Location-Allocation of Emergency Service Systems in Light Traffic

We study the location-allocation optimization problem for emergency service system (ESS) design in the regime of light traffic. Given the time-critical nature of emergency response, performance metrics in ESS location-allocation problems are usually defined as functions of response time, measured from call arrival to the initiation of on-scene service. However, for queued calls that experience waiting, their response-time distributions are analytically complex. As a result, the associated performance metrics are either difficult to compute or highly nonlinear in the location-allocation decisions, rendering subsequent optimization intractable. To address these challenges, this study leverages light-traffic queueing asymptotics to develop tractable queueing-based location-allocation optimization models that explicitly capture decision-dependent stochasticity in demand arrivals, service durations, and server availability. We first derive asymptotic characterizations of the performance loss for queued calls in both single-server and multiserver spatial queues as the demand arrival rate vanishes. Comprehensive simulations demonstrate that the proposed asymptotic approximations accurately capture the actual performance of queued calls when traffic intensity is below 15%, a regime relevant for many ESS applications. We then apply the asymptotic approximation to ESS location-allocation problems in which the service regions of servers are disjoint. The special structure of the asymptotic loss allows a broad class of performance metrics to be represented as bilinear functions of the location-allocation decision variables, leading to tractable mixed-integer linear programming formulations with provable error bound guarantees on solution quality. Numerical experiments show that the proposed models outperform established benchmarks in the literature, yielding solutions that are near-optimal relative to brute-force enumeration while remaining computationally scalable as the number of demand nodes increases. Using real lift-trap rescue data from Singapore, we further show that the recommended location-allocation policy reduces the annual number of late rescues by about 70% compared with the status quo.

Funding: This work was supported by the Singapore MOE AcRF Tier 2 [Grants A-8003521-00-00, A-8002472-00-00] and the Future Resilient Systems project supported by the National Research Foundation Singapore under its CREATE programme. This work was also supported by The Chinese University of Hong Kong’s Improvement on Competitiveness in Hiring New Faculties Funding Scheme.

Supplemental Material: All supplemental materials, including the code, data, and files required to reproduce the results, are available at https://doi.org/10.1287/opre.2024.1272.