\r\nproblem for busy railway stations. Our objective is to allow trains

\r\nto be routed in dense areas that are reaching saturation. Unlike

\r\ntraditional methods that allocate all resources to setup a route for

\r\na train and until the route is freed, our work focuses on the use

\r\nof resources as trains progress through the railway node. This

\r\ntechnique allows a larger number of trains to be routed simultaneously

\r\nin a railway node and thus reduces their current saturation. To

\r\ndeal with this problem, this study proposes an abstract model and

\r\na mixed-integer linear programming formulation to solve it. The

\r\napplicability of our method is illustrated on a didactic example.","references":"[1] A. D\u2019Ariano, Improving Real-Time Train Dispatching: Models,\r\nAlgorithms and Applications. PhD thesis, 2008.\r\n[2] M. Carey, \u201cA model and strategy for train pathing with choice of lines,\r\nplatforms, and routes,\u201d Transportation Research Part B, vol. 28, no. 5,\r\npp. 333\u2013353, 1994.\r\n[3] L. Kroon, \u201cRouting trains through railway stations: complexity issues,\u201d\r\nEuropean Journal of Operational Research, vol. 98, pp. 485\u2013498, 1997.\r\n[4] P. Zwaneveld and L. Kroon, \u201cA decision support system for routing trains\r\nthrough railway stations,\u201d Transactions on the Built Environment, vol. 34,\r\npp. 53\u201358, 1997.\r\n[5] M. Carey and S. Carville, \u201cScheduling and platforming trains at busy\r\ncomplex stations,\u201d Transportation Research Part A: Policy and Practice,\r\nvol. 37, no. 3, pp. 195\u2013224, 2003.\r\n[6] L. Bai, T. Bourdeaud\u2019huy, E. Castelain, and B. Rabenasolo, \u201cA\r\nmixed-integer linear program for routing and scheduling trains through\r\na railway station,\u201d ICORES 2014 - Proceedings of the 3rd International\r\nConference on Operations Research and Enterprise Systems, pp. 445\u2013452,\r\n2014.\r\n[7] P. Pellegrini, G. Marli`ere, and J. Rodriguez, \u201cOptimal train routing and\r\nscheduling for managing traffic perturbations in complex junctions,\u201d\r\nTransportation Research Part B: Methodological, vol. 59, pp. 58\u201380,\r\n2014.\r\n[8] R. M. Lusby, J. Larsen, M. Ehrgott, and D. Ryan, \u201cRailway track\r\nallocation: Models and methods,\u201d OR Spectrum, vol. 33, no. 4, pp.\r\n843\u2013883, 2011.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 152, 2019"}