SPEAKER:  Masakiyo Miyazawa

ABSTRACT:

We are concerned with the stationary distributions of reflecting random walks on the multidimensional nonnegative orthant and other related processes, provided they exist. Such stationary distributions arise in performance evaluation for various queueing systems and their networks. However, it is very hard to obtain them analytically in general, so our interest is directed to analytically tractable characteristics. For this, we consider tail asymptotics of the stationary distributions.

The purpose of this talk is twofold. In the first part, we discuss why we need a reflecting random walk for a queueing network. This includes introducing a new class called a generalized reflecting random walk. In the second part, we overview the current approaches to attack the tail asymptotic problem from a unified viewpoint. Among them, we focus on an analytic function approach, which is recently developed by the author and his colleagues. We like to show its key ideas, and demonstrate how they work. We here mainly consider the tail asymptotics for two dimensional reflecting random walks, but also discuss how we can approach the case of more than two dimensions. We finally note that a similar approach has been and is being studied for a semimartingale reflecting Brownian motion.