论文标题
马尔可夫队的泊松控制
Markovian queues with Poisson control
论文作者
论文摘要
我们研究了由控制器在泊松过程确定的随机时间检查的控制器检查的马尔可夫队队。经检查后，控制器将服务速度设置为等于队列中当前客户数量的最小值和一定的最大服务速度；此服务速度盛行，直到下一个考试时间为止。我们研究了由队列长度和服务器速度的二维马尔可夫过程，特别是两种具有时间尺度分离的制度，特别是针对无限频繁和无限长的检查时间。在中级政权中，该分析被证明是极具挑战性的。为了进一步了解模型动力学，我们然后分析了控制器只是观察者而不会改变服务器速度的模型的两个变体。
We investigate Markovian queues that are examined by a controller at random times determined by a Poisson process. Upon examination, the controller sets the service speed to be equal to the minimum of the current number of customers in the queue and a certain maximum service speed; this service speed prevails until the next examination time. We study the resulting two-dimensional Markov process of queue length and server speed, in particular two regimes with time scale separation, specifically for infinitely frequent and infinitely long examination times. In the intermediate regime the analysis proves to be extremely challenging. To gain further insight into the model dynamics we then analyse two variants of the model in which the controller is just an observer and does not change the speed of the server.
