue length and perform a comparative analysis between the approximate results with established exact results for various distributions, such as exponential (M), k-stage Erlang (E_k), and deterministic (D). The experiment demonstrates that the maximum entropy approach is accurate enough for practical purposes and is a useful method for solving complex queueing systems by using the first moment of the number of customers in the system, which the use is better than the second moment of customers in the system.