Sample path large deviations for multiclass feedforward queueing networks in critical loading

Abstract

We consider multiclass feedforward queueing networks with first in first out and priority service disciplines at the nodes, and class dependent de terministic routing between nodes. The random behavior of the network is constructed from cumulative arrival and service time processes which are as sumed to satisfy an appropriate sample path large deviation principle. We establish logarithmic asymptotics of large deviations for waiting time, idle time, queue length, departure and sojourn-time processes in critical loading. This transfers similar results from Puhalskii about single class queueing net works with feedback to multiclass feedforward queueing networks, and com plements diffusion approximation results from Peterson. An example with renewal inter arrival and service time processes yields the rate function of a reflected Brownian motion. The model directly captures stationary situations.