Train Departure Times Research Articles

Two-phase decomposition method for the last train departure time choice in subway networks

An urban subway network with a number of service lines forms the backbone of the public transport system for a large city of high population, such as Singapore, Hong Kong and Beijing. Passengers in these large cities heavily rely on urban subway networks for their daily life. The departure times of the last trains running on different lines of an urban subway network should be well coordinated in order to serve more passengers who can successfully transfer from one line to another, which is referred to as the last train departure time choice problem. This study aims to develop a global optimization method that can solve the last train departure time choice problem for large-scale urban subway networks. To do so, it first formulates a mixed-integer linear programming (MILP) model by introducing auxiliary binary and integer decision variables. For the real-life and large-scale instances, however, the formulated MILP model cannot be solved directly by the global optimization methods such as branch-and-bound algorithm invoked by CPLEX – one of the powerful optimization solvers because of the instance sizes. An effective two-phase decomposition method is thus proposed to globally solve the large-scale problems by decomposing the original MILP into two MILP models with small sizes. Finally, a real case study from the Beijing subway network is conducted to assess the efficiency and applicability of the two-phase decomposition method and perform the necessary sensitivity analysis of the operational parameters involved in the last train departure time choice problem.

복수 운영체제에서의 철도네트워크 열차슬롯배분 모형 연구

복수의 철도운영자가 철도네트워크를 공동으로 사용하는 경우, 철도운영자별로 열차운행비율, 우선순위 및 착발시각 등에 다툼이 발생하고, 이용수요가 많은 시간대에는 집중적으로 열차운행을 신청하여 열차 경합이 증대되는 현상이 점점 커질 것으로 예상된다. 본 연구는 열차출발시각을 결정변수로 하여 다양하게 주어진 열차시각표에서 열차운행순서, 최소운전시격, 착발시각, 열차우선순위 등을 해석하였으며, 각종 제약조건을 만족하도록 철도운영자들이 신청한 열차시각을 조정하고, 경합 해소가 불가능한 열차는 최종적으로 제거하는 방법을 통하여 목적함수인 철도운영에 현실적으로 적용 가능한 최대 수의 열차슬롯을 찾는 열차슬롯배분 모형을 제시하고자 하였다. It is anticipated that, in cases in which different train operators share railway network, conflicts may occur among train operators with regard to train operation rate, train priorities, and arrival and departure time; besides this, during times when there is high demand for trains, operators will request train operations intensively, steadily increasing train conflict phenomena. In the present study, train operation sequence, minimum headway, arrival and departure time, train priorities, etc., were analyzed, and while using train departure times as decision variables in variably given train schedules, by adjusting train time requested by train operators, and finally rejecting the train times in cases in which conflict resolution is impossible, so that various constraints can be satisfied, a train slot allocation model was suggested to find the objective function, that is, the maximum number of train slots that can be practically applicable to railway operation.

Optimizing the draft passenger train timetable based on node importance in a railway network

ABSTRACTTrain timetable plays an important role in the passenger train operations, which is typically developed or adjusted from the draft train timetable (DTT). The DTT serves as the basic framework and the core component of the train timetable to generate the rough plan of passenger trains, and eventually impacts the performance of the train operations. The paper attempts to develop a draft passenger train timetable under the constrained capacities of arrival–departure tracks and servicing tracks for the passenger train coaching stocks in a passenger railway network. The goals of the DTT are to satisfy the expected arrival/departure time, reduce the number of passenger coaching stocks, and avoid the closely spaced arrival/departure times. We propose a heuristic optimization algorithm based on the node importance to calculate the optimal train arrival and departure times at each arrival/departure station. The proposed model and algorithm are demonstrated in an experimental network with 11 stations and 73 trains in China; the results show that 93.06% of the trains can utilize the minimum passenger coaching stocks, and the equilibrium among passenger trains of the same route daily are improved approximately 20% compared to the actual timetable.

