Maximum entropy solution to a quorum queueing system

For a quorum queueing system, the system size steady-state initial probability vector is usually found by solving a simple system of linear equations, but computation of the system size steady-state tail probability vector requires the inversion of the probability generating function. We use in this paper the initial probability vector to compute the mean system size and then, using the mean system size, we compute the maximum entropy approximation of the tail probability vector, thus avoiding inversion of the probability generating function. In a numerical example, comparison of the initial probability vectors obtained by the exact and approximate methods proved to be excellent. We also show how to compute the tail probability vector.