Pricing of track time in railroad operations: An internal market approach

This paper presents a computable equilibrium model of an internal market for track resources in a railroad. The problem of estimating the value to each train of track capacity, which in turn is used to create the actual train schedules, is formulated as an N-player, noncooperative game with nondisjoint strategy sets. In this model, the effects of other traffic on a given train schedule (the mean and variance of total travel time) are represented by a line delay model for a scheduled railroad on a partially double track rail line. The generalized Nash equilibrium for the resulting game-theoretic model is found as a solution to a quasi-variational inequality problem. The goal of this model is to ascertain how close the prices from the internal market system (the game-theoretic model) comes to globally optimal prices. Data from a major Class I railroad are used to explore this issue in detail.