Stochastic Optimization Model and Solution Algorithm for Robust Double-Track Train-Timetabling Problem

Khan, Muhammad Babar; Zhou, Xuesong

doi:10.1109/tits.2009.2030588

Cited by 65 publications

(27 citation statements)

References 12 publications

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“…In all lines and corridors in the network, there are two parallel tracks, and each track facilitates unidirectional ow and not bidirectional, i.e. there is no opposite direction train, which is a common situation in metro, subway, and high-speed networks; it is of interest as [36,37] covered some earlier research studies. Each station or siding can have one or more capacity, some of which may have no platform for passengers.…”

Section: Problem De Nitionmentioning

confidence: 99%

Train Timetabling on double track and multiple station capacity railway with useful upper and lower bounds

Jadid

Eshghi

2017

Scientia Iranica

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Abstract. Train scheduling has been one of the signi cant issues in the railway industry in recent years since it has an important role in e cacy of railway infrastructure. In this paper, the timetabling problem of a multiple-tracked railway network is discussed. More speci cally, a general model is presented here in which a set of operational and safety requirements is considered. The model handles the trains overtaking in stations and considers the stations' capacity. The objective function is to minimize the total travel time. Unfortunately, the problem is NP-hard, and real-sized problems cannot be solved in an acceptable amount of time. In order to reduce the processing time, we presented some heuristic rules, which reduce the number of binary variables. These rules are based on problem's parameters, such as travel time, dwell time, and safety time of stations, and try to remove the impracticable areas of the solution space. Furthermore, a Lagrangian Relaxation algorithm model is presented in order to nd a lower bound. Finally, comprehensive numerical experiments on the Tehran Metro case are reported. Results show the e ciency of the heuristic rules and also the Lagrangian Relaxation method in a way that the optimum values are obtained for all analyzed problems.

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Section: Problem De Nitionmentioning

confidence: 99%

Train Timetabling on double track and multiple station capacity railway with useful upper and lower bounds

Jadid

Eshghi

2017

Scientia Iranica

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“…Zhou and Zhong (2007) for example have minimised the total travel time on a single-track line. Khan and Zhou (2010) on the other hand have optimised the travel time on a double-track line. They are however treating the double-track as two single-tracks with unidirectional traffic.…”

Section: Graphical Timetablementioning

confidence: 99%

“…The arrival delay induces the actual delays, both primary and secondary, and it can be used for all trains or just some selected ones. Minimising the average or total arrival delay is the objective for many models, for example Vromans et al (2006), Kroon et al (2008b), and Khan and Zhou (2010).…”

Section: Traffic Performance Measuresmentioning

confidence: 99%

Assessment of Robustness in Railway Traffic Timetables

Andersson

2014

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A tendency seen for the last decades in many European railway networks is a growing demand for capacity. An increased number of operating trains has led to a delay sensitive system where it is hard to recover from delays, where even relatively small delays are easily propagating to other traffic.The overall aim of this thesis is to analyse the robustness of railway traffic timetables; why delays are propagating in the network and how the timetable design and dispatching strategies influence the delays. In this context we want to establish quantitative measures of timetable robustness. There is a need for measures that can be used by the timetable constructors. Measures that identify where and how to improve the robustness and thereby indicating how and where margin time should be inserted. It is also important that the measures can capture interdependencies between different trains.In this thesis we introduce the concept of critical points, which is a practical approach to identify robustness weaknesses in a timetable. In contrast to other measures, critical points can be used to identify specific locations in both time and space. The corresponding measure, Robustness in Critical Points (RCP) provides the timetable constructors with concrete suggestions for which trains that should be given more runtime or headway margin. The measure also identifies where the margin time should be allocated to achieve a higher robustness.In a case study we show that the delay propagation is highly related to the operational train dispatching. This study shows that the current prioritisation rule used in Sweden results in an economic inefficiency and therefore should be revised. This statement is further supported by RCP and the importance of giving the train dispatchers more flexibility to efficiently solve conflict situations.

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“…Generally, it is presented in the form of average delay (Khan and Zhou [11], Fischetti et al [9], Kroon et al [14], and Vromans et al [20]), secondary and total delay (Larsen et al [15]), punctuality (Andersson et al [3]), and the number of affected passengers (Dewilde et al [8]). However, the importance of the ex-ante measures cannot be denied because the traffic performance is based on the design quality of the timetable.…”

Section: Introductionmentioning

confidence: 99%

Ex-ante robustness measures for single track train timetables

2017

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Preliminary communicationThe goal of the paper is to propose a measurement to quantify and improve the robustness of the train timetables at the design stage. The paper presents the modeling and application of an ex-ante robustness measure for single track railways, known as the Critical Robustness Measure (CRM). Efficiency of the CRM is demonstrated by comparing the technique with the available ex-ante robustness measures, e.g., the number of trains per hour per section, the total amount of runtime margin for each individual train, sum of shortest headway reciprocals, weighted average distance, marginal runtime difference, robustness at the critical points, and margins along the longest path. Numerical experiment sare conducted on a hypothetical example and a selected single track segment of the Pakistan Railways. Computational results reveal that it is not useful to add the time margins to all activites (e.g., running times, headways) in the timetable because not all components of margins are effective for the robustness of a timetable. Furthermore, the robustness is not statically quantifiable, since it may change with time and be associated with the way of the train's interactions. Keywords: critical points; ex-ante measures; robustness measurement; train timetableEx-ante mjere dugotrajnosti za vozne redove jednokolosiječne željezničke pruge Prethodno priopećenje Cilj je ovoga rada predložiti mjerenje u svrhu kvantificiranja i poboljšanja dugotrajnosti voznih redova već kod izrade. U radu se predstavlja modeliranje i primjena ex-ante mjere dugotrajnosti za vozne jednokolosiječne željezničke pruge, poznate kao Critical Robustness Measure (CRM). Učinkovitost te mjere demonstrira se usporedbom te metode s dostupnim ex-ante mjerama izdržljivosti, tj. brojem vlakova po satu po dionici, ukupnim iznosom granice vremena vožnje za svaki pojedinačni vlak, zbirom najkraćih uzajamnih vemenskih intervala između dva vlaka, ponderiranim prosjekom udaljenosti, marginalnom razlikom u vremenu vožnje, izdržljivosti u kritičnim točkama, i granicama vremena vožnje na najdužoj stazi. Numerički eksperimenti provedeni su na hipotetičkom primjeru i izabranom dijelu jednokolosiječne pruge na pakistanskim željeznicama. Rezultati proračuna pokazuju da nije korisno dodati vremenska ograničenja kod svih aktivnosti (na pr. vrijeme vožnje, vremenski razmak između dva vlaka) u voznom redu jer nisu sve komponente uključene u granicu vremena vožnje korisne za dugotrajnost nekog voznog reda. Nadalje, ta se dugotrajnost ne može statistički kvantificirati budući da se tijekom vremena može promijeniti i povezati s načinom interakcija između vlakova. Ključne riječi: ex-ante mjere; kritične točke; mjerenje dugotrajnosti (izdržljivosti); vozni red vlaka

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Stochastic Optimization Model and Solution Algorithm for Robust Double-Track Train-Timetabling Problem

Cited by 65 publications

References 12 publications

Train Timetabling on double track and multiple station capacity railway with useful upper and lower bounds

Train Timetabling on double track and multiple station capacity railway with useful upper and lower bounds

Assessment of Robustness in Railway Traffic Timetables

Ex-ante robustness measures for single track train timetables

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