An analysis of Wardrop equilibrium and social optimum in congested transit networks

TL;DR

This paper investigates the gap between Wardrop equilibrium and social optimum in congested transit networks, proposing optimization methods to achieve better system efficiency and quantify inefficiencies through the price of anarchy.

Contribution

It introduces two equivalent optimization formulations for the social optimum in transit networks and characterizes the optimal flows, enabling efficiency analysis.

Findings

Proposed two equivalent optimization problems for social optimum.

Characterized the social optimum flows in transit networks.

Enabled computation of the price of anarchy for system efficiency.

Abstract

The effective design and management of public transport systems are essential to ensure the best service for users. The performance of a transport system will depend heavily on user behaviour. In the common-lines problem approach, users choose which lines to use based on the best strategy for them. While Wardrop equilibrium has been studied for the common-lines problem, no contributions have been made towards achieving the social optimum. In this work, we propose two optimisation problems to obtain this optimum, using strategy flow and line flow formulations. We prove that both optimisation problems are equivalent, and we obtain a characterisation of the social optimum flows. The social optimum makes it possible to compute the price of anarchy (PoA), which quantifies the system's efficiency. The study of the PoA enables the effective design and management of public transport systems, guaranteeing the best service to users.