Non-markovian state-dependent networks in critical loading

We establish a heavy traffic limit theorem for the queue-length process in a critically loaded single class queueing network with state-dependent arrival and service rates. A distinguishing feature of our model is non-Markovian state dependence. The limit stochastic process is a continuous-path reflected process on the nonnegative orthant. We give an application to a generalized Jackson network with state-dependent rates.