On SPDEs arising as limits of Many-Server Queues

Thursday, January 17, 2013 - 3:15pm - 4:05pm
Keller 3-180
Kavita Ramanan (Brown University)
Finite-dimensional diffusions have been successfully used as tractable approximations to gain
insight into a large class of queueing systems. We show that certain classes of queueing
systems lead naturally to infinite-dimensional diffusion approximations.
For the particular model of many-server queues, we show that the limit state process
converges to the solution of a stochastic partial differential equation subject to an unusual boundary
condition that involves a coupled Ito equation. We also establish uniqueness of the stationary distribution of the pair
of processes, and describe its implications for the original queueing system. This talk is based on
joint works with Mohammadreza Aghajani and Haya Kaspi.
MSC Code: