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Queues with Updating Information: Finding the Amplitude of Oscillations
arXiv - CS - Performance Pub Date : 2021-04-27 , DOI: arxiv-2104.13350
Philip Doldo, Jamol Pender

Many service systems provide customers with information about the system so that customers can make an informed decision about whether to join or not. Many of these systems provide information in the form of an update. Thus, the information about the system is updated periodically in increments of size $\Delta$. It is known that these updates can cause oscillations in the resulting dynamics. However, it is an open problem to explicitly characterize the size of these oscillations when they occur. In this paper, we solve this open problem and show how to exactly calculate the amplitude of these oscillations via a fixed point equation. We also calculate closed form approximations via Taylor expansions of the fixed point equation and show that these approximations are very accurate, especially when $\Delta$ is large. Our analysis provides new insight for systems that use updates as a way of disseminating information to customers.

中文翻译:

信息更新队列:查找振荡幅度

许多服务系统都向客户提供有关系统的信息,以便客户可以就是否加入做出明智的决定。这些系统中的许多系统都以更新的形式提供信息。因此,关于系统的信息以大小$ \ Delta $的增量定期更新。众所周知,这些更新会导致动态变化。然而,当这些振荡发生时,明确表征这些振荡的大小是一个未解决的问题。在本文中,我们解决了这个开放性问题,并展示了如何通过不动点方程式精确计算这些振荡的幅度。我们还通过定点方程的泰勒展开式计算了闭合形式的近似值,并表明这些近似值非常准确,尤其是在$ \ Delta $大的情况下。
更新日期:2021-04-29
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