General queueing networks: Representation and stochastic monotonicity

We consider a queueing network with a set of multi-server nodes. The arrival, service and routing processes are characterized by arbitrary random sequences. Assume that these are independent of the state of the network. We develop a representation of this general model, relating certain stochastic processes of interest to the above random sequences through a system of equations. A recursive algorithm then generates the realizations of these processes. The main motivation of this study is to investigate some stochastic monotonicity results that have been previously established for Jackson networks. We show that those results also hold for the general network studied here.