Mohammadreza Aghajani (Brown University)

Title: Asymptotic Coupling of an SPDE, with Applications to Many-Server Queues.

Abstract: Many server queues with general service distribution arise in a range of applications including data centers and call centers, and are typically not amenable to exact analysis. Building on earlier work of Kaspi and Ramanan, in a suitable asymptotic regime as the number of servers goes to infinity, we show that the diffusion limit of the many-server queue can be represented in terms of a Markov process that consists of Ito process coupled with an unusual SPDE that takes values in a subset of the Hilbert space $H^1$. Since the Markov process is infinite-dimensional, classical Harris recurrence criteria are not suitable for proving uniqueness of stationary distributions. Instead, we use the so-called asymptotic coupling approach to demonstrate uniqueness of the stationary distribution of this Markov process.