Ergodicity of Many-Server Queues with Abandonment
Dr. Weining Kang
Department of Mathematics and Statistics
University of Maryland, Baltimore County
| Time: noon-1 pm | Location: MP 401 |
Abstract: We consider a queuing system with N identical servers serving a single class of customers in the first-come-first-serve fashion. Customers in the queue will abandon and leave the system when they are out of patience. Existence of stationary distributions of the state descriptor of such a system is established. Moreover, under the uniqueness assumption on the invariant state of the associated fluid model solution, we show that, as the number of servers goes to infinity, the sequence of stationary distributions for the fluid scaled system state descriptors converges to the unique invariant state. We also show some counterexamples when the uniqueness assumption fails to hold.