ON A SINGULAR FEATURE OF CRITICAL G M/1 QUEUES/

In this paper, we consider a critically loaded G/M/1 queue and contras t its transient behaviour with the transient behaviour of stable (or u nstable) G/M/1 queues. We show that the departure process from a criti cal G/M/1 queue converges weakly to a Poisson process. However, as opp osed to the stable (or unstable) case, we show that the departure proc ess of a critical G1/M/1 queue does not couple in finite time with a P oisson process (even though it converges weakly to one). Thus, as the traffic intensity (ratio of arrival to service rates), rho, ranges ove r (0, infinity), the point rho = 1 represents a singularity with regar d to the convergence mode of the departure process.