A new look at departure time choice equilibrium models with heterogeneous users

TL;DR

This paper introduces a systematic, analytical approach to modeling departure time choice equilibrium with heterogeneous users, leveraging optimal transport theory and linear programming to identify conditions for equilibrium patterns.

Contribution

It develops a novel analytical framework for DTCE with heterogeneity, extending to multiple types and revealing the Monge property as key for equilibrium sorting patterns.

Findings

Equilibrium sorting patterns require the Monge property of schedule delay functions.

The approach allows analytical solutions for models with the Monge property.

The method extends to problems with more than two heterogeneity types.

Abstract

This paper presents a systematic approach for analyzing the departure-time choice equilibrium (DTCE) problem of a single bottleneck with heterogeneous commuters. The approach is based on the fact that the DTCE is equivalently represented as a linear programming problem with a special structure, which can be analytically solved by exploiting the theory of optimal transport combined with a decomposition technique. By applying the proposed approach to several types of models with heterogeneous commuters, it is shown that (i) the essential condition for emerging equilibrium "sorting patterns," which have been known in the literature, is that the schedule delay functions have the "Monge property," (ii) the equilibrium problems with the Monge property can be solved analytically, and (iii) the proposed approach can be applied to a more general problem with more than two types of heterogeneities.