In this paper, we consider a critically loaded G/M/1 queue and contrast its transient behaviour with the transient behaviour of stable (or unstable) G/M/1 queues. We show that the departure process from a critical G/M/1 queue converges weakly to a Poisson process. However, as opposed to the stable (or unstable) case, we show that the departure process of a critical G1/M/1 queue does not couple in finite time with a Poisson process (even though it converges weakly to one). Thus, as the traffic intensity (ratio of arrival to service rates), rho, ranges over (0, infinity), the point rho = 1 represents a singularity with regard to the convergence mode of the departure process. [References: 10]
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机译：在本文中，我们考虑了临界负载的G / M / 1队列，并将其瞬态行为与稳定（或不稳定）的G / M / 1队列的瞬态行为进行了对比。我们表明，从关键G / M / 1队列出发的过程几乎没有收敛到泊松过程。但是，与稳定（或不稳定）情况相反，我们表明，关键的G1 / M / 1队列的离开过程在有限的时间内不会与泊松过程耦合（即使它弱收敛到一个）。因此，当交通强度（到达率与服务费率之比）rho超过（0，无穷大）时，点rho = 1代表离港过程收敛模式的奇异点。 [参考：10]
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