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Continuous growth of energy consumption for metro systems has raised the public's concern. Meanwhile, both operators and passengers pursue for efficient metro services, especially during peak hours. This paper aims at designing a bi-objective optimization model and a new solution approach so that the energy conservation of metro trains and less passenger waiting time can be achieved. Firstly, considering complex routes, a multi-particle train operation model with the objectives of punctuality, parking accuracy, energy efficiency and safety provided is established for the minimization of traction energy consumption through investigating the optimal force coefficients and coast positions, while suitable dwell times and headway times of metro trains are found trough building a timetable model, which balances the regenerative energy, transfer and non-transfer passenger waiting time. Secondly, a deep reinforcement learning (DRL) and non-dominated sorting genetic algorithm II (NSGA-II) based two-layer solution approach is introduced for model calculation. Finally, comparison shows that the proposed model can achieve the energy conservation of metro trains by 9.16% with passenger waiting time decreased by 15.88%. More experiments further demonstrate the superiority of the developed model and solution approach. [Display omitted] [ABSTRACT FROM AUTHOR]

• A network-based passenger flow control method is proposed for the oversaturated metro network. • A bi-objective integer linear programming model is formulated. • The equivalent single objective linear integer programming model is deduced. • Numerical examples demonstrate the effectiveness of the proposed approaches. The oversaturated situation is now very common in the metro system of some megacities due to large commuting demands in peak hours, which leads to passenger accumulation on platforms and causes potential accident risks. To improve the transport efficiency and passenger accumulation safety at each station, this paper proposes a cooperative passenger flow control optimization in a specific metro network, in which each passenger can freely switch trains between different metro lines with a single ticket. Through considering the dynamic characteristics and transfer behaviors of passengers, an effective bi-objective integer linear programming model is formulated to characterize the passenger control process, in which the objectives are to minimize the total passenger waiting time and passenger accumulation risks at all the involved stations. To solve the proposed model conveniently, the above model is transformed into a single-objective model through reformulating the risk objective as a threshold-based constraint. Finally, two sets of numerical experiments, including a small-scale case and a real-world instance with operation data of the Beijing metro system, are implemented to demonstrate the performance and effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

As urban rail networks in big cities tend to expand, the synchronization of trains has become a key issue for improving the service quality of passengers because most urban rail transit systems in the world involve more than one connected line, and passengers must transfer between these lines. In contrast to most existing studies that focus on a single line, in this study, we focus on synchronized train timetable optimization in an urban rail transit network, considering the dynamic passenger demand with transfers as well as train loading capacity constraints. First, we propose a mixed-integer programming (MIP) formulation for the synchronization of training timetables, in which we consider the optimization of two objectives. The first objective is to minimize the total waiting time of passengers, involving arriving and transfer passengers. Our second objective is a synchronization quality indicator (SQI) with piecewise linear formulation, which we propose to evaluate the transfer convenience of passengers. Subsequently, we propose several linearization techniques to handle the nonlinear constraints in the MIP formulation, and we prove the tightness of our reformulations. To solve large-scale instances more efficiently, we also develop a hybrid adaptive large neighbor search algorithm that is compared with two benchmarks: the commercial solver CPLEX and a metaheuristic. Finally, we focus on a series of real-world instances based on historical data from the Beijing metro network. The results show that our algorithm outperforms both benchmarks, and the synchronized timetable generated by our approach reduces the average waiting time of passengers by 1.5% and improves the connection quality of the Beijing metro by 14.8%. • Propose an mixed-integer programming (MIP) formulation for the synchronization of train timetables with two objectives. • Propose an synchronization quality indicator (SQI) with piece-wise linear formulation. • Propose several linearization techniques to handle the nonlinear constraints. • Develop a hybrid adaptive large neighbor search algorithm. • Conduct a series of real-world instances based on the historical data of Beijing metro network. [ABSTRACT FROM AUTHOR]

