Train delay and passenger travel time minimization in real-time railway traffic management

Railway service is a key factor to reduce congestion on highways and other means of transport, especially in densely populated areas, and to provide an eco-friendly and sustainable way of transport. In order to attract new customers from other transport modes, European countries defined challenging targets in terms of Quality of Service (QoS) that the railway companies should provide to their customers [2,16,20]. However, while the customers of Train Operating Companies (TOC) are the passengers, the customers of Infrastructure Managers (IM) are the trains operated by the railway companies. This translates to two different views in the problem. This paper addresses the trade-off and the strategic interaction between the objectives of the abovementioned stakeholders, TOC and IM. While the IM objective relates to train delays, the TOC aims at minimizing the passenger travel time. Since in heavily used railway networks any small delay easily propagates to other trains, the IM would like to reschedule trains in real time in order to Francesco Corman Section of Transport Engineering and Logistics, Delft University of Technology Mekelweg 2 – 2628CD Delft, The Netherlands Tel.: +31 15 27 85148 Fax: +31 15 27 81397 E-mail: f.corman@tudelft.nl Andrea D’Ariano, Dario Pacciarelli, Federico Sabene, Marcella Samà Department of Engineering, Università degli Studi Roma Tre via della vasca navale 79 – 00146 Roma, Italy 2 Francesco Corman et al. minimize train delays, taking into account the relative importance of different trains established by the TOC. On the other hand, changing train orders may result in extra delays for those passengers that miss a connection at some station, therefore the TOC would like to keep the connections that are more relevant to the passengers in order to minimize passenger travel times. Therefore, due to the separation of IM and TOC, the actual QoS perceived by the passengers can be viewed as the result of a strategic interaction between IM and TOC, i.e. a game. In this game, the strategy of the TOC consists of defining the relative importance of the different circulating trains, e.g., by specifying a weight for each train equal to the number of passengers that are expected on board the train. The amount of passengers expected on a train can be computed by a passenger routing procedure exploiting common assumption on rationality and information provision to passengers. The strategy of the IM consists of defining a schedule for the trains with minimal total weighted delay of the trains. This paper presents models and algorithms for the study of the strategic interaction between IM and TOC; we are able to compute a Nash equilibrium of the resulting game, that corresponds to a solution of the problem. We moreover consider other solutions of interest, namely (i) an optimal train schedule from the IM viewpoint, (ii) an optimal train schedule from the TOC viewpoint, (iii) a surrogate for the common practice of railway traffic management, and (iv) two compromise solutions for the combined problem of the IM and TOC companies, both defining a Nash solution of a suitable game. The results are evaluated from the point of view of the IM and TOC objectives.