OPERATIONAL PLANNING OF LOCAL WORK ORGANIZATION OF RAILWAY SECTION AND JUNCTION WITH USE OF DYNAMIC MODEL OF TRANSPORTATION PROCESS

Purpose. Development of a method of operational planning of local work of railway sections and units using a dynamic model of the transportation process, which allows a high degree of certainty to plan the formation of local trains, the performance of local work, the needs of production resources for the achievement of the indicators and provide the necessary information to higher-level control system, generating operational planning transportation process at the network level. Methodology. The solution was carried out on the approaches of systems theory, methods of set theory, control theory, scheduling theory, probability theory. A definition of the dynamic model in relation to the object and subject of research. The role and function of the dynamic model in the implementation of administrative procedures - planning, management and monitoring of the transportation process. The requirements for the dynamic model, the implementation of which will ensure the availability of its implementation and the necessary level of quality simulation. The method of operational planning of local work of railway sections and units designed for inductive circuit by sequential decision tasks with progressive expansion of the domain object, and the application to achieve the designated object and subject of study. Findings. Developed a dynamic model of the transportation process is reflected to create an automated system linking train formation forecast timetable of trains on the Belarusian Railways. Analytically set heteroskedasticity residues departure time of trains on the road forecast range in the simulation using this automated system and operational planning horizon to 24 hours. This fact indicates the possibility of the effective use of this method to significantly improve the accuracy of automated scheduling. Originality. An innovative component of the work is the use of simulation methods of transportation process with simultaneous assessment of the technological risks arising within the model used. This risk assessment is inherent in the model and are constantly taken into account in the simulation in order to analyze possible options for the development of the transportation process at railway stations and nodes in operational planning of local work. Practical value. The practical orientation of the results has three main components: a dynamic model and the proposed method is adapted to existing conditions in the railway sector, which allows them to joint implementation on the basis of information-analytical operated traffic control systems; obtained scientific and practical solutions to make it possible to increase the reliability of the results of operational planning of local work of railway sections and units that have a positive impact on the performance of operational work and the general state of the financial and economic activities of the railway; the proposed method makes it possible to scale the objects and purposes of operational planning, is available for use in transport related areas of operational planning and, above all, to address the actual problems of train formation.

Minimizing the maximal weighted lateness of delivering orders between two railroad stations

We consider the planning problem for freight transportation between two railroad stations. We are required to fulfill orders (transport cars by trains) that arrive at arbitrary time moments and have different value (weight). The speed of trains moving between stations may be different. We consider problem settings with both fixed and undefined departure times for the trains. For the problem with fixed train departure times we propose an algorithm for minimizing the weighted lateness of orders with time complexity O(qn2 log n) operations, where q is the number of trains and n is the number of orders. For the problem with undefined train departure and arrival times we construct a Pareto optimal set of schedules optimal with respect to criteria wLmax and Cmax in O(n2 max{n log n, q log v}) operations, where v is the number of time windows during which the trains can depart. The proposed algorithm allows to minimize both weighted lateness wLmax and total time of fulfilling freight delivery orders Cmax.

Distribution analysis of train interval journey time employing the censored model with shifting character

ABSTRACTThe theoretical framework of limited dependent variable models is extended to accommodate a shifting character and thus fit the distribution of train journey time on sections of urban rail network. Data of actual train arrival and departure time at each station are used to calculate the journey time of each railway interval of multi-class trains. The log-normal distribution and normal distribution among a group of theoretical distributions are the most and second most suitable latent distributions of the train interval journey time in the censored models with shifting character. This modified distribution is described by four parameters, namely, the expectation and variance of the latent distribution and the upper and lower bound of the migration interval. The square root of the least square measurement (SRLSM) is taken as a measure, and a traversal search is adopted to determine the above four parameters according to the SRLSM. The average of the SRLSM of the theoretical train interval journey time distribution obtained by using the proposed method on all railway sections is 0.0905. The theoretical framework is the basis of storing hidden rules in data instead of past data of train travel time and optimizing the existing management of rail transit operation.

