A Mathematical Framework for Expanding a Railway’s Theoretical Capacity

Analytical techniques for measuring and planning railway capacity expansion activities have been considered in this article. A preliminary mathematical framework involving track duplication and section sub divisions is proposed for this task. In railways, these features have a great effect on network performance and for this reason they have been considered. Additional motivations have also arisen from the limitations of prior models that have not included them.

Authors:

• Robert L. Burdett
• Bayan Bevrani

Keywords:

• Capacity analysis
• capacity expansion
• railways.

References:

[1] Abril, M., Barber, F., Ingolotti, L., Salido, M. A., Tormos, P., Lova, A.,
2008. An assessment of railway capacity. Transportation Research Part
E: Logistics and Transportation Review, 44, 774-806.
[2] Bevrani, B., Burdett, R. L., Yarlagadda P., 2015. An analysis of the
Iranian national railway network and its capacity. Transport (In Press).
[3] Burdett, R. L., Kozan, E., 2006. Techniques for absolute capacity
determination in railways. Transportation Research B 40(8), 616-632.
[4] Burdett, R. L., Kozan, E., 2009. Techniques for inserting additional
trains into existing timetables. Transportation Research B 43(8), 821-
836.
[5] Burdett, R. L., Kozan, E., 2010. A sequencing approach for train
timetabling. OR Spectrum 32(1), 163-193.
[6] Burdett, R. L., Kozan, E., 2010. Development of a disjunctive graph
model and framework for constructing new train schedules. European
Journal of Operational Research 200(1), 85-98.
[7] Burdett, R. L. (2015). Multi-objective models and techniques for railway
capacity analysis. European Journal of Operational Research. DOI:
10.1016/j.ejor.2015.03.020.
[8] D’Ariano, A., Pacciarelli, D., Pranzo, M., 2007. A branch and bound
algorithm for scheduling trains on a railway network. European Journal
of Operational Research 183(2), 643–57.
[9] Dicembre A., Ricci S., 2011. Railway traffic on high density urban
corridors: capacity, signalling and timetable. Journal of Rail Transport
Planning and Management, 59-68.
[10] Froidh, O., Sipila, H., Warg, J., 2014. Capacity for express trains on
mixed traffic lines. International Journal of Rail Transportation 2, 17-27.
[11] Giandomenico, F. D., Fantechi, A., Gnesi, S., Itria, M. L., 2013.
Stochastic model based analysis of railway operation to support traffic
planning. Software Engineering for Resilient Systems. Lecture Notes in
Computer Science. 8166, 184-198.
[12] Goverde, R. M. P., Corman, F. D’ariano, A., 2013. Railway line
capacity consumption of different railway signalling systems under
scheduled and disturbed conditions. Journal of Rail Transport Planning
& Management 3, 78-94.
[13] Harrod, S., 2009. Capacity factors of a mixed speed railway network.
Transportation Research Part E: Logistics and Transportation Review
45, 830-841.
[14] Kontaxi, E., Ricci, S., 2010. Railway capacity analysis: Methodological
framework and harmonization perspectives. Proceedings of the 12th
World Conference on Transportation Research, Lisboa, Portugal (July).
[15] Kozan, E., Burdett, R. L., 2005. A railway capacity determination model
and rail access charging methodologies. Transportation Planning and
Technology 28(1), 27-45.
[16] Lai, Y. C., Shih M. C., Jong J. C., 2010. Railway capacity model and
decision support process for strategic capacity planning. Transportation
Research Record: Journal of the Transportation Research Board 2197,
19-28.
[17] Lai, Y., Barkan C., 2011. Comprehensive decision support framework
for strategic railway capacity planning. Journal of Transportation
Engineering 137, 738-749.
[18] Lai, Y. C., Shih, M. C., Jong, J. C., 2010. Railway capacity model and
decision support process for strategic capacity planning. Transportation
Research Record: Journal of the Transportation Research Board 2197,
19-28.
[19] Landex, A., 2009. Evaluation of railway networks with single track
operation using the UIC 406 capacity method. Networks and Spatial
Economics, 9, 7-23.
[20] Liu, S. Q., Kozan E., 2009. Scheduling trains as a blocking parallelmachine
job shop scheduling problem. Computers and Operations
Research 36(10), 2840–52.
[21] Liu, S. Q., Kozan E., 2011. Scheduling trains with priorities: a no-wait
blocking parallel machine job shop scheduling model. Transportation
Science 45(2), 175–98.
[22] Lu M., Nicholson G. L., Schmid F., Dai L., Chen L., Roberts C., 2013.
A framework for the evaluation of the performance of railway networks.
International Journal of Railway Technology 2(2), 76-96.
[23] Lui, J., Ahuja, R. K., Sahin, G. (2008), Optimal network configuration
and capacity expansion of railroads. Journal of the Operational Research
Society, 59(7), 911-920.
[24] Mussone, L., Wolfler C.R, 2013. An analytical approach to calculate the
capacity of a railway system. European Journal of Operational Research
228, 11-23.
[25] Shih, M. C., Dick, C. T., Sogin, S. L., Barkan, C. P., 2014. Comparison
of capacity expansion strategies for single-track railway lines with
sparse sidings 2. Transportation Research Board 93rd Annual Meeting.
[26] Singh G., Sier D., Ernst A. T., Gavriliouk O., Oyston R., Giles T.,
Welgama P., 2012. A mixed integer programming model for long term
capacity expansion planning: a case study from the hunter valley coal
chain. European Journal of Operation Research 220, 210-224.
[27] Yaghini, M., Nikoo, N., Ahadi, H. R., 2014. An integer programming
model for analysing impacts of different train types on railway line
capacity. Transport 29, 28-35.