Diffusion Approximation for Open State-Dependent Queueing Networks in the Heavy Traffic Situation

Abstract

We consider open queueing networks in which arrival and service rates are dependent on the state (i.e., queue length) of the network. They are modeled as multidimensional birth and death processes. If a heavy traffic condition is sastisfied on the behavior of arrival and service rates when the queue length becomes very large, it is shown that a properly normalized sequence of queue length converges in law to a reflecting diffusion process.