Operational Schedule Flexibility and Infrastructure Investment: Capacity Trade-Off on Single-Track Railways

To minimize costs, railways carefully match route infrastructure investment to projected traffic levels. Under structured operations according to a rigid timetable, the optimal amount of infrastructure for a given traffic volume can be determined with various models. However, North American railways use flexible operations for which planned train departure times can vary. Schedule flexibility increases the number of possible meet locations on a single track, which can lead to a combination of increased delays and infrastructure investment. When industry practitioners plan rail line capacity for flexible operations, they rarely optimize schedule flexibility and infrastructure investment simultaneously for a given level of service. To increase knowledge of the relationship between these factors, the research reported in this paper simulated operations on two representative single-track routes with rail traffic controller software. A baseline minimum-delay schedule was developed for each route under an initial infrastructure. The experiment design introduced schedule flexibility and infrastructure expansion to examine the interaction between these factors and train delay response. The results suggested that, for a given infrastructure configuration, an immediate increase in train delay occurred with small amounts of schedule flexibility. After this increase, routes became insensitive to further increases in schedule flexibility. Similarly, to maintain a level of service required substantial infrastructure investment for small amounts of schedule flexibility.

Assessment of schedule-based and frequency-based assignment models for strategic and operational planning of high-speed rail services

Despite some substantial limitations in the simulation of low-frequency scheduled services, frequency-based (FB) assignment models are by far the most widely used in practice. They are less expensive to build and less demanding from the computational viewpoint with respect to schedule-based (SB) models, as they require neither explicit simulation of the timetable (on the supply side), nor segmentation of OD matrices by desired departure/arrival time (on the demand side).The objective of this paper is to assess to what extent the lack of modeling capabilities of FB models is acceptable, and, on the other hand, the cases in which such approximations are substantial and more detailed SB models are needed. This is a first attempt to shed light on the trade-off between (frequency-based) model inaccuracy and (scheduled-based) model development costs in the field of long-distance (e.g. High-speed Rail, HSR) service modeling.To this aim, we considered two modeling specifications estimated using mixed Revealed Preferences (RP) and Stated Preferences (SP) surveys and validated with respect to the same case study. Starting from an observed (baseline) scenario, we artificially altered the demand distributions (uniform vs. time-varying demand) and the supply configuration (i.e. train departure times), and analyzed the differences in modal split estimates and flows on individual trains, using the two different model specifications.It resulted that when the demand distribution is uniform within the period of analysis, such differences are significant only when departure times of trains are strongly unevenly spaced in time. In such cases, the difference in modal shares, using FB w.r.t. SB, is in the range of [0%, +5%] meaning that FB models tend to overestimate HSR modal shares. When the demand distribution is not uniform, the difference in modal shares, using FB w.r.t. SB, is in the range of [−10%, +10%] meaning that FB models can overestimate or underestimate HSR modal shares, depending on timetable settings with respect to travelers’ desired departure times. The differences in on-board train flow estimates are more substantial in both cases of uniform and not uniform demand distribution.

Timetable Design for Urban Rail Line with Capacity Constraints

To design an efficient and economical timetable for a heavily congested urban rail corridor, a scheduling model is proposed in this paper. The objective of the proposed model is to find the departure time of trains at the start terminal to minimize the system cost, which includes passenger waiting cost and operating cost. To evaluate the performance of the timetable, a simulation model is developed to simulate the detailed movements of passengers and trains with strict constraints of station and train capacities. It assumes that passengers who arrive early will have more chances to access a station and board a train. The accessing and boarding processes of passengers are all based on a first-come-first-serve basis. When a station is full, passengers unable to access must wait outside until the number of waiting passengers at platform falls below a given value. When a train is full, passengers unable to board must wait at the platform for the next train to arrive. Then, based on the simulation results, a two-stage genetic algorithm is introduced to find the best timetable. Finally, a numerical example is given to demonstrate the effectiveness of the proposed model and solution method.

2P24 Energy-efficient train operation for urban rail transit systems(Shotgun Session)

Application of energy-efficient train operation has been regarded as an effective way to reduce the energy consumption which benefits the cost of operation companies and emission to environment. Most conventional approaches only focused on optimizing the driving strategy for single train, which neglects the influence of timetable on the energy consumption and reuse of the regenerative energy among trains. Based on the optimal train control model, a timetable optimization approach is proposed to achieve the energy-efficient operation for multi-trains in two-track urban rail transit systems, together with a cooperative train control approach for efficient utilization of the regenerative energy by properly adjusting the train departure times. The proposed approaches in this paper extend the optimal train control method, which realizes the combination of the high-level transportation management and the low-level accurate train operation control. With the satisfaction of the passenger transport demand, the presented solution can provide decisions to the operators and drivers for energy-efficient train operations. A case study based on the data of Beijing Yizhuang urban rail transit line is presented and then the simulation result illustrates that the proposed approach can averagely achieve 9.4% energy reduction for one day than the approach only optimizing the single train operation. In addition, the computation time of the analytical algorithm is within 3 seconds, which satisfies the application of real-time train control system.

