Xinwei Bai, UT-EWI-SOR
In this project, we consider random walks in the nonnegative orthant of a space of at least two dimensions. For some random walks with special transition structure, e.g. Jackson networks, the performance measure can be derived explicitly. However, it is difficult to obtain the performance measure of a random walk generally. The goal of the project is to obtain upper and lower bounds on the performance measure of a general random walk by analyzing another perturbed random walk, for which the performance measure can be derived explicitly. The perturbation is done by changing some transition rates on the boundary of the orthant. Moreover, we build a linear program, which provides upper and lower bounds on the performance measure of a general random walk.