Equilibrium distributions

Abstract

In Chapter 4 we saw approximately how queues evolve if they do not vanish. For λ > μ the mean queue simply follows what the fluid approximation predicts, but the uncertainty in the queue length as measured by its standard deviation typically grows as the square root of the cumulative arrivals and departures. If, however, we start with an initial queue Q(0) > 0 and λ is less than the mean queue decreases as illustrated in Fig. 4.5(c). The queue is certain to vanish within a finite time, usually within a time comparable with Q(0)/ (μ-λ).