Train Departure Times Research Articles

Remote control of the technical condition of metro trains using seismological tools

As urban road congestion increases and people shift to using the subway, the safety of under-ground transportation becomes a priority. Therefore, it is necessary to establish a monitoring sys-tem for subway trains to detect malfunctions that occur during operation. The article proposes an engineering seismology method for remote monitoring of the technical condition of metro trains based on the analysis of micro seismic vibrations. This method allows remote control of the dynamic parameters of each train and their deviations from the norm. The authors demonstrate how a seismic recorder placed in a building adjacent to a metro station can be used to monitor changes in the amplitude-frequency spectrum of vibro seismic recordings. It is used to determine the arrival and departure times of trains, and it is shown that observations are best made for departures due to their more pronounced signal amplitude. The recorded signal of a metro train should fall within a certain frequency range, which is determined based on its average values, and any deviation of the observed signal spectrum from this norm indicates changes in the train's condition. The proposed approach not only helps improve passenger safety, but also reduces the risk of emergencies associated with technical malfunctions of rolling stock. In the future, it is possible to develop software equipped with a database of statistical data, which will allow even more efficient control of metro operations and prompt response to any deviations, thus ensuring a high level of safety and comfort for passengers.

How Complex Systems Sometimes Follow Murphy’s Law: Train Delay Prediction at a Station Using Delays at Previous Stops as the Features

Prediction or estimation of the delay of a train is essential to analyze customer behavior. In case of longer delays, there is a high probability that the customer will abort their travel or change the mode/time of travel. The delay propagation from previous stations to the next station creates a chain of these types of customer reactions. Thus, using delays at the previous station to predict the next station’s delay is a good approach to align with customer behavior. The present research attempts to predict the delays at a station using the delays at previous stations. The previous delays at stations are generated by creating lags in the original delays and creating them as one of the prediction features. The present research uses the delay data acquired from Bane NOR from 1 January 2021 to 28 February 2023. This data contains the scheduled and actual departure and arrival times of different trains between Oslo and Trondheim (up and down the line) in the specified period. The machine learning models based on neural networks were used on the data in the present research. Different prediction algorithms, i.e., recurrent neural network (RNN), gated recurrent unit (GRU), and long short-term memory (LSTM), were used. The prediction results are compared to look at the insights of the train delays in the given period. In conclusion, this study highlights how extreme feature engineering can negatively affect the output of a model.

Optimization of the Operation Plan of Airport Express Train with Consideration of Train Departure Time Window

This paper proposes an optimization model for the train operation scheme of the Airport Express Line (AEL) based on the expected arrival time of passengers by the introduction of the train departure time to cope with the time‐dependent passenger flow and provide better prompt train service according to passengers’ demand. Considering factors such as train sections, station arrangement, passenger capacity, departure time windows, passenger flow conservation, and boarding and disembarkation processes, this paper also aims to find the optimal combination of the passengers’ total travel time and the train operation cost. A set of alternative train options is introduced to simplify the model and convert integer variables related to train pairs into 0‐1 variables. The elaborately designed simulated annealing algorithm mainly focuses on the key elements of strategies like initial solution generation, neighborhood solution construction, and the allocation of passenger flows, tailored to the model’s unique features and the time‐dependent passenger flow. Neighborhood solution strategies include the increase or haut of train operations and the adjustment of the number of stops, which refines the solution space and boosts the process efficiency of the heuristic algorithm. Additionally, the model and algorithm proposed in this paper are practiced during the peak hour of Nanjing Metro Line S1 for empirical validation. The research findings demonstrate that the optimized train operation scheme is better synchronized with the fluctuating number of time‐dependent passenger flows and exhibits notable improvement in computational efficiency and convergence.

Optimization of train schedule with uncertain maintenance plans in high-speed railways: A stochastic programming approach

In high-speed railways, unexpected disturbances on maintenance activities may cause serious delays of the scheduled trains and greatly affect the service quality for traveling passengers. In contrast to most existing studies that focused on deterministic maintenance activities, this paper develops a two-stage stochastic programming approach to address the optimization of train schedules under uncertain maintenance plans. Specifically, in the first stage, we aim to determine the departure times of trains from the origin station, since this information needs to be public to passengers in advanced. The objective function is to minimize the expected travel time of trains under uncertain duration time of maintenance activities. In the second stage, given the specific information of maintenance activities, we generate the train schedule by adjusting the stop patterns, train orders and the assignment of tracks at key stations. Due to the computational difficulties arising from the large number of discrete decision variables, we particularly develop a dual decomposition based solution approach to solve the two-stage stochastic model. Our approach decomposes the original problem into a set of scenario-dependent subproblems with much fewer number of variables, which greatly improves the computational efficiency. Finally, we conduct several sets of real-world instances based on the Beijing–Guangzhou high-speed railway corridor to verify the effectiveness of the proposed model and solution approach. The results demonstrate that our approach evidently outperforms state-of-art solvers (Gurobi), especially for large-scale instances that Gurobi cannot even return feasible solutions.

