Demand Equilibria in Spatial Service Systems

37 Pages Posted: 16 Apr 2024

See all articles by John Gunnar Carlsson

John Gunnar Carlsson

University of Southern California - Epstein Department of Industrial & Systems Engineering

Xiaoshan Peng

Indiana University - Kelley School of Business

Ilya Ryzhov

affiliation not provided to SSRN

Date Written: April 14, 2024

Abstract

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 impact other customers' decisions. The service provider can also influence service quality by adjusting service rates at each facility. 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. 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.

Keywords: spatial service systems, geographical partitioning, Voronoi diagrams, equilibrium analysis

Suggested Citation

Carlsson, John Gunnar and Peng, Xiaoshan and Ryzhov, Ilya, Demand Equilibria in Spatial Service Systems (April 14, 2024). Available at SSRN: https://ssrn.com/abstract=4794156 or http://dx.doi.org/10.2139/ssrn.4794156

John Gunnar Carlsson

University of Southern California - Epstein Department of Industrial & Systems Engineering ( email )

United States

Xiaoshan Peng (Contact Author)

Indiana University - Kelley School of Business ( email )

1309 East Tenth Street
Bloomington, IN 47405-1701
United States

Ilya Ryzhov

affiliation not provided to SSRN

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