Abstract
We deal with an online problem arising from bus/tram/train disposition problems. In particular, we look at the case in which the delay is unknown and the vehicle can only wait in a station so as to minimize the passengers’ waiting time.
We present deterministic polynomial-time optimal algorithms and matching lower bounds for several problem versions. In addition, all lower bounds also apply to randomized algorithms, thus implying that using randomization does not help.
A preliminary version of this paper appeared in [2].
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Adenso-Díaz, B., Gonzáles, M.O., Gonzáles-Torre, P.: On-line timetable re-scheduling in regional train services. Transportation Research 33B, 287–398 (1999)
Anderegg, L., Penna, P., Widmayer, P.: Online train disposition: to wait or not to wait? In: Proc. ATMOS (2002); also available in the Electronic Notes in Theoretical Computer Science 66(6), 32–41 (2002)
Bertossi, A., Carraresi, P., Gallo, G.: On some matching problems arising in vehicle scheduling models. Networks 17, 271–281 (1987)
Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press, Cambridge (1998)
Brucker, P., Hurink, J.L., Rolfes, T.: Routing of railway carriages: A case study. In: Memorandum No. 1498, Fac. of Mathematical Sciences. Univ. of Twente, Fac. of Math. Sciences (1999)
Cicerone, S., D’Angelo, G., Di Stefano, G., Frigioni, D., Navarra, A.: Delay management problem: Complexity results and robust algorithms. In: Yang, B., Du, D.-Z., Wang, C.A. (eds.) COCOA 2008. LNCS, vol. 5165, pp. 458–468. Springer, Heidelberg (2008)
Dantzig, G., Fulkerson, D.: Minimizing the number of tankers to meet a fixed schedule. Nav. Res. Logistics Q 1, 217–222 (1954)
Fiat, A., Woeginger, G. (eds.): Online Algorithms: The State of the Art. LNCS, vol. 1442. Springer, Heidelberg (1998)
Gatto, M., Glaus, B., Jacob, R., Peeters, L., Widmayer, P.: Railway delay management: Exploring its algorithmic complexity. In: Hagerup, T., Katajainen, J. (eds.) SWAT 2004. LNCS, vol. 3111, pp. 199–211. Springer, Heidelberg (2004)
Gatto, M., Jacob, R., Peeters, L., Schöbel, A.: The computational complexity of delay management. In: Kratsch, D. (ed.) WG 2005. LNCS, vol. 3787, pp. 227–238. Springer, Heidelberg (2005)
Gatto, M., Jacob, R., Peeters, L., Widmayer, P.: Online delay management on a single train line. In: Geraets, F., Kroon, L.G., Schoebel, A., Wagner, D., Zaroliagis, C.D. (eds.) Railway Optimization 2004. LNCS, vol. 4359, pp. 306–320. Springer, Heidelberg (2007)
Ginkel, A.: Event-activity networks in delay management. Master’s thesis, University of Kaiserslautern (2001)
Ginkel, A., Schöbel, A.: To Wait or Not to Wait? The Bicriteria Delay Management Problem in Public Transportation. Transportation Science 41(4), 527 (2007)
Heimburger, D.E., Herzenberg, A.J., Wilson, N.H.M.: Using simple simulation models in operational analysis of rail transit lines: Case of study of boston’s red line. Transportation Research Record 1677, 21–30 (1999)
Jensen, J.L.W.V.: Sur les fonctions convexes et les inégalités entre les valeurs moyennes. Acta Mathematica 30(1), 175–193 (1906)
Mansilla, S.: Report on disposition of trains. Technical report, ETH Zürich (2001)
O’Dell, S.W., Wilson, N.H.M.: Optimal real-time control strategies for rail transit operations during disruptions. In: Computer-Aided Transit Scheduling. Lecture Notes in Economics and Math. Sys., pp. 299–323 (1999)
Schöbel, A.: A model for the delay management problem based on mixed-integer programming. In: Proc. ATMOS 2001 (2001); also available in the Electronic Notes in Theoretical Computer Science 50(1), 1–10 (2001)
Suhl, L., Biederbick, C., Kliewer, N.: Design of customer-oriented dispatching support for railways. In: Computer-Aided Scheduling of Public Transport. Lecture Notes in Economics and Mathematical Systems, vol. 505, pp. 365–386. Springer, Heidelberg (2001)
Zhu, P., Schnieder, E.: Determining traffic delays through simulation. In: Computer-Aided Scheduling of Public Transport. Lecture Notes in Economics and Math. Sys., pp. 387–398 (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Anderegg, L., Penna, P., Widmayer, P. (2009). Online Train Disposition: To Wait or Not to Wait?. In: Ahuja, R.K., Möhring, R.H., Zaroliagis, C.D. (eds) Robust and Online Large-Scale Optimization. Lecture Notes in Computer Science, vol 5868. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05465-5_17
Download citation
DOI: https://doi.org/10.1007/978-3-642-05465-5_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05464-8
Online ISBN: 978-3-642-05465-5
eBook Packages: Computer ScienceComputer Science (R0)