A Poisson-Charlier approximation for nonstationary queues

In this paper, we develop a new approximation for nonstationary multiserver queues with abandonment. Our method uses the Poisson-Charlier polynomials, which are a discrete orthogonal polynomial sequence that is orthogonal with respect to the Poisson distribution. We show that by appealing to the Poisson-Charlier polynomials that we can estimate the mean, variance, and probability of delay of our nonstationary queueing system with good accuracy. Lastly, we provide a numerical example that illustrates that our approximations are effective.