Considering the service quality and energy efficiency, this paper develops a multi-objective timetable optimization approach for subway system. First, we analyze the variation on the passenger flow at stations, and propose the concept of passenger waiting time. Second, we develop a speed-profile-generation approach to search for the energy-efficient speed profile under the condition of a given section trip time. Then we formulate a multi-objective timetable optimization model to minimize the passenger time and energy consumption by controlling section trip time and station dwell time, in which passenger time includes both waiting time and traveling time. We respectively employ the ideal-point compromise approach, linearly weighted compromise approach and fuzzy linear programming approach to find the suboptimal solution, via performing a genetic algorithm. With the operation data from Beijing Yizhuang and 4-Daxing subway lines of China, we conduct extensive case studies to demonstrate the effectiveness of our model. The results show that the passenger waiting time and energy consumption can be reduced during both peak and off-peak hours. The proposed model and algorithm can be developed to a decision support system for dispatchers to schedule trains in the real world. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

With the sharp increase of passenger travel demands in an urban rail transit (URT) network, more and more stations suffer an over-saturated and congested situation during peak hours, which often leads to colossal passenger accumulation in platforms, especially in transfer platforms. Under this state, the passenger flow guidance is a useful method to release the passengers' pressure and balance the passenger accumulation imbalance. In order to calculate the passenger flow traveling data and the passenger flow guidance (PFG) time, a multi-agent simulation model is firstly established. And then, a two-phase integrated passenger flow assignment based on the backtracking algorithm (BA) is proposed for generating guidance information to minimize total passenger waiting time and release passenger congestion. Besides, a passenger compliance degree to the guidance information is defined to stimulate the passengers' response to the guidance information in the real world. Finally, a real-world example of the Chongqing subway network with five metro lines and 95 stations is implemented to verify the performance and effectiveness of the proposed method. The total passenger waiting time is decreased by 5.62% under the passenger flow guidance approach. [ABSTRACT FROM AUTHOR]

This paper focuses on how to minimize the total passenger waiting time at stations by computing and adjusting train timetables for a rail corridor with given time-varying origin-to-destination passenger demand matrices. Given predetermined train skip-stop patterns, a unified quadratic integer programming model with linear constraints is developed to jointly synchronize effective passenger loading time windows and train arrival and departure times at each station. A set of quadratic and quasi-quadratic objective functions are proposed to precisely formulate the total waiting time under both minute-dependent demand and hour-dependent demand volumes from different origin–destination pairs. We construct mathematically rigorous and algorithmically tractable nonlinear mixed integer programming models for both real-time scheduling and medium-term planning applications. The proposed models are implemented using general purpose high-level optimization solvers, and the model effectiveness is further examined through numerical experiments of real-world rail train timetabling test cases. [ABSTRACT FROM AUTHOR]

Public transportation is one of the most essential services in urban areas. The average passenger waiting time at a stop is an important criterion in evaluating the quality of public transportation systems. Accurate measurement of the average waiting time (AWT) at stops leads to more appropriate and timely schedules. Researchers in the past developed formulations for measuring the AWT at stops based on the assumptions that passengers arrive at stops in a uniform manner and buses arrive at stops independently. Studies on transportation systems in different cities indicate that using these formulations does not result in an accurate measure of the AWT and that there is a significant difference between the observed AWT and the one estimated by these formulations. Researchers related the cause of this discrepancy to the violation of the assumptions of uniform passenger arrival times and independent headways. We show that when the number of buses is not large (even when these assumptions hold true) the existing formulations still lack adequate accuracy. In this paper, we examine the process of formula development that resulted in a formulation that overestimates the AWT; we then propose accurate formulas for estimating the AWT with dependent and independent headways. A discrete simulation model has also been developed to further verify the inaccuracy of the existing formulations and to evaluate the performance of the proposed formulations. Furthermore, as a case study, the AWT at a bus stop in the Tehran bus transportation system has been studied and the accuracy of the proposed formulations has been examined and compared with that of the existing one. [ABSTRACT FROM AUTHOR]

The paper presents computer simulation approach to developing optimal bus scheduling under stochastic and deterministic network environments with static and dynamic demand. The primary objective is to minimize the total passenger waiting time. The mean transit demand at each stop and the travel time between neighboring bus stops are assumed as known information. An example route showing an application of the proposed model is presented. Comparisons between waiting times under different network scenarios have been made using the example route. The results obtained from the analyses are promising and thus the method can be implemented as a substitute to real time control strategies when implementation cost is an issue as the latter is relatively expensive. It may also be used in coordination with the real time control strategies to reduce holding time. In addition, it can assist transit users in planning their trips in advance so that misleading travel information is reduced. [ABSTRACT FROM AUTHOR]