Performance analysis of multiclass queueing networks

The subject of this abstract is performance analysis of multiclass queueing networks. The objective is to estimate steady-state queue lengths in queueing networks, assuming a priori that the scheduling policy implemented brings the system to a steady state, namely is stable. We propose a very general methodology based on Lyapunov functions, for the performance analysis of infinite state Markov chains and apply it specifically to multiclass exponential type queueing networks. We use, in particular, linear and piece-wise linear Lyapunov function to establish certain geometric type lower and upper bounds on the tail probabilities and bounds on expectation of the queue lengths. The results proposed in this paper are the first that establish geometric type upper and lower bounds on tail probabilities of queue lengths, for networks of such generality. The previous results on performance analysis can in general achieve only numerical bounds and only on expectation and not the distribution of queue lengths.