Gram Charlier Expansion for Time Varying Multiserver Queues with Abandonment

In this paper, we introduce a new approximation for estimating the dynamics of multiserver queues with abandonment. The approximation involves a four-dimensional dynamical system that uses the skewness and kurtosis of the queueing distribution via the Gram Charlier expansion. We show that the additional information captured in the skewness and kurtosis allows us to estimate the dynamics of the mean and variance much better than fluid and diffusion limit theorems or other methods that use only mean and variance behavior. Lastly, our approach also yields accurate approximations for the probability of delay, which is an important metric for quality of service.