On pathwise behavior of queues

In this paper the authors study the sample-path behavior of the workload process in a single server queue without imposing the stationarity hypothesis. In particular they study the stability or worst case growth properties and show that the growth rate is of the form O(t’α), α>1, depending on the rate of convergence of the pathwise average of the work brought into the system. The authors then study the existence of empirical means and in particular show that a pathwise version of the Pollaczek-Khinchine formula plays an important role. Finally, they give conditions under which the present results hold knowing the rate or intensity of the arrival process. The results highlight the limitations of pure sample-path techniques.