Dynamic Passenger Demand Research Articles

A copula-based approach for multi-modal demand dependence modeling: Temporal correlation between demand of subway and bike-sharing

As a representative mode of shared mobility, bike-sharing serves not only as a convenient way to conduct short-distance trips in urban areas, but also as a feeder mode to public transit, forming the Bike and Ride (BnR) system. Conducting management for such a hybrid multi-modal system faces various challenges, including the complex interactions between bike-sharing and other modes, highly dynamic passenger demand, and the difficulty of accessing direct transfer data. To overcome such difficulties, our study proposes a framework for assessing the dependency between the two usage modes. Firstly, a Dynamic-Time-Warping-based (DTW) method is utilized to determine the catchment area (CA) between the two modes, allowing the BnR-related tendency similarity under a given time scale to be considered. Then, the patterns of probabilistic dependence between travel demand of the two modes are obtained by a copula-based approach, which separates correlations under specific usage levels from single modal demands. A case study on the multi-modal system formed by docked bike-sharing and subway in New York is conducted to validate the proposed framework. The tendency similarity is found to be most pronounced within 500 m on average under a 4-hour interval. For each formed station group (SG), the best-fitted copula type is selected, capturing the strong tail correlations present only at specific usage levels. The results show a variety of different correlation patterns within SGs, despite the close geographic locations they may share. Areas of potential transfer resistance between the two modes are identified, which is more evident in first-mile-related (FMR) activities. In contrast, the two modes display more weak connections in last-mile-related (LMR) activities. The obtained results can be utilized by bike-sharing service providers to analyze demand distributions and conduct efficient station-level rebalancing. Compared to previous methods, our proposed framework is computationally inexpensive since no direct transfer of data or complex inference network is required. It incorporates statistically significant spatial–temporal information, allowing for a more accurate determination of the bi-modal assessment range. Moreover, considering that single-mode influences are mathematically removed, the resulting correlation in principle links to the strength of the connections between the two modes. Therefore, it can be assessed as an indicator of the reliability of the multi-modal system.

Synchronization of train timetables in an urban rail network: A bi-objective optimization approach

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%.

Spatiotemporal synchronous coupling algorithm for urban rail transit timetables design under dynamic passenger demand

This paper focuses on the problem of designing the schedule of urban rail transit systems under dynamic passenger demand considering limited train capacity and congestion. From the point of view of operators, the goal of timetable optimization consists of using as few as possible service trains to transport the arriving passengers to their destinations securely and quickly. On the other hand, passengers want to spend the minimum time travelling to their destinations, including the time they wait on platforms until they board the first and successive trains in case of transferring between lines. Due to the variability of passenger flows and the difficulty in exactly solving full-day timetabling problems in short computation times, it is difficult in practice to use the approaches proposed in the literature. Moreover, when the capacity of trains is considered and oversaturation conditions emerge, the problem becomes even more complex, converting into a challenge the design of schedules from an operational point of view. By considering fixed train dwell times at stations and train running times between stations, we first propose a non-linear programming formulation to model the problem of determining the most convenient interdeparture times of services at the first station of a line, aiming at minimizing the waiting time of passengers. Since the dynamic behaviour of passenger demand and the maximum sectional passenger flow are approximately synchronous, an innovative method, the spatiotemporal synchronization coupling algorithm, based on working with the time-varying maximum sectional passenger flow instead of the demand patterns is proposed to quickly solve in an approximate way the demand-driven timetabling problem. The proposed approach is applied to a real case of Chengdu Metro Line 1 in China. The results show the effectiveness of the algorithm, both in terms of computational effort and in terms of reducing the waiting time currently experienced by passengers.

