Stop Schedule Research Articles

Effective passenger flow congestion propagation model for multi-mode rail transit networks

ABSTRACT During peak passenger flow periods, congestion propagation directly affects the operational safety and efficiency of multi-mode rail transit interconnections. By analyzing the key factors affecting congestion propagation, such as the train stop schedule, and considering parameters such as the basic reproduction number and propagation threshold, this study proposes a multi-mode rail transit susceptible-infected-recovered-susceptible (MRT-SIRS) epidemic model to analyze passenger flow congestion propagation. Simulation experiments and sensitivity analyses using data from the multi-mode rail transit in Beijing, China, were conducted to examine the influence mechanism of key factors on congestion propagation. The degree of influence of each factor was investigated using Gray correlation analysis. Each key factor, including the propagation and recovery rates, influences congestion propagation differently. The results of this study may provide theoretical support for the efficient operation and management of multi-mode rail transit systems.

A fully polynomial time approximation scheme for a stop schedule of a transportation line without branches

For a transportation line without branches, passenger service scheduling is mainly concerned with the determination of stop schedules for planned service trips. A mixed-integer programming method is proposed to maximize customer satisfaction by minimizing the total number of in-vehicle passengers during trips. A heuristic algorithm is proposed for a given number of service trips, in which the error bound of the heuristic is restricted by the number of stations. When the given number of service trips is sufficient to provide express services for all origin–destination pairs, the heuristic provides an optimal solution. However, the error bound of the heuristic approaches infinity as the number of stations increases. A fully polynomial time-approximation algorithm is proposed, where the number of service trips is a decision variable. Finally, the proposed algorithm was applied to the stop-schedule problem of a river bus operating along the Han River in Seoul, Korea.

Two-stage robust railway line-planning approach with passenger demand uncertainty

A railway line-planning problem is one of the fundamental problems in the strategic planning of railway operations. Operation zone, frequency, stop schedule, and passenger distribution for each train based on passenger demand are determined to minimize both the operation cost of the railway enterprise and the total travel cost to the passengers. However, passenger demand uncertainty makes balancing transport capacity and fluctuating demand challenging. Therefore, this paper proposes a two-stage robust optimization model wherein the nominal line plan is determined in the first stage (i.e., the case in which passenger demand has no fluctuation) and the rescheduled line plan based on the nominal line plan is determined according to the demand realization in the second stage. A Lagrangian relaxation algorithm and some strengthening techniques are designed. The model and algorithm are tested on real-world instances of the Wuhan–Guangzhou high-speed railway line under uncertain passenger demands. Computational results indicate that the proposed solution algorithm can yield a high-quality solution in 3600 s. In addition, the proposed two-stage robust solution can help minimize both operation and travel costs on average when compared with the nominal solution under uncertainty realization.

A Benders Decomposition Algorithm for the Passenger Train Service Planning

Railway transport becomes a more popular transportation in many countries due to its large transport capacity, low energy consumption, and benign environment. The passenger train service planning is the key of the rail operations system to balance the transport service and the passenger demand. In this paper, we propose a mixed binary linear programming formulation for the passenger train service planning to optimize the train route, frequency, stop schedule, and passenger assignment simultaneously. In addition, we analyze the computational complexities of the model and develop a Benders decomposition algorithm with valid inequalities to solve this problem. Finally, our model and algorithm are tested on a real-world instance of the Beijing-Shanghai high-speed railway line. The computational results show that our approach can solve these problems within reasonable solution time and small optimality gaps (less than 2.5%).

Optimizing a High-Speed Railway Operation Plan Based on Train Capacity and Service Frequency

AbstractIn this paper, a model to optimize a high-speed railway operation plan by dividing it into a train route plan and train stop schedule plan was developed based on the train capacity and serv...

Seat allocation model for high-speed railway passenger transportation based on flexible train composition

Seat inventory control is a crucial technique for railway revenue management. In literature, most of the existing seat allocation models assume a fixed capacity like classical revenue management. To extend the literature, this paper relaxes the assumption of fixed capacity by flexible train composition and discusses the effect of flexible train composition. The probabilistic nonlinear programming model is proposed for high-speed railway passenger service network formed by multi trains with different stop schedule plans. The model is transformed into equivalent linear programming which can be solved by ILGO CPLEX quickly. This paper makes seat inventory control and train composition decisions simultaneously considering stochastic demand and passenger choice behaviour. Numerical experiment results show that the policy under flexible train composition is superior to that under fixed train composition. The sensitive analysis shows that demand intensity, fare classes and elasticity of demand have a significant impact on the policy. The proposed model can provide a decision-making basis for discount sales and ticket allocation under flexible train composition in railway passenger operation.

