A diffusion approximation for a generalized Jackson network with reneging Josh Reed * and Amy R. Ward Department of Industrial and Systems Engineering Georgia Institute of Technology Atlanta, GA 30332 Published in Proceedings of the 42nd Annual Allerton Conference on Communication, Control, and Computing, Sept. 29- Oct. 1, 2004 Abstract We consider a generalized Jackson network with reneging customers in heavy traffic. In particular, each customer joining a particular station may abandon the network if his service does not begin within a station-dependent, exponential amount of time. We establish that in heavy traffic this system can be approximated by a multi-dimensional regulated Ornstein-Uhlenbeck process. 1 Introduction In many practical applications, customers faced with long waiting times abandon the system before receiving service, or renege. We incorporate this behavior into a generalized Jackson network by assuming that each customer joining a particular station reneges from the network if his service does not begin within an exponentially distributed amount of time. Our objective is to study the stationary behavior of the network. Of course, the stationary distribution of a (conventional) Jackson network without reneging does not, in general, have an explicit analytical form. Therefore, having little hope of an exact analysis, we develop heavy traffic limit theorems that support stationary distribution approximations. In contrast to the work of Reiman [8] for conventional Jackson networks, our limit diffusion process is a multi-dimensional regulated Ornstein-Uhlenbeck (O-U) process, rather than a regulated Brownian motion (RBM). Much is known about RBM; see, for example, the work of Harrison and Reiman [5] [4], Harrison and Williams [6], Harrison and Dai [3], and Shen et al [9]. Although work on RO-U processes is more recent, its stationary behavior also appears tractable. To begin, a straightforward adaptation of * Corresponding author, email: je-reed@isye.gatech.edu