Title: Gaussian Skewness Approximation for Dynamic Rate Multi-Server Queues with Abandonment
Speaker: William A. Massey, Edwin S. Wilsey Professor, Princeton University
Abstract: The multi-server queue with non-homogeneous Poisson arrivals and customer abandonment is a fundamental queueing model with dynamic rates. It arises in large scale service systems such as call centers and hospitals. Moreover, understanding their stochastic evolution is key to the analysis of fork-join systems that model the coordination of such queues.
Scaling the arrival rates and number of servers in the QED regime gives us the fluid and diffusion limits for Markovian service networks. These scaling asymptotics are also the Halfin-Whitt scaling for multi-server queues.
These fluid and diffusion limits suggests a Gaussian approximation for this queueing process. The mean and variance are easily computed from a two-dimensional dynamical system for the limiting processes. Recent work by Ko and Gautum found that a modified version of these differential equations yield better Gaussian estimates of the original queueing system distribution.
We introduce here a new closure approximation method where the fluid limit is a one-dimensional version of the method and Ko and Gautum’s work is a two-dimensional version. This broader view yields a new three-dimensional version of this method that constructs a quadratic function of a Gaussian random variable to estimates the mean, variance, and third cumulative moment.