Rough asymptotics for tandem non-homogeneous M/G/∞ queues via Poissonized empirical processes

We obtain a large deviations principle and moderate deviations principle for the joint distribution of the queue length processes and departure process for tandem M/G/∞ queues. The results are obtained by applying a result providing necessary and sufficient conditions on a class of functions for a large deviations principle and moderate deviations principle to hold for a Poissonized empirical process over the class of functions. As an application, we examine how large queue lengths and numbers of departures are built up.