Energy‐efficient train timetabling for a medium‐speed maglev line considering propulsion and suspension energy consumption

AbstractThis paper addresses the energy‐efficient train timetabling problem for MSM systems, where both propulsion and suspension energy consumption are considered. The timetable design problem is modelled as a bi‐level model for a complete two‐way MSM line. The upper level determines the train departure time at the first station, which makes train operations more convenient for passengers. The lower level uses an empirical description of the train energy consumption as a function of segment running times, and an energy‐efficient timetable optimization model is built. In doing so, all the services in both directions along a certain planning horizon are considered while attending to a known passengers’ demand. Moreover, the convenience of considering energy consumption as part of a broad objective function that includes other relevant costs is pointed out. Then, a unified sequential solution algorithm is developed for an efficient and accurate solution of the bi‐level model. Experiments show that the proposed framework can generate a holographic timetable of energy‐efficient MSM containing multi‐dimensional variables such as time, space, velocity, and electrical quantities.

Integrated energy‐efficient optimization for urban rail transit timetable

AbstractThe energy‐efficient optimization of the train timetable should be carried out on the basis of meeting passenger demand and determining the train operation plan. This paper proposes an integrated energy‐efficient optimization framework for the train timetable. Firstly, two energy‐efficient optimization strategies for this problem are proposed: inter‐station running time allocation and regenerative braking energy utilization. The first strategy aims to reduce the traction energy consumption, realized by selecting the profile based on a given set of speed profiles for each inter‐station sector when ensuring a stable travel time of train routing. The second strategy is intended to fully utilize the regenerative energy feedback from braking trains, realized by setting the departure time of trains based on a small‐range headway adjustment. Then, an integrated energy‐efficient optimization model of the timetable is developed and solved using the genetic algorithm. Finally, a case study of the Guangzhou Metro Line 8 is presented to verify the effectiveness of the method. The results show that the utilization rate of regenerative braking energy in the optimized timetable increases by 8.60%, and the total energy consumption decreases by 9.52%. Regenerative energy utilized roughly doubles during peak hours and increases more than twice as much during off‐peak hours.

Development of enhanced method for planning train locomotives ready to operate the next day

A series of methods for planning the use of train locomotives has been developed. However, existing scientific research does not clearly specify how the arrival and departure times of freight trains are determined in train schedules, and locomotives are assigned to trains based on the condition of “Locomotive waits for train”. This article proposes a methodology for determining the average time of stay for train locomotives and trains at the boundaries of train sidings for all scenarios ranging from the condition of “Train waits for locomotive” to “Locomotive waits for train”. The EGM program has been developed and created for calculating the fleet of freight locomotives based on the graphical movement time of trains, and an enhanced method for planning the effective use of train locomotives has been developed based on minimizing the downtime of rolling stock within the boundaries of towing sidings.

Integrated freight car routing and train scheduling

Rail freight transportation is involved with highly complex logistical processes and requires a lot of resources such as locomotives or wagons. Thus, cost-efficient strategies for routing freight cars in a cargo network are of great interest for railway companies. When it comes to single wagon load traffic, trains are usually formed by collecting individual freight cars into batches at shunting yards, in order to transport them jointly to their destinations. The problem of finding optimal routes and schedules for single freight cars is typically solved in two steps: (i) determining routes for the freight cars in the railway network by solving the Single-freight car routing problem (SCRP), and (ii) deciding on time schedules for trains by solving the freight train scheduling problem (FTSP). Since train departure and arrival times, as well as freight car routes are highly interdependent, one aims to solve the SCRP and the FTSP simultaneously. For smooth and convenient operational processes many railway companies apply the concept of a routing matrix. This matrix defines unique routes between all shunting yards that are used for all shipments. In this work, we present an integrated mathematical model based on time discretization, that jointly solves the SCRP and FTSP and enforces the routing matrix concept. To the best of our knowledge, this is the first work that combines all three aspects. The approach is tailored for Rail Cargo Austria’s (RCA) needs, incorporating train capacities, yard capacities, and restrictions regarding travel times. We perform an extensive computational study based on real-world data provided by RCA. Besides the performance we analyze the utilization of trains, waiting times of freight cars, and the number of shunting processes.

