On the asymptotic behaviour of closed multiclass queueing networks

An expression for the generating function of the normalising constant is obtained for a closed, multiclass Markovian queueing network in terms of similar functions for networks with one fewer class. In this way a recursive algorithm can be implemented to calculate normalising constants, and hence, many performance measures, in terms of the normalising constant function for single class networks, which is well understood. The technique is illustrated for a simple two-class network and explains simply some interesting asymptotic properties.