Computing stationary distributions of diffusion processes.

Jim Dai (ORIEi, Cornell & Georgia Tech)

Diffusion models have been used to approximate queues arising from service systems such as customer call centers, hospital wards, and cloud computing infrastructure. For example, semimartingale reflecting Brownian motions (SRBMs) are used to approximate networks of queues and piecewise Ornstein-Ulenbeck processes are used to approximate many-server queues.

In this talk, I will describe a finite element algorithm to compute the stationary distribution of a diffusion process. The computed stationary distribution can be used for the design and performance analysis of the original system. This algorithm can also be adapted to compute the stationary distribution of an infinite state Markov chain. A key to the convergence of the algorithm is the proper choice of a reference density. Computational experiences and challenges will also be discussed.