Optimization of Metro Trains Operation Plans Based on Passenger Flow Data Analysis

Metro intelligent system produces massive passenger flow and traffic data every day, among which route, station, and operation data are important for optimizing the train operation scheme. We collect passenger flow information of Shenzhen metro, analyze the passenger flow pattern and its distribution characteristics based on the data warehouse of the Hadoop platform, and optimize the train operation scheme in this paper. Using dynamic passenger flow data, an optimization model with train departure and dwell time as decision variables and passenger waiting time, passenger ride time, train full load ratio, and train operation balance as objectives is developed. An improved parallel genetic algorithm (GA) incorporating a simulated annealing algorithm (SAA) and an optimal individual retention strategy is used to find the optimal result. To verify the usefulness of the method, simulation experiments are conducted on the optimization model and method using the real passenger flow and train operation data of Shenzhen metro, and the simulation results are compared with the original plan.

Last train timetabling optimization for minimizing passenger transfer failures in urban rail transit networks: A time period based approach

In order to improve the time accessibility of URT networks for passengers traveling in the late evening, it is more important to coordinate the train timetables among different lines than to prolong the service time alone. This paper focuses on train timetabling optimization for the last time period of daily URT service. Different from the existing last train timetabling model optimizing the last train timetables alone and considering only the last train passengers, this study expands the optimizing object to the train timetables in the entire period and broaden the beneficiary to all the transfer passengers in the period. An optimization model is developed for minimizing the total passenger transfer failures in such a way that the departure and arrival times of the last trains and non-last trains are made integrated coordination. To solve for large-scale URT networks, we design an ABC algorithm that is verified computationally efficient. A method evaluating the impact of small last train delays on the optimized timetables is proposed to help URT operators in identifying the most “dangerous” delay locations and the most vulnerable transfer relationships. Finally, a case study on Shanghai URT network demonstrates that the proposed period-based train timetabling approach is effective in reducing passenger transfer failures at both the network level and the station level. Comparison analysis shows that the proposed model significantly outperforms the existing last train timetabling model in improving transfer accessibility as well as train connections.

First-Train Timetable Synchronization in Metro Networks under Origin-Destination Demand Conditions

This paper focuses on how to synchronize network-wide timetables of first trains in an urban metro system, in which the train-connection-based route can be exactly determined for each first-train-attached origin-destination (OD) demand pair. With the help of even headway scheduling on each line, the problem is actually to adjust the departure times of first trains and connecting trains from their origin stations and the departure interval on each line. Subjected to train operation and connection constraints, a biobjective nonlinear integer programming model is formulated to minimize the total travel time of OD-dependent passenger demands and the deviation between the known and expected schedules. Then, the Nondominated Sorted Genetic Algorithm-II (NSGA-II) is adopted to solve the proposed model, and an improved technique is elaborated to reduce the alternative route choices. Finally, numerical experiments are conducted to demonstrate the effectiveness and availability of the proposed model and methods.

Optimization method of urban rail train operational plan based on O-D time-varying demand

PurposeUnder the constraints of given passenger service level and coupling travel demand with train departure time, this study optimizes the train operational plan in an urban rail corridor to minimize the numbers of train trips and rolling stocks considering the time-varying demand of urban rail passenger flow.Design/methodology/approachThe authors optimize the train operational plan in a special network layout, i.e. an urban rail corridor with dead-end terminal yard, by decomposing it into two sub-problems: train timetable optimization and rolling stock circulation optimization. As for train timetable optimization, the authors propose a schedule-based passenger flow assignment method, construct the corresponding timetabling optimization model and design the bi-directional coordinated sequential optimization algorithm. For the optimization of rolling stock circulation, the authors construct the corresponding optimization assignment model and adopt the Hungary algorithm for solving the model.FindingsThe case study shows that the train operational plan developed by the study's approach meets requirements on the passenger service quality and reduces the operational cost to the maximum by minimizing the numbers of train trips and rolling stocks.Originality/valueThe example verifies the efficiency of the model and algorithm.

