Assessment of flexible timetables in real-time traffic management of a railway bottleneck Andrea D’Ariano a , Dario Pacciarelli b, * , Marco Pranzo c a Department of Transport and Planning, Delft University of Technology, The Netherlands b Dipartimento di Informatica e Automazione, Universita ` Roma Tre, Via della Vasca Navale, 79, 00146 Roma, Italy c Dipartimento di Ingegneria dell’Informazione, Universita ` di Siena, Italy Received 7 December 2006; received in revised form 30 July 2007; accepted 31 July 2007 Abstract A standard practice to improve punctuality of railway services is the addition of time reserves in the timetable to recover perturbations occurring in operations. However, time reserves reduce line capacity, and the amount of time reserves that can be inserted in congested areas is, therefore, limited. In this paper, we investigate the new concept of flexible timetable as an effective policy to improve punctuality without decreasing the capacity usage of the lines. The principle of a flexible timetable is to plan less in the timetable and to solve more inter-train conflicts during operations. The larger degree of free- dom left to real-time management offers better chance to recover disturbances. We illustrate a detailed model for conflict resolution, based on the alternative graph formulation, and analyze different algorithms for resolving conflicts, based on simple local rules or global optimization. We compare the solutions obtained for different levels of flexibility and buffer time inserted in the timetable. An extensive computational study, based on a bottleneck area of the Dutch railway network, confirms that flexibility is a promising concept to improve train punctuality and to increase the throughput of a railway network. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Flexible timetable; Conflict resolution; Real-time train scheduling 1. Introduction The management of railway traffic in congested areas is usually based on off-line timetable design. Building a timetable may require several months, during which many variants are discussed in depth and all possible conflicts among trains are solved. In real-time, trains are managed with strict adherence to the timetable. How- ever, when train runs are perturbed (causing primary delays), signaling and route conflicts may arise with respect to the scheduled train paths (thus propagating to other trains as secondary delays). For this reason, time reserves are usually inserted in the timetable in order to reduce the effects of minor perturbations (Carey 0968-090X/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.trc.2007.07.006 * Corresponding author. Tel.: +39 0655173238; fax: +39 065573030. E-mail addresses: a.dariano@tudelft.nl (A. D’Ariano), pacciarelli@dia.uniroma3.it (D. Pacciarelli), pranzo@dii.unisi.it (M. Pranzo). Available online at www.sciencedirect.com Transportation Research Part C 16 (2008) 232–245 www.elsevier.com/locate/trc