A Scheduling Approach for the Combination Scheme and Train Timetable of a Heavy-Haul Railway

Heavy-haul railway transport is a critical mode of regional bulk cargo transport. It dramatically improves the freight transport capacity of railway lines by combining several unit trains into one combined train. In order to improve the efficiency of the heavy-haul transport system and reduce the transportation cost, a critical problem involves arranging the combination scheme in the combination station (CBS) and scheduling the train timetable along the trains’ journey. With this consideration, this paper establishes two integer programming models in stages involving the train service plan problem (TSPP) model and train timetabling problem (TTP) model. The TSPP model aims to obtain a train service plan according to the freight demands by minimizing the operation cost. Based on the train service plan, the TTP model is to simultaneously schedule the combination scheme and train timetable, considering the utilization optimal for the CBS. Then, an effective hybrid genetic algorithm (HGA) is designed to solve the model and obtain the combination scheme and train timetable. Finally, some experiments are implemented to illustrate the feasibility of the proposed approaches and demonstrate the effectiveness of the HGA.

Estimating left behind patterns in congested metro systems: a Bayesian model

Purpose During rush hours, many passengers find it difficult to board the first train due to the insufficient capacity of metro vehicles, namely, left behind phenomenon. In this paper, a data-driven approach is presented to estimate left-behind patterns using automatic fare collection (AFC) data and train timetable data. Design/methodology/approach First, a data preprocessing method is introduced to obtain the waiting time of passengers at the target station. Second, a hierarchical Bayesian (HB) model is proposed to describe the left behind phenomenon, in which the waiting time is expressed as a Gaussian mixture model. Then a sampling algorithm based on Markov Chain Monte Carlo (MCMC) is developed to estimate the parameters in the model. Third, a case of Beijing metro system is taken as an application of the proposed method. Findings The comparison result shows that the proposed method performs better in estimating left behind patterns than the existing Maximum Likelihood Estimation. Finally, three main reasons for left behind phenomenon are summarized to make relevant strategies for metro managers. Originality/value First, an HB model is constructed to describe the left behind phenomenon in a target station and in the target direction on the basis of AFC data and train timetable data. Second, a MCMC-based sampling method Metropolis–Hasting algorithm is proposed to estimate the model parameters and obtain the quantitative results of left behind patterns. Third, a case of Beijing metro is presented as an application to test the applicability and accuracy of the proposed method.

Simultaneous Optimization of Train Timetabling and Platforming Problems for High-Speed Multiline Railway Network

The optimization problems of train timetabling and platforming are two crucial problems in high-speed railway operation; these problems are typically considered sequentially and independently. With the construction of high-speed railways, an increasing number of interactions between trains on multiple lines have led to resource assignment difficulties at hub stations. To coordinate station resources for multiline train timetables, this study fully considered the resources of track segments, station throat areas, and platforms to design a three-part space-time (TPST) framework from a mesoscopic perspective to generate a train timetable and station track assignment simultaneously. A 0-1 integer programming model is proposed, whose objective is to minimize the total weighted train running costs. The construction of a set of incompatible vertexes and links facilitates the expression of difficult constraints. Finally, example results verify the validity and practicability of our proposed method, which can generate conflict-free train timetables with a station track allocation plan for multiple railway lines at the same time.

Optimizing Train Timetable Based on Departure Time Preference of Passengers for High-Speed Rails

Passengers would like to choose the most suitable train based on their travel preferences, expenses, and train timetable in the high-speed railway corridor. Meanwhile, the railway department will constantly adjust the train timetable according to the distribution of passenger flows during a day to achieve the optimal operation cost and energy consumption saving plan. The question is how to meet the differential travel needs of passengers and achieve sustainable goals of service providers. Therefore, it is necessary to design a demand-oriented and environment-friendly high-speed railway timetable. This paper formulates the optimization of train timetable for a given high-speed railway corridor, which is based on the interests of both passengers and transportation department. In particular, a traveling time-space network with virtual departure arc is constructed to analyze generalized travel costs of passengers of each origin-destination (OD), and bilevel programming model is used to optimize the problem. The upper integer programming model regards the minimization of the operating cost, which is simplified to the minimum traveling time of total trains, as the goal. The lower level is a user equilibrium model which arranges each OD passenger flow to different trains. A general advanced metaheuristic algorithm embedded with the Frank–Wolfe method is designed to implement the bilevel programming model. Finally, a real-world numerical experiment is conducted to verify the effectiveness of both the model and the algorithm.

An Efficient Hybrid Approach for Scheduling the Train Timetable for the Longer Distance High-Speed Railway

Compared with other modes of transportation, a high-speed railway has energy saving advantages; it is environmentally friendly, safe, and convenient for large capacity transportation between cities. With the expansion of the high-speed railway network, the operation of high-speed railways needs to be improved urgently. In this paper, a hybrid approach for quickly solving the timetable of high-speed railways, inspired by the periodic model and the aperiodic model, is proposed. A space–time decomposition method is proposed to convert the complex passenger travel demands into service plans and decompose the original problem into several sub-problems, to reduce the solving complexity. An integer programming model is proposed for the sub-problems, and then solved in parallel with CPLEX. After that, a local search algorithm is designed to combine the timetables of different periods, considering the safety operation constraints. The hybrid approach is tested on a real-world case study, based on the Beijing–Shanghai high-speed railway (HSR), and the results show that the train timetable calculated by the approach is superior to the real-world timetable in many indexes. The hybrid approach combines the advantages of the periodic model and the aperiodic model; it can deal with the travel demands of passengers well and the solving speed is fast. It provides the possibility for flexible adjustment of a timetable and timely response to the change of passenger travel demands, to avoid the waste of transportation resources and achieve sustainable development.