论文标题
在有限的时间间隔内与$ m/m/m/\ infty $队列的出发数量
On the number of departures from the $M/M/\infty$ queue in a finite time interval
论文作者
论文摘要
在本文中，我们在有限的时间间隔中分析了从最初空的$ m/m/m/\ infty $系统的出发人数。我们在从时间来源开始的一个指数分布的时间内观察系统。然后，我们考虑了吸收的马尔可夫链，描述了系统中的到达和出发数量，直到观察者离开系统，触发马尔可夫链的吸收。吸收的马尔可夫链的发电机在某些希尔伯特空间中引起了一个自助式操作员。然后，光谱理论的使用使我们能够计算$ m/m/m/\ infty $系统的几个瞬态特征的拉普拉斯变换（即，马尔可夫链的过渡次数，直到吸收，从系统中出发等）。分析扩展到某些有限整数$ c $}的有限容量/c/c $系统。
In this paper, we analyze the number of departures from an initially empty $M/M/\infty$ system in a finite time interval. We observe the system during an exponentially distributed period of time starting from the time origin. We then consider the absorbed Markov chain describing the number of arrivals and departures in the system until the observer leaves the system, triggering the absorption of the Markov chain. The generator of the absorbed Markov chain induces a selfadjoint operator in some Hilbert space. The use of spectral theory then allows us to compute the Laplace transform of several transient characteristics of the $M/M/\infty$ system (namely, the number of transitions of the Markov chain until absorption, the number of departures from the system, etc.). The analysis is extended to the finite capacity $MM/c/c$ system for some finite integer $c$}.
