### Gaussian Skewness Approximation for Dynamic Rate Multi-Server Queues with Abandonment

- Series
- School of Mathematics Colloquium
- Time
- Thursday, January 26, 2017 - 11:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Bill Massey – Princeton

The multi-server queue with non-homogeneous Poisson arrivals and
customer abandonment is a fundamental dynamic rate queueing model for
large scale service systems such as call centers and hospitals. Scaling
the arrival rates and number of servers gives us fluid and diffusion
limits. The diffusion limit suggests a Gaussian approximation to the
stochastic behavior. The fluid mean and diffusion variance can form a
two-dimensional dynamical system that approximates the actual transient
mean and variance for the queueing process. Recent work showed that a
better approximation for mean and variance can be computed from a related
two-dimensional dynamical system. In this spirit, we introduce a new
three-dimensional dynamical system that estimates the mean, variance,
and third cumulant moment. This surpasses the previous two approaches by
fitting the number in the queue to a quadratic function of a Gaussian
random variable. This is based on a paper published in QUESTA and is
joint work with Jamol Pender of Cornell University.