Demand Equilibria in Spatial Service Systems

Problem definition: A service is offered at certain locations (“facilities”) in a geographical region. Customers can appear anywhere in the region, and each customer chooses a facility based on travel distance as well as expected waiting time. Customer decisions affect waiting times by increasing the load on a facility, and thus, they impact other customers’ decisions. The service provider can also influence service quality by adjusting service rates at each facility. Methodology/results: Using a combination of queueing models and computational geometry, we characterize demand equilibria in such spatial service systems. An equilibrium can be visualized as a partition of the region into service zones that form as a result of customer decisions. Service rates can be set in a way that achieves the best-possible social welfare purely through decentralized customer behavior. Managerial implications: We provide techniques for computing and visualizing demand equilibria as well as calculating optimal service rates. Our analytical and numerical results indicate that in many situations, resource allocation is a far more significant source of inefficiency than decentralized behavior. Funding: J. G. Carlsson was funded by the METRANS Transportation Consortium Grant NCST-USC-RR-24-12 and the Office of Naval Research Grant N00014-24-1-2277-P00001. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2023.0434 .