We introduce a Markov queueing system with Poisson arrivals, exponential services, and jockeying between two parallel and equivalent servers. An arriving customer admits to the shortest line. Every transition, of only the last customer in line, from the longer line to the shorter line may accompanied by a certain fixed cost. Thus, a transition from the longer queue to the shorter queue occurs whenever the difference between the lines reaches a certain discrete threshold (d = 2, 3, …). In this study, we focus on the stochastic analysis of the number of transitions of an arbitrary customer.

中文翻译：

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使用 JOCKEYING 的最短排队系统的新面貌

我们引入了一个马尔可夫排队系统，该系统具有泊松到达、指数服务以及两个并行和等效服务器之间的竞争。到达的客户承认最短的路线。每次从排队的最后一位顾客从较长的线路到较短的线路的转变都可能伴随着一定的固定成本。因此，每当行之间的差异达到某个离散阈值时，就会发生从较长队列到较短队列的转换（d= 2, 3, ...)。在这项研究中，我们专注于对任意客户的转换次数的随机分析。