Many service systems use technology to notify customers about their expected waiting times or queue lengths via delay announcements. However, in many cases, either the information might be delayed or customers might require time to travel to the queue of their choice, thus causing a lag in information. In this paper, we construct a neutral delay differential equation model for the queue length process and explore the use of velocity information in our delay announcement. Our results illustrate that using velocity information can have either a beneficial or detrimental impact on the system. Thus, it is important to understand how much velocity information a manager should use. In some parameter settings, we show that velocity information can eliminate oscillations created by delays in information. We derive a fixed point equation for determining the optimal amount of velocity information that should be used and find closed-form upper and lower bounds on its value. When the oscillations cannot be eliminated altogether, we identify the amount of velocity information that minimizes the amplitude of the oscillations. However, we also find that using too much velocity information can create oscillations in the queue lengths that would otherwise be stable.

中文翻译：

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通过新型延迟公告限制具有延迟信息的队列中的振荡

许多服务系统使用技术通过延迟公告通知客户他们的预期等待时间或队列长度。但是，在许多情况下，信息可能会延迟，或者客户可能需要时间前往他们选择的队列，从而导致信息滞后。在本文中，我们为队列长度过程构建了一个中性延迟微分方程模型，并探索了在延迟公告中速度信息的使用。我们的结果表明，使用速度信息可以对系统产生有益或有害的影响。因此，了解经理应该使用多少速度信息非常重要。在一些参数设置中，我们表明速度信息可以消除信息延迟造成的振荡。我们推导出一个不动点方程来确定应该使用的最佳速度信息量，并找到其值的封闭形式的上限和下限。当振荡不能完全消除时，我们确定使振荡幅度最小的速度信息量。然而，我们还发现使用过多的速度信息会在队列长度中产生振荡，否则会保持稳定。