Investigation of a Pricing Model for Railway Track Slots and Stochastic Demand Consideration on Road Networks

Robert König, Master Thesis, Winter 2007/08

Supervisors: Martin Fuchsberger, Vania Dos Santos Eleuterio, Max Fehr, Philipp Schmidt

The first part of this project concerns fair pricing of allocated track slots on a railway network in Switzerland. There are several parties with different views and influences on the price: the infrastructure owner(s), cargo companies, passenger traffic companies, the government etc. We call a price "fair", if the tracks are allocated in a socially optimal way. The model develloped by Nesterov and de Palma in 2000 for the road traffic assignment was adapted for the problem. The model allows a price formulation where the resulting user equilibrium flow corresponds to the social optimum flow at minimal cost. This master thesis investigates the differences between the prices according to the model and the prices proposed by a study from the Institute of Transport Planning and Systems at the ETH Zurich. Although the case study showed that the model is suited to model fair prices, it also points out that the model's practicability is dependent on the number of routing alternatives inside the considered railway network.

The lack of routing alternatives in the case study lead our focus back to road networks. In traffic assignment problems it is usually assumed that the number of drivers which are traveling from an origin to a destination is given in some form. In this thesis we look at demand uncertainty. In particular a definition of user equilibrium and social optimum is proposed in the situation of stochastic demand similar to the concepts of the static traffic assignment model of Nesterov and de Palma. The traffic behaviour is then investigated on the Sioux Falls network using stochastic demand. Recall that selfish behaviour leads to congestions in the network, i.e. drivers experience additional delays. To decrease these congestions arising in the network we augmented the traveltime of the travel arcs (stricter speed limitations) based on observed delays. We considered two kind of delays: the delays based on the stochastic demand user equilibrium and the average delays of all sample delays. The numerical results showed that adding the first delays does not decrease the average total congestion as much as adding the average delays, but the occurence frequency of congestions is smaller. Hence it remains unclear which of the two delays serves the purpose of reducing congestions better.