The Gini index of demand imbalances in public transport

Daniel Hörcher,Daniel J Graham

doi:10.1007/s11116-020-10138-4

Abstract

The paper studies a general bidirectional public transport line along which demand varies by line section. The length of line sections also varies, and therefore their contribution to aggregate (line-level) user and operational costs might be different, even if demand levels were uniform. The paper proposes the Gini index as a measure of demand imbalances in public transport. We run a series of numerical simulations with randomised demand patterns, and derive the socially optimal fare, frequency and vehicle size variables in each case. We show that the Gini coefficient is a surprisingly good predictor of all three attributes of optimal supply. These results remain robust with inelastic as well as elastic demand, at various levels of aggregate demand intensity. In addition, we find that lines facing severe demand imbalances generate higher operational cost and require more public subsidies under socially optimal supply, controlling for the scale of operations. The results shed light on the bias introduced by the assumption of homogeneous demand in several existing public transport models.

Highlights

Short-run supply optimisation has a long-standing history at the boundary between transport planning and economics
Delivering the core contribution of the paper, in a series of randomised numerical simulations we show that the Gini index can be identified as an important predictor of the socially optimal service frequency and vehicle size
This study investigates the impact of line-level demand imbalances on the socially optimal public transport supply, including service frequency and vehicle size, and the economic and financial performance of service provision

Summary

Introduction

Short-run supply optimisation has a long-standing history at the boundary between transport planning and economics. Hörcher and Graham (2018) show in the simplest back-haul setting that the asymmetry in demand between jointly served markets may have crucial impact on (1) the optimal capacity, (2) the equilibrium occupancy rate of vehicles and the crowding experience of passengers, (3) optimal pricing decisions, and (4) the financial and economic performance of public transport provision In this follow-up paper we expand the spatial scope of analysis from the back-haul problem to entire public transport lines. Travel times on line sections range between less than 2 min to more than 5 min, which implies that the share of inter-station markets in operational and user costs might not be uniform either For this reason, a more compact measure of the joint distribution of demand levels and social costs will be required to study the impact of line-level demand fluctuations

Methodology

Conclusions

Findings

Compliance with ethical standards