This paper presents an equilibrium-based modeling framework for emergency response (ER) workload balancing for robust operations in metropolitan areas. The problem is formulated as a non-linear mathematical program (NLP), which determines the optimal maximum workload for each ER station such that the weighted sum of the area-wide expected response time and its variation is minimized. The concept of Marginal Cost of Uncertainty (MCU) is introduced to measure the impact of a station's workload increase on the robustness of the area-wide service performance. The solution of the NLP is proved to be equivalent to a state of equilibrium in which all stations have a minimum MCU. An iterative solution methodology is developed, which adopts a modified version of the Frank-Wolfe decomposition algorithm for convex optimization. The workload is iteratively balanced among adjacent stations until the state of equilibrium is achieved. At equilibrium, no station can reduce its MCU value by unilaterally shifting a part of its workload to any other station(s) in the area. The developed framework is applied to determine the optimal workload balancing strategy for 58 fire stations serving the City of Dallas. The framework is shown to enhance the robustness of the ER service performance especially in situations with imbalanced workloads.

本文提出了一种基于平衡的建模框架，用于紧急响应（ER）工作负载平衡，以实现大都市地区的稳健运营。该问题被表述为非线性数学程序 (NLP)，它确定每个 ER 站的最佳最大工作负载，从而使区域范围内的预期响应时间及其变化的加权和最小化。引入不确定性边际成本（MCU）的概念来衡量站点工作负载增加对区域服务性能稳健性的影响。NLP 的解被证明等价于所有站点具有最小 MCU 的平衡状态。开发了一种迭代求解方法，该方法采用凸优化的 Frank-Wolfe 分解算法的修改版本。工作负载在相邻站点之间迭代平衡，直至达到平衡状态。在平衡状态下，任何站点都不能通过单方面将其部分工作负载转移到该区域中的任何其他站点来降低其 MCU 值。开发的框架用于确定服务于达拉斯市的 58 个消防站的最佳工作负载平衡策略。该框架被证明可以增强 ER 服务性能的稳健性，特别是在工作负载不平衡的情况下。开发的框架用于确定服务于达拉斯市的 58 个消防站的最佳工作负载平衡策略。该框架被证明可以增强 ER 服务性能的稳健性，特别是在工作负载不平衡的情况下。开发的框架用于确定服务于达拉斯市的 58 个消防站的最佳工作负载平衡策略。该框架被证明可以增强 ER 服务性能的稳健性，特别是在工作负载不平衡的情况下。