S. Saad | F. Ossart | J. Bigeon | E. Sourdille | H. Gance
OPEN ACCESS
The present work addresses traffic rescheduling in case of electric infrastructure failure. The power available for train traction is restricted and the traffic must be reorganized according to this constraint. The system behaviour is computed using a dynamic multi-physics railway simulator which gives physi- cal quantities such as the train speed profiles, voltage along the catenary lines and temperatures. The rescheduling problem relies on this non-linear model, with a large number of continuous and discrete variables, constraints on dynamic outputs (typically voltage limits) and a high computation cost. We propose a rescheduling process based on sensitivity analysis in order to analyse the behaviour of this complex system and obtain information about the adjustment operations needed in order to reschedule the traffic in an optimal way. Our approach is based on statistics, with predefined variation ranges of the input parameters. In a first stage, variance decomposition-based sensitivity analysis (generalized Sobol indexes) is used for prioritization and fixing factors; then regional sensitivity analysis is used for factor mapping. The proposed approach has been tested on a simple case, with a nominal traffic running on a single-track line. The considered incident is the loss of a feeding power substation. The variables to be adjusted are the time interval between departure times and speed reduction in the vicinity of the faulty substation. The results show that increasing the time interval between trains is the most influential vari- able. Pareto-optimal fronts are also built in order to perform multi-criteria analysis according to travel- ling time, train delays and traction energy.
global sensitivity analysis, Monte Carlo filtering, railway simulation, regional sensitivity analysis, rescheduling, Sobol indexes
[1] Krasemann, J., Greedy algorithm for railway traffic re-scheduling during disturbances: a Swedish case. Progress in IET Intelligent Transport Systems, 4(4), pp. 375–386, 2010. DOI: 10.1049/iet-its.2009.0122.
[2] Dundar, S. & Sahin I., Train rescheduling with genetic algorithms and artificial neural networks for single-track railways. Transportation Research Part C, 27, pp. 1–15, 2013. DOI: 10.1016/j.trc.2012.11.001.
[3] Schachtebeck, M. & Schobel, A., To wait or not to wait – and who goes first? Delay management with priority decisions. Transportation Science, 44, pp. 307–321, 2010. DOI: 10.1287/trsc.1100.0318.
[4] Schobel, A., Integer programming approaches for solving delay management problem. Algorithmic Methods for Railway Optimization, Springer-Verlag: Berlin, Heidelberg, pp. 145–170, 2007.
[5] Schobel, A., Capacity constraints in delay management. Public Transportation, 1, pp. 135–154, 2009. DOI: 10.1007/s12469.
[6] Dollevoet, T.A.B., Huisman, D., Schmidt, M. & Schobel, A. Delay management with rerouting of passengers. Transportation Science, 46, pp. 74–89, 2009. DOI: 10.1287/trsc.1110.0375.
[7] D'ariano, A., Pacciarelli, D., Sama, M. & Corman, F. Microscopic delay management: minimizing train delays and passenger travel times during real-time railway traffic control. IEEE International Conference on Models and Technologies for Intelligent Transportation Systems, Naples, Italy, 2017.
[8] Louwerse, I. & Huisman, D., Adjusting a railway timetable in case of partial or a complete blockades. Progress in European Journal of Operational Research, 235(3), pp. 583–593, 2014. DOI: 10.1016/j.ejor.2013.12.020. S. Saad et al., Int. J. Transp. Dev. Integr., Vol. 2, No. 3 (2018) 283
[9] Ghaemi, N., Goverde, R. & Cats, O., Railway disruption timetable: short-turnings in case of complete blockage. IEEE International Conference on Intelligent Rail Transportation (ICIRT), 2016, Birmingham, UK.
[10] Zhan, S., Kroon, L., Veelenturf, L. & Wagenaar, J., Real-time-high-speed train rescheduling in case of a complete blockage. Progress in Transportation Research Part B, 78, pp. 182–201. 2016. DOI: 10.1016/j.trb.2015.04.001.
[11] Narayanaswami, S. & Rangaraj, N., Modelling disruptions and resolving conflicts optimally in a railway schedule. Computers & Industrial Engineering, 64, pp. 469–481, 2013. DOI: 10.1016/j.cie.2012.08.004.
[12] Binder, S., Maknoon, Y. & Bierlaire, M., Passenger-oriented railway disposition timetables in case of severe disruptions. 15th Swiss Transport Research Conference, April 2015, Switzerland.
[13] Binder, S., Maknoon, Y. & Bierlaire, M., Efficient exploration of the multiple objectives of the railway timetable rescheduling problem. 17th Swiss Transport Research Conference, Monte Verita/Ascona, 2016.
[14] Veelenturf, L.P., Kidd, M.P., Cacchiani, V., Kroon, L.G. & Toth, P., A railway timetable rescheduling approach for handling large scale disruptions. Transportation Science, 50, pp. 841–886, 2014. DOI: 10.1287/trsc.2015.0618.
[15] Cacchiani, V., Huisman, D., Kidd, M., Kroon, L., Toth, P., Veelenturf, L. & Wagenaar, J., An overview of recovery models and algorithms for real-time railway rescheduling. Transportation Research Part B, 63, pp. 15–37, 2014. DOI: 10.1016/j.trb.2014.01.009.
[16] Lusby, R.M., Larsen, J., Ehrgott, M. & Ryan, D. Railway track allocation: models and methods. OR Spectrum, 33, pp. 843–883, 2011. DOI: 10.1016/S0377-2217(00)00087-4.
[17] Cacchiani, V. & Toth, P., Nominal and robust train timetabling problems. European Journal of Operational Research, 219, pp. 727–737, 2012. DOI: 10.1016/j.ejor.2011.11.003.
[18] Desjouis, B., Remy, G., Ossart, F., Marchand, C., Bigeon J. & Sourdille, E., A new generic problem formulation dedicated to electrified railway systems. International Conference on Electrical Systems for Aircraft, Railway, Ship Propulsion and Road Vehicles (IEEE ESRAS), Germany, March, 2015.
[19] Saltelli, A., Tarantola, S. & Campolongo, F., Global Sensitivity Analysis: The Primer, John Wiley & sons, Ltd, 2008.
[20] Sobol, I.M., Sensitivity Estimates for Nonlinear Mathematical Models, Institute of Applied Mathematics, Russian Academy of Sciences: Moscow, pp. 404–414, 1993.
[21] Saltelli, A., Tarantola, S. & Campolongo, F., Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models, London, 2004.
[22] Hoeffding, W., A class of statistics with asymptotically normal distribution. The Annals of Mathematical Statistics, 19(3), pp. 293–325, 1948. DOI: 10.1214/aoms/1177730196.
[23] Saltelli, A., Making best use of model evaluations to compute sensitivity indices. Computer Physics Communications, 145, pp. 280–297, 2002. DOI: 10.1016/S0010-4655(02)00280-1.
[24] Gamboa, F., Janon, A., Klein, T. & Lagnoux, A., Sensitivity indices for multivariate outputs. Comptes Rendus Mathematique, 351(7–8), pp. 307–310, 2013. DOI: 10.1016/j.crma.2013.04.016.
[25] Hornberger, G.M. & Spear, R.C., Eutrophication in Peel Inlet, I, the problem: defining behaviour and a mathematical model for the phosphorus scenario. Water Research, 14, pp. 29–42, 1980. DOI: 10.1016/0043-1354(80)90039-1.