Research on the Last Train Connection in the Urban Mass Transit System

With the urban rail transit becoming more and more networked, determining the departure time of last trains has been an important part for the urban rail transit network operations organization. First analyze two aspects of passengers and vehicles to determine reasonable time intervals of last trains, then analyze last train departure time optimization, minimizing the total loss in the transfer station as the objective to build the mathematical model, by adding and shifting line at the transfer station to reduce the connection direction loss, an auxiliary line being added or not according to the operating time so as to determine the final operation result. Finally, use the Beijing subway to verify and the result shows that the method has practical significance for the improvement of urban rail transit operation organization.

A new approach for improving the performance of freight train timetabling of a single-track railway system

A new approach for improving the performance of freight train timetabling for single-track railways is proposed. Using the idea of a fixed-block signaling system, we develop a matrix representation to express the occupation of inter- and intra-station tracks by trains illustrating the train blocking time diagram in its entirety. Train departure times, dwell times, and unnecessary stopping are adjusted to reduce average train travel time and single train travel time. Conflicts between successive stations and within stations are identified and solved. A fuzzy logic system is further used to adjust the range of train departure times and checks are made to determine whether dwell times and time intervals can be adjusted for passenger and freight trains at congested stations to minimize train waiting times. By combining manual scheduling expertise with the fuzzy inference method, timetable efficiency is significantly improved and becomes more flexible.

Study on Connection Optimization of Last Train Departure Time on Urban Mass Transit Network

The operation and management of urban mass transit network put forward higher requirements for last trains‘ transfer connection. Based on the analysis of coordination relationship and timeliness of accessible routes, this paper puts forward a dynamic passenger volume distribution method according to the generalized travel cost. Then the connection optimization model of last train departure time is built to increase accessible passenger volume and reduce passengers’ transfer waiting time of all OD pairs for last trains. Finally, the validity and rationality of this model and algorithm is verified with numerical analysis.

Research on Optimization of the Passenger Train Departure Time Domain for Reducing Passenger Train Stock Amount

A method was proposed to reduce the amount of train stock by optimizing the passenger train departure time domain. The objective function is the minimum total turn-round time of passenger train stock. The constraints include the dwell time in departure station and turn-back station, the interval time. The optimization model of the passenger train departure time domain was built. Design the heuristic algorithm to solve the proposed model. Taking the Zhengzhou station as an example, each passenger train departure time domain is calculated by utilizing the proposed model. Comparing the calculated departure time domain with the real departure time, the effectiveness of the model is calculated.

A practical model for last train rescheduling with train delay in urban railway transit networks

Last train timetable rescheduling aims at coordinating the arrival and departure times of feeder trains with connecting trains at transfer stations to eliminate the effect of unexpected incidents in train operations. It has become a challenging problem in the operations and management of urban railway transit networks because of high complexities in coordination among lines. In this paper, we propose a rescheduling model for last trains with the consideration of train delays caused by incidents that occurred in train operations. In the model, two aspects are considered. On one hand, we try to minimize the running time and the dwell time, and to maximize the average transfer redundant time and the network accessibility. On the other hand, we expect to minimize the difference between the original timetable and the rescheduled one. A genetic algorithm is developed to solve this problem. The case study of Beijing railway transit network shows that once a delay occurs in a section, the most effective way to adjust the timetable consists of adjusting the running time of trains that have strong transfer relationships with the delay section. If the delay is not substantially long, the suggested model would neutralize the influence of the delay.

