Abstract
We provide competitive analyses for the online delay management problem on a single train line. The passengers that want to connect to the train line might arrive delayed at the connecting stations, and these delays happen in an online setting. Our objective is to minimize the total passenger delay on the train line.
We relate this problem to the Ski-Rental problem and present a family of 2-competitive online algorithms. Further, we show that no online algorithm for this problem can be better than Golden Ratio competitive, and that no online algorithm can be competitive if the objective accounts only for the optimizable passenger delay.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Anderegg, L., Penna, P., Widmayer, P.: Online train disposition: to wait or not to wait? In: Wagner, D. (ed.) Electronic Notes in Theoretical Computer Science, vol. 66, Elsevier, Amsterdam (2002)
Biederbick, C., Suhl, L.: Improving the quality of railway dispatching tasks via agent-based simulation. In: Allan, J., Brebbia, C.A., Hill, R.J., Sciutto, G., Sone, S. (eds.) Computers in Railways IX, Proceedings of the 9th International Conference on Computer Aided Design, Manufacture and Operation in the Railway and Other Mass Transit Systems (COMPRAIL), Dresden, Germany, pp. 785–795. WIT Press, Southampton, Boston (2004)
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)
Heimburger, D., Herzenberg, A., Wilson, N.: Using simple simulation models in the operational analysis of rail transit lines: A case study of the MBTA’s red line. Transportation Research Record 1677, 21–30 (1999)
Karlin, A., Manasse, M., Rudolph, L., Sleator, D.: Competitive snoopy caching. Algorithmica 3(1), 79–119 (1988)
O’Dell, S., Wilson, N.: 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. Springer, Heidelberg (1999)
Schöbel, A.: A model for the delay management problem based on mixed-integer-programming. In: Zaroliagis, C. (ed.) Electronic Notes in Theoretical Computer Science, vol. 50, Elsevier, Amsterdam (2001)
Schöbel, A.: Optimization in Public Transportation: Stop Location, Delay Management and Tariff Zone Design in a Public Transportation Network. In: Optimization and Its Applications, vol. 3, Springer, Heidelberg (2007)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gatto, M., Jacob, R., Peeters, L., Widmayer, P. (2007). Online Delay Management on a Single Train Line. 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_17
Download citation
DOI: https://doi.org/10.1007/978-3-540-74247-0_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74245-6
Online ISBN: 978-3-540-74247-0
eBook Packages: Computer ScienceComputer Science (R0)