One-Dependent Regenerative Processes and Queues in Continuous Time
One-Dependent Regenerative Processes and Queues in Continuous Time
复制标题
连续时间内的单相关再生过程和队列
DOI：
10.1287/moor.15.1.175
复制
发表时间：
1990
期刊：
影响因子：
--
通讯作者：
K. Sigman
中科院分区：
文献类型：
--
作者：
K. Sigman
基于对连续时间排队的研究，定义了一种“一依赖”再生过程，并给出了它的遍历性质。我们证明了连续时间Harris递归马尔可夫过程HRMP是这种类型的，并在此基础上给出了HRMP的遍历性的不同证明。接下来，我们引入了由HRMP支配的标记点过程MPP的新概念，并由此得到了一类依赖于1的再生的MPP。这一类包括独立更新过程的叠加、从FIFO GI/GI/c队列的离开过程、马尔可夫调制的到达和来自GI/GI/1/0队列的丢失流溢出。我们还给出了当输入是由HRMP管理的MPP时，将连续时间中的排队表示为HRMP的一般框架，从而获得了连续时间的模拟[20]。在这种情况下，我们考虑带反馈的单服务台排队和串联排队。最后，考虑到再生型模拟的可能性，我们给出了一种单相依再生过程的CLT。
Motivated by the study of queues in continuous time, a "one-dependent" regenerative process is defined and its ergodic properties are given. We show that a continuous time Harris recurrent Markov process HRMP is of this type and give a different proof of the ergodic properties of HRMP's based on this fact. We next introduce the new notion of a marked point process mpp governed by a HRMP and by doing so obtain a class of mpp's that are one-dependent regenerative. This class is shown to include the superposition of independent renewal processes, the departure process from a FIFO GI/GI/c queue, Markov modulated arrivals and the loss stream overflow from a GI/GI/1/0 queue. We also present a general framework for representing queues in continuous time as HRMP's when the input is a mpp governed by a HRMP and thus obtain a continuous time analogue of [20]. In this context we consider a single server queue with feedback and a tandem queue. Finally, due to the potential for regenerative type simulation, we state a CLT for one-dependent regenerative processes.