Optimizing the loaded train combination problem at a heavy-haul marshalling station

In this paper, we address a loaded train combination problem at a heavy-haul marshalling station. This problem lies on assigning/combining loaded inbound trains to/into heavier outbound trains, and determining the actual departure time of outbound trains. By using a time-discretized modelling technique, we formulate the studied problem as a mixed integer linear programming model, to minimize the weighted sum of the total railcar dwell time and the total railcar extra transfer time. Several variable fixing rules and valid inequalities are designed to strengthen the proposed model. An iterated search algorithm, in which an intensification search and a neighborhood search are executed iteratively, is developed to solve large-scale problems efficiently. In the intensification search, the proposed model is reduced into a simpler assignment model to compute an incumbent solution, by fixing the departure time of outbound trains. In the neighborhood search, a rolling horizon heuristic is designed to improve the incumbent solution, by dividing the departure period of outbound trains into multiple overlapped shorter stages, and re-optimizing the solution in each stage while maintaining that in other stages unchanged. Different scales of instances, randomly generated from a real-world marshalling station in one of the busiest Chinese heavy-haul railways, are used to test the proposed approaches. Computational results demonstrate that our algorithm computes (near-)optimal solutions (with a maximum relative gap of 1.73% only) for all the tested instances within a maximum computation time shorter than 13 min. Our approach can also find better solutions (with an average improvement rate of 3.27%) in shorter computation time, when compared to the empirical method used in practice.

An iterative heuristic for passenger-centric train timetabling with integrated adaption times

In this paper we present a method to construct a periodic timetable from a tactical planning perspective. We aim at constructing a timetable that is feasible with respect to infrastructure constraints and minimizes total perceived passenger travel time. In addition to in-train and transfer times, our notion of perceived passenger time includes the adaption time (waiting time at the origin station). Adaption time minimization allows us to avoid strict frequency regularity constraints and, at the same time, to ensure regular connections between passengers’ origins and destinations. The combination of adaption time minimization and infrastructure constraints satisfaction makes the problem very challenging.The described periodic timetabling problem can be modelled as an extension of a Periodic Event Scheduling Problem (PESP) formulation, but requires huge computing times if it is directly solved by a general-purpose solver for instances of realistic size. In this paper, we propose a heuristic approach consisting of two phases that are executed iteratively. First, we solve a mixed-integer linear program to determine an ideal timetable that minimizes the total perceived passenger travel time but neglects infrastructure constraints. Then, a Lagrangian-based heuristic makes the timetable feasible with respect to infrastructure constraints by modifying train departure and arrival times as little as possible. The obtained feasible timetable is then evaluated to compute the resulting total perceived passenger travel time, and a feedback is sent to the Lagrangian-based heuristic so as to possibly improve the obtained timetable from the passenger perspective, while still respecting infrastructure constraints. We illustrate the proposed iterative heuristic approach on real-life instances of Netherlands Railways and compare it to a benchmark approach, showing that it finds a feasible timetable very close to the ideal one.

Optimization of train timetables in high-speed railway corridors considering passenger departure time and seat-class preferences

ABSTRACT There are a number of trains running in high-speed railway (HSR) corridors throughout the day, which results in diverse passenger travel choices. Passengers can select their preferred train according to their favorite departure time and seat class based on a fixed train timetable, that is, the selection differences from departure time to seat classes are dramatic. The train timetable determines the distribution of passenger flow on trains, and the requirement distribution in turn affects the train timetable. To address this game relationship, this paper develops a method to optimize uneven running train timetables with a given total number of trains considering passenger departure time and seat-class preferences. We analyze the impact of departure time and seat class on passenger choice behaviors and build a time-space-seat 3-dimensional network to account for these choices. Then, the impedance function of each type of arc in the network is designed. In addition, a bi-level programming model is constructed to optimize the train timetable in the HSR corridor; the upper-level model calculates train departure time, arrival time and dwelling time at each station and determines the assignment of car lists with different seat classes for each train. The lower-level model is used to distribute the passenger flow to each train. Combined with the user equilibrium principle, a complex genetic algorithm embedded with the Frank–Wolfe method is designed to reasonably distribute passenger flows to each train. Finally, we take the Lanzhou-Xi’an HSR as an example to test both the model and the algorithm. The results show that the optimal train timetable can meet the requirements of both seat class and departure time with appropriate solution time limitations.

Optimization of Simultaneous Delivery and Pickup Wagon Scheme on Hybrid Siding Network of Railway Terminal

Aiming at the local freight train transit system in railway terminal, the optimization of simultaneous delivery and pickup wagon scheme on hybrid siding network is presented. The problem is formulated as a mathematical programming model. The objective function intends to minimize shunting engines’ operating cost, wagons’ travelling cost, and penalty cost for exceeding the retrieval time window. Some constraints indicating the relationship between delivery and pickup wagons, relationship between radial branches and operation batches, relationship between local wagon groups’ retrieved time and outbound train departure time, and relationship between tasks and operation batches are considered in the model. As an NP problem, using traditional method to solve the model is difficult and inefficient. A novel two‐stage hybrid optimization procedure is proposed. Firstly, the three‐phase approach composed of coding task sequence, dividing task batch, and generating access order sequence population is developed to generate initial solution. Secondly, an asynchronous iteration heuristic is provided. The iteration object is given as the expression form of the solution representing the delivery and pickup wagon sequence and then the initial iteration population is generated. Furthermore, the primary updating iteration population with pending and remaining groups is introduced to optimize iteration object Then, the senior updating iteration population with Lévy flight searching is also introduced to optimize further iteration object. Finally, the experimental scenarios are designed to test the proposed approach. Also, the proposed approach is compared with some other approaches and the performance of the proposed approach is evaluated by some different sized instances.

