Demand-Oriented Train Timetabling Integrated with Passenger Train-Booking Decisions

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.

This paper describes how, given the complexity and number of constraints to be taken into account, train timetabling is a difficult and time-consuming task. A feasible train timetable should specify the departure and arrival time of each train to each location of its journey so that the line capacity and other operational constraints are met. Traditionally, train timetables have been generated manually by drawing trains on the time-distance diagram, where train schedules are manually adjusted so that all constraints are fulfilled. This process can take a long time and it usually stops once a feasible timetable is found. The difficulty of the process increases in complex and high-loaded networks and the resulting timetabling may be far from optimal. This paper presents MOM: a friendly, flexible, computer-based Decision Support System (DSS) whose main goal is to support the railway planner to efficiently obtain optimized train timetables. The system generates feasible and high quality timetables by considering the set of constraints of the problem and optimization criteria related to the use of railway infrastructures and operator requirements. The railway planner can obtain several solutions automatically, by modifying certain parameters (departure interval, frequencies, among others). Hence, the user can analyze them and take decisions about conditions related to railway traffic and infrastructure. Furthermore, an important feature of the DSS is the consideration of hard and soft constraints which makes the search process more flexible and reaches better solutions. The developed DSS offers assistance in train scheduling, conclusions about the maximum capacity of the network, identifying bottlenecks, determining the consequences of changes, providing support in the resolution of incidents, and alternative planning in on-line scheduling for real traffic control. This DSS software is being successfully used by the Spanish Manager of Railway Infrastructure (ADIF).

Recovery time in the rail industry is the additional time that is included in train timetables over and above the minimum journey time necessary often with the explicit aim of improving punctuality. Recovery time is widely used in railways in a number of countries but prior to this study there has been no investigation of the rail users’ point of view. Perceived recovery time, such as being held outside stations and prolonged stops at stations, might have some premium valuation due to the frustration caused. If perceived recovery time in train timetables does carry a premium, then the benefits of improved punctuality achieved by it will be reduced. This paper is the first to investigate passengers’ views and preferences on the use of recovery time. We summarise the findings of a large study and provide estimates of passengers’ valuations of recovery time, both relative to in-vehicle time and late time, that can be used for economic appraisal purposes. Overall, we find most passengers support the use of recovery time but the context is important. Only 13% of users disapprove of its use as a tool to reduce lateness. The estimated premia vary by demand characteristics and are significant in some contexts, although on average are of a small magnitude. The applicability of the estimates is demonstrated through the appraisal of an actual scheme in the UK. We observe that the introduction of more recovery time along with the subsequent improvement in reliability can lead to significant reductions in generalised journey time, even when recovery time carries a valuation premium. We must however strike a word of caution since we note that there were higher than expected proportions of non-traders in the survey which may have affected the results; future studies into the topic should look to minimise the proportion of non-traders. This study provides valuable and necessary first steps in this challenging topic.

Optimization-based Train Timetables Generation for Taiwan High-speed Rail System Considering Circulation and Disturbances

For single-track railway sections, the development of an optimal train timetable is a task of particular importance and constitutes a core component of train flow planning. On single-track railway sections, train conflicts, queueing delays, and overtaking of trains operating at different speeds and in opposite directions lead to an increase in overall delay. In this regard, the problem of developing a balanced timetable by regulating train speeds and optimally determining stations for overtaking operations is of significant relevance. The objective of this study is to design a balanced train timetable with a minimum delay coefficient, taking into account the influence of train running speeds. An optimization model is proposed that considers permissible speed constraints to determine the optimal running speeds of each train along the railway line. The proposed model aims to minimize total delay time while accounting for differences in train arrival times at stations, safety requirements, and speed relationships. The proposed model has practical significance in increasing the line capacity and carrying capacity of railway sections, as well as in improving transportation efficiency compared to existing methods and enhancing operational stability under conditions of uneven traffic flows. Keywords: railway section, balanced train timetable, optimal train crossing, predefined constraints, minimum delay coefficient.

The State Railway of Thailand provides passengers with train location information on their Web site, which includes the name of the last station that each train arrives at or departs from, along with the timestamps and the accumulative train delay (in minutes) from the train timetable. This information allows passengers to intuitively predict the arrival time at their station by adding the last known train delay to the scheduled arrival time. This paper aims at providing a more accurate prediction of passenger train's arrival times using the historical travel times between train stations. Two algorithms that use train location information and historical travel times are proposed and evaluated. The first algorithm uses the moving average of historical travel times. The second algorithm utilizes the travel times of the k-nearest neighbors (k-NN) of the last known arrival time. To evaluate the proposed algorithms, we collected six months of data for three different trains and calculated prediction errors using mean absolute error (MAE). The prediction errors of the proposed algorithms are compared to the prediction errors of the baseline algorithm that predicts the arrival time by adding the last known train delay to the scheduled train arrival time. Both algorithms outperform the baseline prediction. The algorithm based on moving average travel time improves the prediction error by 22.9 percent on average, and the algorithm based on k-NN improves the prediction error by 23.0 percent on average (k=16).