Passenger Transfer Efficiency Optimization Modelling Research with Simulations

An integrated optimization model is newly developed in this research to improve passenger transfer efficiency of an urban rail station by minimizing average waiting time of transfers in this station with rationalizing the arrival and departure time of trains in view of transfer passenger flows and their feeder services. Corresponding algorithm is also designed to search for the optimal solution to the objective function of the proposed model. A representative urban rail transfer station in Beijing is studied as example to validate the effect of transfer optimization with the new model. Comparative simulations confirm that the proposed model is able to effectively reduce the waiting time of each transfer in a station. This is significant for systematically improving the operation safety of an urban rail transfer station with faster evacuations of transfer passengers as well as substantially saving travel time of passengers making transfers in this station.

Scheduling algorithm with controllable train speeds and departure times to decrease the total train tardiness

A B S T R A C T The problem of generating a train schedule for a single - track railway sy s tem i s addressed in this paper. A three stage scheduling is proposed to reduce the total train tardiness. We derived an appropriate job-shop scheduling algorithm called DR-algorithm. In the first stage, by determining appropriate weights of the dispatching rules, a pre-schedule is constructed. In the second stage, on the basis of the pre-schedule, the departure times of the trains are modified to reduce the number of conflicts in using railway sections by different trains. In the third stage, a train speed control helps the scheduler to change the trains' speeds in order to reduce the train tardiness and to reach other objectives. The factual train schedule is based on the modified train speeds and on the modified departure times of the trains. The experimental running of the DR-algorithm on the benchmark instances showed this algorithm can solve train scheduling problems in a close to optimal way. In particular, the total train tardiness was reduced about 20% due to controlling train speeds and the departure times of the trains.

Exact formulations and algorithm for the train timetabling problem with dynamic demand

In this paper we study the design and optimization of train timetabling adapted to a dynamic demand environment. This problem arises in rapid train services which are common in most important cities. We present three formulations for the problem, with the aim of minimizing passenger average waiting time. The most intuitive model would consider binary variables representing train departure times but it yields to non-linear objective function. Instead, we introduce flow variables, which allow a linear representation of the objective function. We provide incremental improvements on these formulations, which allows us to evaluate and compare the benefits and disadvantages of each modification. We present a branch-and-cut algorithm applicable to all formulations. Through extensive computational experiments on several instances derived from real data provided by the Madrid Metropolitan Railway, we show the advantages of designing a timetable adapted to the demand pattern, as opposed to a regular timetable. We also perform an extensive computational comparison of all linear formulations in terms of size, solution quality and running time.

Estimating the robustness of long-haul train plans

In Australia, and elsewhere, the movement of trains on long-haul rail networks is usually planned in advance. Typically, a train plan is developed to confirm that the required train movements and track maintenance activities can occur. The plan specifies when track segments will be occupied by particular trains and maintenance activities. On the day of operation, a train controller monitors and controls the movement of trains and maintenance crews, and updates the train plan in response to unplanned disruptions. It can be difficult to predict how good a plan will be in practice. The main performance indicator for a train service should be reliability – the proportion of trains running the service that complete at or before the scheduled time. We define the robustness of a planned train service to be the expected reliability. The robustness of individual train services and for a train plan as a whole can be estimated by simulating the train plan many times with random, but realistic, perturbations to train departure times and segment durations, and then analysing the distributions of arrival times. This process can also be used to set arrival times that will achieve a desired level of robustness for each train service.

Sequencing Optimization Method for Drawing Train Operation Diagram of High-Speed Railway

It is a very complicated work for optimizing the train operation diagram for railway enterprise. In order to improve the quality and reduce the computing time of train operation diagram, an initial relaxant train operation diagram is drawn ignoring the constraints among different train running lines firstly in this paper. Secondly based on this initial relaxant train operation diagram, through devising the multi-parallelogram and weighted directed graph representation of train operation diagram, the train operation diagram is optimized via the directed graph by the strategies such as exchanging operation order, increasing dwell time and expanding departure time, and then the sequencing optimization method is designed for drawing train operation diagram using computer, which aim to minimize the total passenger train travel time under the constraints of train arriving-departing interval time, train minimum dwell time, train travel time, train departure time and comprehensive maintenance time. A numerical example is given to show that this sequencing optimization method can effectively draw the passenger train operation diagram of high-speed railway.