This thesis presents an equilibrium-based modeling framework for emergency response (ER) workload balancing to achieve robust operation in large-scale metropolitan areas. The problem is formulated as a non-linear mathematical program (NLP), which determines the optimal workload cutoff for each ER station such that the weighted sum of the area-wide expected response time and its variation are minimized. The concept of Marginal Cost of Uncertainty (MCU) is introduced to measure the impact of a station’s workload increase on 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 shifted 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 especially under operation scenarios with imbalanced workloads.

Degree Date

Spring 4-26-2019

Document Type


Degree Name



Civil and Environmental Engineering


Prof. Khaled Abdelghany

Subject Area

Civil Engineering, Computer Science



Creative Commons License

Creative Commons Attribution-Noncommercial 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License