PIECEWISE-LINEAR TEST FUNCTIONS FOR STABILITY AND INSTABILITY OF QUEUING-NETWORKS

We develop the use of piecewise linear test functions for the analysis of stability of multiclass queueing networks and their associated flu id limit models. It is found that if an associated LP admits a positiv e solution, then a Lyapunov function exists. This implies that the flu id limit model is stable and hence that the network model is positive Harris recurrent with a finite polynomial moment. Also, it is found th at if a particular LP admits a solution, then the network model is tra nsient.