In this paper, we consider a \(\text {Cox}/G_t/\infty \) 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 timescale variations often observed in practice. We prove a homogenization property for this system, which yields an approximation by an \(M_t/G_t/\infty \) queue with some effective 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.

在本文中，我们考虑随机环境中的\（\ text {Cox} / G_t / \ infty \）无限服务器排队模型。更具体地说，我们服务器中的到达率被建模为高度波动的随机过程，可以说它考虑到了在实践中经常观察到的一些较小的时间尺度变化。我们证明了该系统的均质性，它通过具有一些有效参数的\（M_t / G_t / \ infty \）队列产生近似值。我们的局限性结果包括对活动服务器数量的描述，累计的总输入量和存储方程式的解。因此，在所考虑的快速振荡环境中，我们展示了如何通过更经典的马尔可夫系统来近似随机环境中的排队系统。