Infinite server queues in a random fast oscillatory environment
Infinite server queues in a random fast oscillatory environment
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DOI：
10.1007/s11134-021-09704-z
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发表时间：
2020-04
期刊：
影响因子：
1.2
通讯作者：
Yiran Liu;Harsha Honnappa;S. Tindel;N. Yip
中科院分区：
文献类型：
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作者：
Yiran Liu;Harsha Honnappa;S. Tindel;N. Yip
本文考虑一类随机环境下的有限服务台排队模型。更具体地说，我们的服务器的到达率被建模为一个高度波动的随机过程，这可以说考虑到了实践中经常观察到的一些小的时间尺度变化。我们证明了该系统的齐次化性质，给出了一个带有一些有效参数的排队逼近。我们的限制结果包括对活动服务器数量的描述、总累积输入和存储方程的解。因此，在所考虑的快速振荡环境下，我们证明了随机环境中的排队系统如何被更经典的马尔可夫系统逼近。
In this paper, we consider ainfinite 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 anqueue 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.