Admission control and service rate speedup may be used during periods of congestion to minimize customer waiting in different service settings. In a healthcare setting, this can mean sending patients to alternative care facilities that may take more time and/or provide less ideal treatment. While waiting can be detrimental to patient outcomes, strategies used to control congestion can also be costly. In this work, we examine a multi-server queueing system that considers both admission control and speedup. We use dynamic programming to characterize properties of the optimal control and find that in some instances the optimal policy has a simple form of a threshold policy. Leveraging this insight, we examine a queueing system where speedup is used when the number of customers (patients) in the system exceeds some threshold and admission control is used when that number exceeds some (potentially different) threshold. Using a fluid model and a stochastic loss model, we develop a methodology to derive approximations for the probability that speedup will be applied, the probability that admission control will be applied and the expected queue length customers experience. We use the approximations as the basis for a greedy heuristic to derive a near optimal solution to the original stochastic optimization problem. We use simulation to demonstrate the quality of these approximations and find that they can be quite accurate and robust. This analysis can provide insight to managers deciding how to balance admission control and speedup in service settings: when and to what extent to use each.

在拥堵期间可以使用准入控制和服务速率加速，以最大程度地减少客户在不同服务设置中的等待时间。在医疗保健环境中，这可能意味着将患者送往可能需要更多时间和/或提供较不理想治疗的替代性医疗机构。虽然等待可能不利于患者的预后，但用于控制交通拥堵的策略也可能代价高昂。在这项工作中，我们研究了同时考虑准入控制和加速的多服务器排队系统。我们使用动态编程来表征最优控制的特性，并发现在某些情况下，最优策略具有阈值策略的简单形式。利用这种见解，我们研究一种排队系统，其中当系统中的客户（患者）数量超过某个阈值时使用加速，而当该数量超过某个（可能不同）阈值时使用入场控制。通过使用流体模型和随机损失模型，我们开发了一种方法来推导应用加速的概率，应用准入控制的概率以及预期的队列长度客户体验的近似值。我们使用近似值作为贪婪启发式算法的基础，以得出原始随机优化问题的近似最优解。我们使用仿真来证明这些近似的质量，并发现它们可以非常准确和可靠。