A network belongs to the monotone separable class if its state variables are homogeneous and monotone functions of the epochs of the arrival process and if it satisfies a separability condition to be defined in the talk. This framework contains several classical queueing network models, including generalized Jackson networks, max plus networks, multi-server queues, and various classes of stochastic Petri nets.

Backward coupling arguments and subadditive ergodic theory allow one to derive the stability region for such networks in the case of stationary and ergodic driving sequences.

This framework also allows one to derive several results in the case of i.i.d. driving sequences, like for instance the speed of convergence to the stationary regime or the asymptotics of the tails of the stationary state variables.