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Buffer Time Optimization in the Function of Timetable Stability
Branimir Duvnjak, Tomislav Josip Mlinarić, Danko Kezić
Keywords:simulation modelling, Petri net, buffer time, headway, traffic optimisation, traffic segmentation


Timetable stability depends on the regularity of trains. Any deviation from the planned timetable leads to its instability. Railway network characteristics determine the capacities of the transport service. Depending on the capacity calculation method, time components are added to the minimum headway to ensure timetable stability. The UIC 405 method is simple and can be used on all railways. The disadvantage is that the calculations are based on average data. According to the method, the minimum headway consists of the time of the average headway interval, additional time and the buffer time. The additional time is precisely defined by the number of APB sections, while the buffer time is in the average value. When creating the timetable, the goal is optimal utilisation of the infrastructure. If the headway is too long, the capacity is not used, and if it is too short, timetable instability will ensue. Instead of averaging, this work calculates a buffer time that depends on the ratio of the travel time of the previous and the following trains. In this way, the headway is optimised and the calculation of the UIC 405 method is improved.


[1] Čičak M. Modeliranje u željezničkom prometu [Modelling in railway traffic]. Zagreb: Institut prometa i veza; 2005.
[2] Jovanović P, et al. Optimal allocation of buffer times to increase train schedule robustness. European Journal of Operational Research. 2017;256(1):44–54. DOI: 10.1016/j.ejor.2016.05.013.
[3] Zieger S, Weik N, Nießen N. The influence of buffer time distributions in delay propagation modelling of railway networks. Journal of Rail Transport Planning & Management. 2018;8(3-4):220–232. DOI: 10.1016/j.jrtpm.2018.09.001.
[4] Wang M, et al. Determining the level of service scale of public transport system considering the distribution of service quality. Journal of Advanced Transportation. 2022;2022():1–14. DOI: 10.1155/2022/5120401.
[5] Shang P, Li R, Yang L. Demand-driven timetable and stop pattern cooperative optimization on an urban rail transit line. Transportation Planning and Technology. 2020;43(1):78–100. DOI: 10.1080/03081060.2020.1701757.
[6] Landex A, Kaas AH. Planning the most suitable travel speed for high frequency railway lines. 2005.
[7] Bešinović N, Quaglietta E, Goverde RMP. A simulation-based optimization approach for the calibration of dynamic train speed profiles. Journal of Rail Transport Planning & Management. 2013;3(4):126–136. DOI: 10.1016/j.jrtpm.2013.10.008.
[8] Kroon L, et al. Stochastic improvement of cyclic railway timetables. Transportation Research Part B: Methodological. 2008;42(6):553–570. DOI: 10.1016/j.trb.2007.11.002.
[9] Hassannayebi E, et al. Timetable optimization models and methods for minimizing passenger waiting time at public transit terminals. Transportation Planning and Technology. 2017;40(3):278–304. DOI: 10.1080/03081060.2017.1283156.
[10] Li S, Xu R, Han K. Demand-oriented train services optimization for a congested urban rail line: Integrating short turning and heterogeneous headways. Transportmetrica A: Transport Science. 2019;15(2):1459–1486. DOI: 10.1080/23249935.2019.1608475.
[11] Duvnjak B, Mlinarić TJ, Humić R. Establishing the capacities in the inner city – Suburban rail passenger transport. In: Lakušić S. (ed.) Road and rail infrastructure IV: Proceedings of the Conference CETRA 2016. Zagreb: Department of Transportation, Faculty of Civil Engineering, University of Zagreb; 2016. p. 557–565.
[12] Restel F, Wolniewicz Ł, Mikulčić M. Method for designing robust and energy efficient railway schedules. Energies. 2021;14(24):8248. DOI: 10.3390/en14248248.
[13] Yang Y, Du P. Optimization of the suburban railway train operation plan based on the zonal mode. Promet – Traffic&Transportation. 2021;33(3):425–436. DOI: 10.7307/ptt.v33i3.3608.
[14] Shang P, Li R, Yang L. Demand-driven timetable and stop pattern cooperative optimization on an urban rail transit line. Transportation Planning and Technology. 2020;43(1):78–100. DOI: 10.1080/03081060.2020.1701757.
[15] Duvnjak B, Mlinarić TJ, Haramina H. Improvement of passenger service quality by application of the new model of railway system (on the railway line Zagreb Main Station – Dugo Selo). In: Ivanjko E, et al. (eds) Proceedings of the International Scientific Conference “The Science and Development of Transport” (ZIRP 2020). Zagreb: Faculty of Transport and Traffic Sciences University of Zagreb; 2020. p. 47–55.
[16] Weik N, Niebel N, Nießen N. Capacity analysis of railway lines in Germany – A rigorous discussion of the queueing based approach. Journal of Rail Transport Planning & Management. 2016;6(2):99–115. DOI: 10.1016/j.jrtpm.2016.06.001.
[17] Mlinarić TJ, et al. Uloga regionalnog prijevoza u razvoju putničkog prometa u Republici Hrvatskoj [Role of the regional railway traffic in development of passenger transport service in Republic of Croatia]. In: Šakić Ž. (ed.) KoREMA – Tridesetdrugi skup o prometnim sustavima s međunarodnim sudjelovanjem „Automatizacija u prometu“ [KoREMA – Thirty-Second Conference on Transport Systems with International Participation „Automation in Traffic“]. Zagreb: KoREMA; 2012. p. 190–195.
Copyright (c) 2023 Branimir Duvnjak, Tomislav Josip Mlinarić, Danko Kezić

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