Optimal High-Speed Railway Timetable by Stop Schedule Adjustment for Energy-Saving

Timetable optimization techniques offer opportunity for saving energy and hence reducing operational costs for high-speed rail services. The existing energy-saving timetable optimization is mainly concentrated on the train running state adjustment and the running time redistribution between two stations. Not only the adjustment space of timetables is limited, but also it is hard for the train to reach the optimized running state in reality, and it is difficult to get feasible timetable with running time redistribution between two stations for energy-saving. This paper presents a high-speed railway energy-saving timetable based on stop schedule optimization. Under the constraints of safety interval and stop rate, with the objective of minimizing the increasing energy consumption of train stops and the shortest travel time of trains, the high-speed railway energy-saving timetable optimization model is established. The fuzzy mathematics programming method is used to design an efficient algorithm. The proposed model and algorithm are demonstrated in the actual operation data of Beijing-Shanghai high-speed railway. The results show that the total operating energy consumption of the train is reduced by 3.7%, and the total travel time of the train is reduced by 11 minutes.

Application of a Mixed Integer Programming Model in Coordinating Stopping Schedules of Intra- and Inter-trains for a High Speed Rail Line

In a high speed rail network, there are usually two types of trains running on a single rail line, which are intra-trains and inter-trains. Inappropriate stopping schedules for both types of trains may cause negative influence on train operation, e.g., stopping schedules lack regularity, inter-trains consume too much route capacity of intra-trains, and intra-passengers are transported by inter-trains instead. This paper applies a mixed integer programming model in coordinating stopping schedules of intra- and inter-trains for a high speed rail line. The goal is to increase regularity of both types of trains on a main rail line, in the meanwhile, to rationalize the division of labor of intra- and inter-trains in term of transporting intra- and inter-passengers. A numerical experiment is implemented based on a real-world instance. The results show that a series of coordination indicators are improved compared to those of an original train stopping schedule, which demonstrates the effectiveness of our application approach.

Data analytics for occupancy pattern learning to reduce the energy consumption of HVAC systems in office buildings

In the last few years, the collecting and processing of occupancy data have become emerging issues since they can affect, either directly or indirectly, several energy operations in buildings. The application of data analytics-based methods makes it possible to exploit the potentialities of occupancy related knowledge to enhance the energy management in buildings. A methodology, aimed at implementing an occupancy-based HVAC system operation schedule, is presented in this article. The process is based on the convenience of displacing groups of occupants with similar occupancy patterns to the same thermal zone. An optimisation of the stop schedule of an HVAC system has been investigated, considering a typical week’s occupancy patterns. The methodology was used to analyse the Zaanstad Town Hall (The Netherlands), considering anonymous occupancy data for a monitoring period of four months. The resulting optimised schedule was tested, through an energy simulation approach, considering a model calibrated with real energy consumption data. The savings related to the energy consumption of the HVAC system, as a result of the implementation of the strategy, in comparison to an occupancy-independent operation schedule amounted to 14%. The proposed process can be generalized and drive energy managers in evaluating optimised occupancy-based HVAC system operation schedules.

The Optimization of Passengers’ Travel Time under Express-Slow Mode Based on Suburban Line

The suburban line connects the suburbs and the city centre; it is of huge advantage to attempt the express-slow mode. The passengers’ average travel time is the key factor to reflect the level of rail transport services, especially under the express-slow mode. So it is important to study the passengers’ average travel time under express-slow, which can get benefit on the optimization of operation scheme. First analyze the main factor that affects passengers’ travel time and then mine the dynamic interactive relationship among the factors. Second, a new passengers’ travel time evolution algorithm is proposed after studying the stop schedule and the proportion of express/slow train, and then membrane computing theory algorithm is introduced to solve the model. Finally, Shanghai Metro Line 22 is set as an example to apply the optimization model to calculate the total passengers’ travel time; the result shows that the total average travel time under the express-slow mode can save 1 minute and 38 seconds; the social influence and value of it are very huge. The proposed calculation model is of great help for the decision of stop schedule and provides theoretical and methodological support to determine the proportion of express/slow trains, improves the service level, and enriches and complements the rail transit operation scheme optimization theory system.

