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 (RO-U). We also derive necessary and sufficient conditions under which the RO-U has a stationary distribution, explicitly determining the analytical form of this distribution under some special conditions.
(Joint with Amy Ward)
