Stability of a Queue Fed by Scheduled Traffic at Critical Loading
研究了计划到达过程（顾客按固定间隔安排但实际到达时间有随机扰动）的单服务器队列，发现即使利用率等于1，队列仍可能稳定，且稳定条件仅要求扰动的正部有界支撑，但该条件不可逆。
Performance of a queueing system with scheduled arrivals A scheduled arrival sequence is one in which customers are scheduled to arrive at constant interarrival times, but each customer’s actual arrival time is perturbed from her scheduled arrival time by a random perturbation. In “Stability of a Queue Fed by Scheduled Traffic at Critical Loading”, V.F. Araman and P.W. Glynn consider a single server queue with deterministic service times in which customers arrive following a scheduled arrival process. Unlike a queue fed by renewal traffic, this queue is shown to be stable even when the utilization is equal to one. It is also shown that for finite mean perturbations, a necessary and sufficient condition for stability is when the positive part of the perturbation has bounded support, with no requirement on the negative part of the perturbation. Perhaps surprisingly, this criterion is not reversible, in the sense that such a queue can be stable for a scheduled traffic process in forward time, but unstable for the time-reversal of the same traffic process.