Non-Markovian state dependent networks in critical loading
  We establish heavy traffic limit theorems for queue-length processes in critically loaded single class queueing networks 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 generalised Jackson networks with state-dependent rates. 
Chihoon Lee, Anatolii puhalskii
math.PR