论文标题
在关键加载时通过预定流量喂养的队列的稳定性
Stability of a Queue Fed by Scheduled Traffic at Critical Loading
论文作者
论文摘要
考虑单个服务器队列的工作负载过程，并具有确定性的服务时间，在该服务时间内根据计划的流量过程到达。预定的到达序列是客户计划到达不断到达的时间，但是每个客户的实际到达时间都会通过随机扰动从计划到达的时间来扰动。在本文中，我们考虑了一个急需的队列，其中服务率等于到达率。与续签流量喂养的队列不同，即使存在关键负载，该队列也可以稳定。当扰动具有有限的平均值时，我们确定稳定性的必要条件。也许令人惊讶的是，标准不是可逆的，因为在向前时间的预定流量过程中，这种队列可以稳定，但对于同一流量过程的时间反转不稳定。
Consider the workload process for a single server queue with deterministic service times in which customers arrive according to a scheduled traffic process. A scheduled arrival sequence is one in which customers are scheduled to arrive at constant interarrival times, but each customer actual arrival time is perturbed from her scheduled arrival time by a random perturbation. In this paper, we consider a critically loaded queue in which the service rate equals the arrival rate. Unlike a queue fed by renewal traffic, this queue can be stable even in the presence of critical loading. We identify a necessary and sufficient condition for stability when the perturbations have finite mean. Perhaps surprisingly, the 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.
