Abstract
Real-time railway operations are subject to stochastic disturbances. However, a railway timetable is a deterministic plan. Thus a timetable should be designed in such a way that it can absorb the stochastic disturbances as well as possible. To that end, a timetable contains buffer times between trains and supplements in running times and dwell times. This paper first describes a stochastic optimization model that can be used to find an optimal allocation of the running time supplements of a single train on a number of consecutive trips along the same line. The aim of this model is to minimize the average delay of the train. The model is then extended such that it can be used to improve a given cyclic timetable for a number of trains on a common railway infrastructure. Computational results show that the average delay of the trains can be reduced substantially by applying relatively small modifications to the timetable. In particular, allocating the running time supplements in a different way than what is usual in practice can be useful.
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References
Bergmark, R.: Railroad capacity and traffic analysis using SIMON. In: Allan, J., Brebbia, C.A., Hill, R.J., Sciutto, G. (eds.) Computers in Railways V, pp. 183–191. WIT Press, Ashurst (1996)
Birge, J.R., Louveaux, F.: Introduction to Stochastic Programming, Springer, New York (1997)
Carey, M.: Ex ante heuristic measures of schedule reliability. Transportation Research B 33(7), 473–494 (1999)
Goverde, R.M.P.: The Max-Plus Algebra approach to railway timetable design. In: Mellitt, B., Hill, R.J., Allan, J., Sciutto, G., Brebbia, C.A. (eds.) Computers in Railways VI, pp. 339–350. WIT Press, Ashurst (1998)
Haldeman, L.: Automatische Analyse von IST-Fahrplen, Master’s thesis (in German), ETH Zürich, Switzerland (2003)
Hallowell, S.F., Harker, P.T.: Predictuing on-time performance in scheduled railroad operations: methodology and application to train scheduling. Transportation Research A 32(6), 279–295 (1998)
Higgins, A., Kozan, E.: Modelling train delays in urban networks. Transportation Science 32(4), 346–357 (1998)
Huisman, T., Boucherie, R.J.: Running times on railway sections with heterogeneous train traffic. Transportation Research Part B 35, 271–292 (2001)
Jochim, H.E.: Verspätung auf Stammstrecken: wie man ihrer nicht Herr wird. Der Nahverkehr (in German), 3 (2004)
König, H.: VirtuOS: Simulieren von Bahnbetrieb (in German). Betrieb und Verkehr 50(1-2), 44–47 (2001)
de Kort, A.F.: Advanced railway planning using Max-Plus algebra. In: Allan, J., Brebbia, C.A., Hill, R.J., Sciutto, G. (eds.) Computers in Railways VII, pp. 257–266. WIT Press, Ashurst (2000)
Linderoth, J.T., Shapiro, A., Wright, S.J.: The emprirical behavior of sampling methods for stochastic programming. Optimization Technical Report 02-01. University of Wisconsin-Madison (2002)
Middelkoop, D., Bouwman, M.: Train network simulator for support of network wide planning of infrastructure and timetables. In: Allan, J., Brebbia, C.A., Hill, R.J., Sciutto, G. (eds.) Computers in Railways VII, pp. 267–276. WIT Press, Ashurst (2000)
Mühlhans, E.: Berechnung der Verspätungsentwicklung bei Zugfahrten. Eisen-bahntechnische Rundschau 39, 465–468 (1990)
Nachtigall, K.: Periodic network optimization with different arc frequencies. Discrete Applied Mathematics 69, 1–17 (1996)
Peeters, L.W.P.: Cyclic railway timetable optimization. Ph.D. thesis, Erasmus University Rotterdam, Rotterdam School of Management (2003)
Petersen, E.R., Taylor, A.J.: A structured model for rail line simulation and optimization. Transportation Science 18, 192–206 (1982)
Rudolph, R.: Allowances and margins in railway scheduling. In: Proceedings of WCRR 2003, Edinburgh, pp. 230–238 (2003)
Schwanhäußer, W.: The status of German railway operations management in research and practice. Transportation Research A 28(A), 495–500 (1994)
Serafini, P., Ukovich, W.: A mathematical model for Periodic Event Scheduling Problems. SIAM Journal on Discrete Mathematics 2, 550–581 (1989)
Soto y Koelemeijer, G., Iounoussov, A.R., Goverde, R.M.P., van Egmond, R.J.: PETER, a performance evaluator for railway timetables. In: Allan, J., Brebbia, C.A., Hill, R.J., Sciutto, G. (eds.) Computers in Railways VII, pp. 405–414. WIT Press, Ashurst (2000)
U.I.C.: Timetable recovery margins to guarantee timekeeping - Recovery margins, Leaflet 451-1, U.I.C. Paris, France (2000)
Vromans, M.J.C.M.: Reliability of railway services. Ph.D. thesis, Erasmus University Rotterdam, Rotterdam School of Management (2005)
Wahlborg, M.: Simulation models: important aids for Banverket’s planning process. In: Allan, J., Brebbia, C.A., Hill, R.J., Sciutto, G. (eds.) Computers in Railways V, pp. 175–181. WIT Press, Ashurst (1996)
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Kroon, L.G., Dekker, R., Vromans, M.J.C.M. (2007). Cyclic Railway Timetabling: A Stochastic Optimization Approach. In: Geraets, F., Kroon, L., Schoebel, A., Wagner, D., Zaroliagis, C.D. (eds) Algorithmic Methods for Railway Optimization. Lecture Notes in Computer Science, vol 4359. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74247-0_2
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DOI: https://doi.org/10.1007/978-3-540-74247-0_2
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