Collaborative Optimization of Stop Schedule Plan and Ticket Allotment for the Intercity Train

As regards the ticket allotment issue of the intercity passenger corridor designed for different train grades, the matching relationship between the ticket allotment and the passenger flow demand is studied. The passenger flow conversion equation which is based on the collaborative optimization of the intercity train stop schedule plan and ticket allotment is established. Then the mathematical model aiming at the maximum revenue of intercity train system and the highest satisfaction from the passengers is established. The particle swarm harmony search algorithm is designed to solve the model. The example verifies the effectiveness of the model and algorithm, which indicates that, through the collaborative optimization of the stop schedule plan and ticket allotment for different grades intercity trains, the sectional utilization rate of the train can be improved; meanwhile, the optimum matching between the intercity train revenue and the passenger satisfaction can be realized.

Robust stop-skipping patterns in urban railway operations under traffic alteration situation

In this paper an operation mode which is based on the stop-skipping approach is studied in urban railway lines under uncertainty. In this mode, each train follows a specific stop schedule. Trains are allowed to skip any intermediate stations to increase the commercial speed and to save energy consumption. As the commercial speed increases, the number of required trains in operation reduces and results eliminating unnecessary costs. To that end, a new mathematical model is proposed to reach the optimum stop schedule patterns. In the planning step, based on the traffic studies, the headway distributions are computed for different weekdays, and holidays. However, in practice, because of many unexpected events, the traffic may alter from what is planned. Therefore, in this condition, a robust plan is required that is optimized and immunized from uncertainty. In this paper, a new robust mathematical model, as well as two heuristic algorithms including (1) a decomposition-based algorithm and (2) a Simulated Annealing (SA) based algorithm is proposed. Finally, an Iranian metro line is studied and the optimum patterns are presented and analyzed.

Hybrid stop schedule of urban rail train

Purpose: In order to better serve the transport demand of urban area by rail, target at the Ur-ban Rail Train Stop Schedule problem. Design/methodology/approach: Bi-level mathematical programming model and game relation was used. Findings: A 0-1 bi-level mathematical programming model for urban rail transit hybrid Stop Schedule is developed when game relation between train Stop Schedule and passenger transfer choice is considered. Research limitations/implications: The research is still in progress. Practical implications: ChongQing urban rail line 2 was taken as an example, the practical application of the model has proved its feasibility and efficiency. Originality/value: A 0-1 bi-level mathematical programming model for urban rail transit hybrid Stop Schedule is developed. The upper level model is Stop Schedule targeting at the optimal profit from the operators side. The lower level model is passenger routing aims to minimize total travel time. According to its features, the bi-level model is integrated in order to be directly solvable by optimizing software.

Assessing Energy Consumption of High-speed Trains based on Mechanical Energy

Normally, not all the stopping sections of a high-speed rail (HSR) are long enough for a train to achieve the initially fixed target speed. By taking this crucial attribution of HSR into consideration, an assessment model for energy consumption of a high-speed train (HST) is established based on its mechanical energy. An example based on real data in China effectively demonstrates the model. It is found that both the target speed and stopping frequency have significant effects on HST energy consumption. If the target speed rises from 200 to 350km/h, the increasing percentages of energy consumption are 133%, 140%, 149% and 153% respectively for HSTs of the four examined stop schedules: all-stop, skip-stop, large-stop and non-stop. The non-stop HST consumes the less energy whereas all-stop HST consumes the most under equivalent conditions. Moreover, the travel speed of an HST with high target speed and frequent stopping is not significantly higher than that of an HST with lower target speed and less frequent stopping, but the former's energy consumption is strikingly more than the latter's. The findings might help rail departments to make a more environmental-friendly HST operation scheme by integrating its target speed and stop schedule.

Continuous approximation for skip-stop operation in rail transit

Operating speed of a transit corridor is a key characteristic and has many consequences on its performance. It is generally accepted that an increased operating speed for a given fleet leads to reduced operating costs (per kilometer), travel and waiting times (three changes that can be computed precisely), an improved comfort and level of service, which can attract new passengers who are diverted from automobile (items harder to estimate precisely). That is why several operation schemes which aim to increase the operating speed are studied in the literature, such as deadheading, express services, and stop skipping.A novel category of solutions to this problem for one-way single-track rail transit is to perform accelerated transit operations with fixed stopping schedules. The concept is quite simple: as the time required for stopping at each station is an important part of travel time, reducing it would be a great achievement. Particular operations that take advantage of this idea already exist. This paper focuses on one of them: the skip-stop operation for rail transit lines using a single one-way track. It consists in defining three types of stations: AB stations where all the trains stop, and A and B stations where only half of the trains stop (stations type A and B are allocated interchangeably). This mode of operation is already described in the literature (Vuchic, 1973, 1976, 2005) and has been successfully implemented in the Metro system of Santiago, Chile.This work tackles the problem with a continuous approximation approach. The problem is described with a set of geographically dependent continuous parameters like the density of stations for a given line. Cost functions are built for a traditional (all-stop) operation and for skip-stop operation as described above. A simple example is presented to support this discussion. Finally, a discussion about the type of scenarios in which skip-stop operations are more beneficial is presented.

