An analysis of queues with delayed information and time-varying arrival rates
An analysis of queues with delayed information and time-varying arrival rates
复制标题
具有延迟信息和时变到达率的队列分析
DOI：
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发表时间：
2018
期刊：
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通讯作者：
Elizabeth Wesson
中科院分区：
文献类型：
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作者：
Jamol Pender;R. Rand;Elizabeth Wesson
了解延迟信息如何影响排队系统是一个重要的研究领域。然而，当前的许多文献都忽略了许多排队系统的一个重要特征，即非平稳到达。非固定到达模拟了这样一个事实：客户倾向于在一天中的某些时间而非以恒定速率访问服务。在本文中，我们分析了两个二维确定性流体模型，该模型结合了基于延迟队列长度信息和时变到达的客户选择行为。在第一个模型中，顾客收到的队列长度信息延迟了常数 $$\Delta $$Δ。在第二个模型中，顾客通过队列长度的移动平均来接收有关队列长度的信息，其中移动平均窗口为 $$\Delta $$Δ。我们分析了时变到达率的影响，并使用渐近分析表明，时变到达率不会影响临界延迟，除非时变到达率的频率是临界延迟的两倍。当到达率的频率是临界延迟的两倍时，稳定性会通过由模型参数确定的楔形而放大。因此，这个问题使我们能够将非线性动力学、参数激励、延迟和时变队列的理论结合在一起，以深入了解信息对排队系统的影响。
Understanding how delayed information impacts queueing systems is an important area of research. However, much of the current literature neglects one important feature of many queueing systems, namely non-stationary arrivals. Non-stationary arrivals model the fact that customers tend to access services during certain times of the day and not at a constant rate. In this paper, we analyze two two-dimensional deterministic fluid models that incorporate customer choice behavior based on delayed queue length information with time-varying arrivals. In the first model, customers receive queue length information that is delayed by a constant $$\Delta $$Δ. In the second model, customers receive information about the queue length through a moving average of the queue length where the moving average window is $$\Delta $$Δ. We analyze the impact of a time-varying arrival rate and show using asymptotic analysis that the time-varying arrival rate does not impact the critical delay unless the frequency of the time-varying arrival rate is twice that of the critical delay. When the frequency of the arrival rate is twice that of the critical delay, then the stability is enlarged by a wedge that is determined by the model parameters. As a result, this problem allows us to combine the theory of nonlinear dynamics, parametric excitation, delays, and time-varying queues together to provide insight into the impact of information on queueing systems.