Models for the capacity planning of large railway networks

The constrains for the planning process are strongly related to the operation principle of the regarded railway system. In most cases the fixed block operation principle is applied. In this case, the railway infrastructure is divided into sections that can be occupied by just one train at a time. The run of a train can hence be regarded as a subsequent occupation of sections.

At planning stage, trains of various different companies need to be scheduled on the railway infrastructure. Conflicts occur, if two or more trains occupy one section of the railway infrastructure at the same time.
In order to perform capacity planning, we need a conflict free schedule which allows us to calculate a technically feasible demand to evaluate the capacity consumption in parts of the railway infrastructure.

The ongoing process of liberalisation in the EU railway system aims to provide free access to any company on the railway infrastructure. This motivates the need for a transparent conflict solving procedure of the train scheduling problem. There are several ways to solve conflicts in a schedule. A dispatcher can shift trains in time, he can assign a different route to the train or he can adjust the run of a train by changing his speed or prolonging a stop in a train station in order to solve a conflict.

These conflict solving procedures effect the train operating companies, since they want to provide best service to their customers. Travelling delays for example, are undesired by travellers and may prevent the customers from choosing this train operating company again.

If the dispatcher would know all effects on the companies quantitatively, we would be able to optimise the conflict solving procedure and could find a conflict free schedule that minimises these effects. However, the quantitative impact of a conflict solving decision on the company’s revenue is private information and is thus not shared with concurrent companies. Even if there is a dispatcher, the companies might not tell him the truth in order to manipulate the dispatcher’s decisions.

We show that a game theoretical approach can be used in order to evaluate an optimal decision. Therefore we reduce the railway system to a task allocation model and assess the scheduling decisions monetarily.

Under the assumption that the quantitative impact of the conflict solving procedure is private information, we show that conflicts can be solved adequately without having a central entity/dispatcher.

Since we regard monetary effects of the conflict solving procedures, we could use the game theoretic approach and the reduced model of the railway system in order to perform pricing. Future research will determine whether mechanism design can be used in order to implement a pricing mechanism for this game theoretical setting.