Traffic Modeling and Validation for Intersecting Metro Lines by Considering the Effect of Transfer Stations

This paper proposes a nonlinear discrete event state-space model for intersecting metro lines considering the effect of transfer stations. Disturbances such as technical problems in the rolling stock and signaling systems can cause deviations in the predefined train departure times. Any delay in the metro traffic system will increase over time and propagate to other trains, leading to instability which will reduce the efficiency of the system. Transfer stations in metro networks are designed to transfer passengers between trains on different intersecting metro lines. Therefore, traffic modelling of the metro transportation system requires consideration of the effect of such transfer stations. After introducing a discrete event nonlinear model for intersecting metro lines with one or two transfer stations, the accuracy and effectiveness of the introduced model to describe the dynamic behavior of metro traffic system has been evaluated and verified using the results of simulations based on real data from two intersecting lines on the Tehran metro network.

First train timetabling and bus service bridging in intermodal bus-and-train transit networks

Subway system is the main mode of transportation for city dwellers and is a quite significant backbone to a city's operations. One of the challenges of subway network operation is the scheduling of the first trains each morning and its impact on transfers. To deal with this challenge, some cities (e.g. Beijing) use bus ‘bridging’ services, temporarily substituting segments of the subway network. The present paper optimally identifies when to start each train and bus bridging service in an intermodal transit network. Starting from a mixed integer nonlinear programming model for the first train timetabling problem, we linearize and reformulate the model using the auxiliary binary variables. Following that, the bus bridging model is developed to cooperate with the first train operation for reducing long transfer waiting times. After realizing the low computational efficiency of solving the integrated model, a tailored algorithm is designed to optimally solve the first train timetabling and bus service bridging problems. The exact models and algorithms are applied to the Beijing subway network to test their effectiveness and computational efficiency. Numerical results show that our approaches decrease the total passenger waiting time by 53.4% by a combined effect of adjusting the first train departure times and operating 27 bridging buses on 7 routes.

A virtual resource-based method for formulating the safety headway of opposing trains arriving at the same station on a single-track railway line

ABSTRACT In train rescheduling, the arrival and departure times of trains at stations are normally constrained by many operations rules that must be respected. Therefore, different methods were proposed to describe train operations for preventing train conflicts, especially concerning the safety headways. This paper develops a virtual resource-based method in place of the commonly used big-M method and ‘either-or’ constraints for reformulating the safety headway of opposing trains arriving at the same station on a single-track rail. This new formulation can provide an efficient decomposition mechanism by decomposing the original complex problem into several single train-based subproblems. A resource-oriented mixed-integer linear programming model based on a time-space network is developed to minimize the total train delay time with cumulative flow variables used to describe time-space resources occupation. We also present a set of numerical experiments based on a single-track railway line in China to evaluate the validity of the proposed method.

Multi-stage timetable rescheduling for high-speed railways: a dynamic programming approach with adaptive state generation

A dynamic programming (DP) approach with adaptive state generation and conflicts resolution is developed to address the timetable-rescheduling problem (TRP) at relatively lower computation costs. A multi-stage decision-making model is first developed to represent the timetable-rescheduling procedure in high-speed railways. Then, an adaptive state generation method by reordering the trains at each station is proposed to dynamically create the possible states according to the states of previous stages, such that the infeasible states can be removed and the search space is reduced. Then, conflicts are resolved by retiming the arrival and/or departure times of trains. Furthermore, the state transfer equation is built and Bellman equation is developed to derive the solution to minimize the total delay time (TT). A series of simulation experiments and a real-world case study are used to evaluate the performance of the proposed method. The simulation experiments indicate that the proposed method is able to find the optimal timetable with appropriate overtaking at right stations and reduce the total delay by 62.7% and 41.5% with respect to the First-Come-First-Serve (FCFS) and First-Schedule-First-Serve (FSFS) strategy that are widely used in practice. Comparing to the intelligent scheduling method (e.g., Ant Colony Optimization and Particle Swarm Optimization), similar objective performance can be achieved at a much lower cost of computation time, which make the proposed method more applicable to the TRP in daily operation of high-speed railway.