Highway toll allocation problem revisited: new methods and characterizations

TL;DR

This paper introduces new methods for highway toll allocation, characterizes them axiomatically, compares their properties, and evaluates their performance using real-world data.

Contribution

It proposes two novel toll allocation rules, characterizes them axiomatically, and integrates them into a general family of methods, advancing the understanding of toll distribution strategies.

Findings

New allocation methods outperform existing ones in certain scenarios

Axiomatic characterizations clarify the properties of each method

Performance evaluation demonstrates practical applicability

Abstract

This paper considers the highway toll allocation problem (Wu, van den Brink, and Est\'evez-Fern\'andez in Transport Res B-Meth 180:10288, 2024). The aim is to allocate the tolls collected from the users of a highway across the various road sections. To this end, the authors propose, among others, the Segments Equal Sharing method, which is characterized and reinterpreted as a specific solution of a cooperative game associated with the problem. This paper presents two new allocation rules: the Segments Proportional Sharing method and the Segments Compensated Sharing method. We axiomatically characterize these new methods and compare their properties to those of the Segments Equal Sharing method. Furthermore, we also examine the relationship of these methods to the solution of the associated cooperative game. We conclude the methodological study by introducing a general family of segment allocation methods that includes the three aforementioned rules. Finally, we evaluate the performance of these methods using a real-world dataset.