论文标题
在随机快速振荡环境中无限服务器队列
Infinite server queues in a random fast oscillatory environment
论文作者
论文摘要
在本文中，我们考虑在随机环境中$ g_t/g_t/\ infty $ infty $ infinite服务器排队模型。更具体地说，我们的服务器中的到达率被建模为一个高度波动的随机过程，可以说考虑到一些在实践中经常观察到的小时尺度变化。我们显示了该系统的均质化属性，该属性通过$ M_T/g_t/\ infty $ queue产生了带有修改参数的近似值。我们的限制结果包括描述活动服务器数量，总累积输入以及存储方程的解决方案。因此，在正在考虑的快速振荡环境中，我们展示了如何通过更古典的马尔可夫系统近似随机环境中的排队系统。
In this paper, we consider a $G_t/G_t/\infty$ infinite server queueing model in a random environment. More specifically, the arrival rate in our server is modeled as a highly fluctuating stochastic process, which arguably takes into account some small time scale variations often observed in practice. We show a homogenization property for this system, which yields an approximation by a $M_t/G_t/\infty$ queue with modified parameters. Our limiting results include the description of the number of active servers, the total accumulated input and the solution of the storage equation. Hence in the fast oscillatory context under consideration, we show how the queuing system in a random environment can be approximated by a more classical Markovian system.
