Train Timetable Design for Shared Railway Systems using a Linear Programming Approach to Approximate Dynamic Programming (original) (raw)

In the last 15 years, the use of rail infrastructure by different train operating companies (shared railway system) has been proposed as a way to improve infrastructure utilization and to increase efficiency in the railway industry. Shared use requires coordination between the infrastructure manager and multiple train operators in a competitive framework, so that regulators must design appropriate capacity pricing and allocation mechanisms. However, the resulting capacity utilization from a given mechanism in the railway industry cannot be known in the absence of operations. Therefore assessment of capacity requires the determination of the train timetable, which eliminates any potential conflicts in bids from the operators. Although there is a broad literature that proposes train timetabling methods for railway systems with single operators, there are few models for shared competitive railway systems. This paper proposes a train timetabling model for shared railway systems that explicitly considers network effects and the existence of multiple operators requesting to operate several types of trains traveling along different routes in the network. The model is formulated and solved both as a mixed integer linear programming (MILP) problem (using a 2 commercial solver) and as a dynamic programming (DP) problem. We solve the DP formulation with a novel algorithm based on a linear programming (LP) approach to approximate dynamic programming (ADP) that can solve much larger problems than are computationally intractable with commercial MILP solvers. The model simulates the optimal decisions by an infrastructure manager for a shared railway system with respect to a given objective function and safety constraints. This model can be used to evaluate alternative capacity pricing and allocation mechanism. We demonstrate the method for one possible capacity pricing and allocation mechanism, and show how the competing demands and the decisions of the infrastructure manager under this mechanism impact the operations on a shared railway system for all stakeholders. Keywords-Shared railway systems capacity planning, train timetabling problem, linear programming approach to approximate dynamic programming, adaptive learning, q-factors 1. INTRODUCTION In the last 15 years, several countries have promoted the use of shared railway systems that allow independent operators to access the infrastructure. This enables higher levels of infrastructure utilization (Gomez-Ibanez and de Rus, 2006). However, shared railway corridors require coordination between the infrastructure manager-typically the owner of the infrastructure-and multiple train operators (Gomez-Ibanez, 2003). This coordination involves determining which trains can access the infrastructure at each time (capacity allocation) and the access price they need to pay (capacity pricing). According to (Roth, 2002) and (Vazquez, 2003), ideal capacity pricing and allocation mechanisms should be reproducible and transparent, easy to understand, and non-discriminatory (especially when the operators compete in the same market). Simple capacity pricing and allocation rules are used in other network industries (such as electric power or telecommunication). However, in the railway industry, the characteristics of the network and operations critically affect capacity and safety. According to (Krueger et al., 1999) railway capacity is defined as "a measure of the ability to move a specific amount of traffic over a defined rail with a given set of resources under a specific service plan." As a result, the implications for the railway system of the capacity pricing and allocation mechanism remain unclear, even for simple mechanisms used in other contexts. In other words, to understand the implications of capacity regulation in the rail industry, we have to recognize that infrastructure capacity utilization is endogenous: it