A Greedy-Based Computer Algorithm for Train Stop Schedule in High-Speed Railway Network

The study constructs a stop schedule model for high-speed railway. A greedy-based algorithm is proposed and the problem is divided into 3 stages to decrease its difficulty to an acceptable extent. Some greedy principles are applied and series of optimal models are constructed to solve the problem. The result of the sample shows that the models and algorithms in the study are effective.

Continuous Approximation for Skip-Stop Operation in Rail Transit

Operating speed of a transit corridor is a key characteristic and has many consequences on its performance. It is generally accepted that an increased operating speed for a given fleet leads to reduced operating costs (per kilometer), travel and waiting times (three changes that can be computed precisely), an improved comfort and level of service, which can attract new passengers who are diverted from automobile (items harder to estimate precisely). That is why several operation schemes which aim to increase the operating speed are studied in the literature, such as deadheading, express services, stop skipping, etc.A novel category of solutions to this problem for one-way single-track rail transit is to perform accelerated transit operations with fixed stopping schedules. The concept is quite simple: as the time required for stopping at each station is an important part of travel time, reducing it would be a great achievement. Particular operations that take advantage of this idea already exist. This paper focuses on one of them: the skip-stop operation for rail transit lines using a single one-way track. It consists in defining three types of stations: AB stations where all the trains stop, and A and B stations where only half of the trains stop (stations type A and B are allocated interchangeably). This mode of operation is already described in the literature [1–3] and has been successfully implemented in the Metro system of Santiago, Chile.This work tackles the problem with a continuous approximation approach. The problem is described with a set of geographically dependent continuous parameters like the density of stations for a given line. Cost functions are built for a traditional (all-stop) operation and for skip-stop operation as described above. A simple example is presented to support this discussion. Finally, a discussion about the type of scenarios in which skip-stop operations are more beneficial is presented.

Operational Impacts of Using Restricted Passenger Flow Assignment in High-Speed Train Stop Scheduling Problem

One key decision basis to the train stop scheduling process is the passenger flow assignment, that is, the estimated passengers’ travel path choices from origins to destinations. Many existing assignment approaches are stochastic in nature, which causes unbalanced problems such as low efficiency in train capacity occupancy or an irrational distribution of transfer passengers among stations. The purpose of this paper is to propose a train stop scheduling approach. It combines a passenger flow assignment procedure that routes passenger travel paths freely within a train network and is particularly capable of incorporating additional restrictions on generating travel paths that better resemble the rail planner’s purpose of utilizing capacity resources by introducing four criteria to define the feasibility of travel path used by a traveler. Our approach also aims at ensuring connectivity and rapidity, the two essential characteristics of train service increasingly required by modern high-speed rails. The effectiveness of our approach is tested using the Chinese high-speed rail network as a real-world example. It works well in finding a train stop schedule of good quality whose operational indicators dominate those of an existing stochastic approach. The paper concludes with a comprehensive operational impact analysis, further demonstrating the value of our proposed approach.

Train Stop Scheduling in a High‐Speed Rail Network by Utilizing a Two‐Stage Approach

Among the most commonly used methods of scheduling train stops are practical experience and various “one‐step” optimal models. These methods face problems of direct transferability and computational complexity when considering a large‐scale high‐speed rail (HSR) network such as the one in China. This paper introduces a two‐stage approach for train stop scheduling with a goal of efficiently organizing passenger traffic into a rational train stop pattern combination while retaining features of regularity, connectivity, and rapidity (RCR). Based on a three‐level station classification definition, a mixed integer programming model and a train operating tactics descriptive model along with the computing algorithm are developed and presented for the two stages. A real‐world numerical example is presented using the Chinese HSR network as the setting. The performance of the train stop schedule and the applicability of the proposed approach are evaluated from the perspective of maintaining RCR.