In a high-speed railway (HSR) corridor, railway companies provide diverse train services with different features such as departure time, running speed, and fare. Furthermore, passengers have varying preferences, which influence their travel choices. Focusing on this problem, this paper proposed a novel train timetable optimization model based on departure time and pricing strategy to analyze their impact on passengers’ travel choices with a consistent operating speed. Additionally, an extended time-space-fare network is constructed to visualize this process. The generalized cost of each arc in the network is used as a criterion for evaluating passenger selection. Then, we adapted a passenger flow distribution method based on the user equilibrium (UE) principle to allocate the passenger flow to each train. We also developed a bi-level planning model with passenger allocation as the lower-level model and timetable decision as the upper-level one to optimize collaboratively. Finally, a genetic algorithm integrated with the Frank-Wolfe method is designed to seek the optimal timetable and pricing strategy and a concrete numerical example in Lanzhou-Xi’an HSR is taken to investigate the effectiveness of the proposed model and algorithm.

Rescheduling rail networks with maintenance disruptions using Problem Space Search

For the current status of e-commerce logistics and distribution terminal node layout,this article considers planners and customers both benefit, while also considering the impact of the end node distribution route for cost.A bi-level programming model of end nodes location was constructed. The upper level model is the smallest in the conditions of transport costs and fixed costs as much as possible to attract customer demand, lower programming model considers the distance, the price of services and quality of service that influence customer choice behavior, and customer demand for the costs of terminal nodes distribution is studied.Finally, a numerical example verifies the feasibility of the model and algorithm.

A bi-level programming model is used to describe the continuous equilibrium network design problem in this paper. Traffic demand and supply that are both random are described to be, respectively, truncated normal distribution and logarithmic normal distribution. At the upper level model, the optimization objective is to minimize the mean of total impedance of network system and enhancement of road capacity as decision-making variables. The constrained condition is investment budget. The lower level program is formulated as a user equilibrium traffic assignment model, which link flow defined as the decision-making variable. Above all, a Monte Carlo simulation-based genetic algorithm was provided to solve the bi-level model and a satisfied result on the calculation and analysis of a small tested road network can be had.

Modelling and managing the integrated morning-evening commuting and parking patterns under the fully autonomous vehicle environment

To enhance the resilience of urban rail transit networks in dealing with interference events and facilitating rapid network recovery, this paper focuses on studying damaged urban rail transit networks and proposes comprehensive resilience evaluation indexes for urban rail transit networks that take into account two dimensions: network topology and passenger travel path selection. A bi-level programming model is constructed to maximize the comprehensive toughness, where the upper-level model is an integer planning model for determining the optimal recovery sequence of the affected stations under interference events that result in station closure or inoperability. The lower-level model is a passenger flow allocation model aiming to minimize travelers’ impedance. A genetic algorithm and Dijkstra’s labeling algorithm are used to solve the upper model as well as the shortest path of the lower model, respectively. Using a real-world urban rail transit network as an example, this research applies different recovery strategies, random recovery, node importance-based recovery, and comprehensive toughness-based recovery, across five common interference scenarios to analyze the recovery sequence of stations in each scenario. The modeling results show that the comprehensive toughness-based restoration strategy yields the most favorable results for the rail transportation network, followed by the node importance-based restoration strategy. In addition, the network’s toughness varies more significantly when employing different restoration strategies during target interference, as compared to the random and range interference scenarios.

This article investigates how to simultaneously optimize both strategic and tactical decisions in the supply chain network design. For this purpose, a bi-level programming model is developed in which supply chain network design problem is considered as a strategic decision in the upper-level model, while the lower-level model contains the assembly line balancing as a tactical decision. In addition, the problem is extended to include push–pull strategy where decisions such as production amount and inventory level of each component in manufacturers are made. Based on the special structure of the model, a heuristic method is proposed to solve the developed bi-level model. A numerical example is employed to show the performance of proposed method in terms of feasibility and convergence. Finally, computational experiments on several problem instances are presented to demonstrate the applications of developed model and the solution method.

To ensure the equity of exclusive bus lane (EBL) allocation under multimodal traffic conditions, a bi-level programming model is first constructed. The upper-level model is the minimum total system cost considering the Gini coefficient and the lower-level model constructed a stochastic user equilibrium (SUE) model based on logit loading. Secondly, a heuristic algorithm combining an improved genetic algorithm (GA) and a method of the successive average method (MSA) is designed. Finally, the Nguyen and Dupuis networks are used as examples to verify and analyze the effectiveness, superiority and sensitivity of the model and algorithm. The results show that the method can effectively obtain the optimal solution of the upper-level model as 15,004 RMB, the Gini coefficient is 0.31, and the equity is at a relatively reasonable level. Compared with the different allocation schemes, the proposed scheme has a higher bus sharing rate and lower Gini coefficient. At the same time, when the actual demand is twice the basic demand, the bus share rate is the largest, 65%, and the Gini coefficient is the smallest at 0.3. The bus share rate decreases with the increase in the proportion of high time value travelers, which fully verifies the sensitivity of the model to the type of traveler.

An economic analysis of a multi-modal transportation system with ride-sourcing services and multi-class users