Queues with Slowly Varying Arrival and Service Processes
研究一种M/G/1排队系统的推广，其中到达率和服务时间分布由缓慢变化的马尔可夫链控制，利用可分解性方法推导队长稳态分布，适用于时变参数场景如库存、电话、计算机网络等。
We examine a generalisation of the M/G/1 queue. The arrival and service processes are governed by a Markov chain which determines the rate of arrival and the service time distribution from a finite set. This Markov chain is assumed to vary “slowly”, so that we are able to derive analytical results for the stationary distribution of the queue length using an approach based on decomposability. The practical interest of this model stems from the numerous applications where the parameters of queueing systems are time varying, such as inventory models, telephone systems, time-sharing systems, computer networks with bursty traffic, etc. We also show how this approach can be extended to arbitrary networks of queues and in particular to those with product form solution.