: Mobility-Driven Integration of Heterogeneous Urban Cyber-Physical Systems Under Disruptive Events

With the rapid development of cities, heterogeneous urban cyber-physical systems are designed to improve citizens’ experience, e.g., navigation and delivery service. However, the integration of services is not designed for disruptive events, an oversight that has rippling effects on service quality. For example, urban transportation systems consist of multiple transport modes that have complementary characteristics of capacities, speeds, and costs, facilitating smooth passenger transfers by planned schedules. Such integration may experience significantly increased delays during disruptions. Current solutions rely on a substitute service to transport passengers from and to affected areas using ad-hoc schedules and static routes, which are inefficient and do not utilize mobility patterns of mobile systems, e.g., dynamic passenger demand. To coordinate heterogeneous transportation systems under disruptions, we design a service to automatically select and integrate part of three systems (subway, bus, and taxi) using systems’ mobility patterns, e.g., predicted supply and demand. The service is presented in a normal version, eRoute, considering both subway and bus, and in a version taking taxis into account, called enhanced eRoute. We implement and evaluate eRoute with datasets including subway, bus and taxi, and a fare collection system. The data-driven evaluation results show that eRoute improves the ratio of served passengers per time interval by up to 11.5 times and reduces the average traveling time by up to 82.1 percent compared with existing solutions.

Joint Optimization of Ticket Pricing and Allocation on High-Speed Railway Based on Dynamic Passenger Demand during Pre-Sale Period: A Case Study of Beijing–Shanghai HSR

Against the background of the gradual deepening of China Railway’s market-oriented reform, and in order to improve the revenue and competitiveness for high-speed railway (HSR) passenger transport, this paper studies the joint optimization problem of the high-speed railway ticket pricing and allocation considering the dynamic demand characteristics of passengers during the pre-sale period. Firstly, we use the compound non-homogeneous Poisson process to describe the passengers’ ticket-purchasing process and use the sparse method to simulate the passengers’ ticket demand during the pre-sale period. Secondly, taking the ticket pricing and allocation as the decision variables and considering the full utilization of the train seat capacity, a stochastic nonlinear-programming mathematical model is established with the goal of maximizing the train revenue. A particle swarm algorithm is designed to solve the model. Finally, this study takes the G19 train running on the Beijing–Shanghai HSR in China as a case study to verify the effectiveness of the model and algorithm. The results show that the joint optimization scheme of ticket pricing and allocation considering dynamic demand yields a revenue of CNY 601,881, which increases the revenue by 1.01% with a small adjustment of the price compared with the fixed ticket price and pre-allocation scheme. This study provides scientific support for the decisions made by railway transportation enterprises, which is conducive to further increasing the potential ticket revenue and promoting sustainable development.

Demand-oriented integration optimization of train timetabling and rolling stock circulation planning with flexible train compositions: A column-generation-based approach

Train timetabling and rolling stock circulation planning are two important optimization problems that arise in the daily operations of urban rail transit lines. This study proposes a novel approach to simultaneously optimize the train timetable and rolling stock circulation plan with flexible train compositions on an urban rail transit line in order to better match the passenger demand and supplied transport capacity, and further improve operation flexibility and extract gains in efficiency, in which the dynamic passenger demand is particularly considered in the formulation process. We first propose two integer linear programming models that are formulated on time-space networks by considering flexible coupling/splitting activities. The models consist of restricted master problems for optimizing the total generalized cost and subproblems that are used to generate different train composition routes. An effective column-generation-based diving heuristic algorithm is developed to solve the problem of interest, and it is able to simultaneously obtain the train timetable and rolling stock circulation plan. Several sets of experimental scenarios, involving relatively small-scale cases and a case derived from real-world Shanghai Metro data, are tested to verify the effectiveness of the proposed model and algorithm.

Demand-driven train timetabling for air and intercity high-speed rail synchronization service

ABSTRACT Synchronizing air and intercity high-speed railway (A-IHSR) services has recently been developing vigorously. Train timetables are critical for improving A-IHSR synchronization. This paper proposes a method to optimize intercity high-speed railway (IHSR) timetables based on the dynamic passenger demand of the A-IHSR. An integer non-linear programming (INLP) model is formulated to minimize the passenger waiting time, in which rigorous train capacity, oversaturation situation, and skip-stop are also taken into consideration. We also extend the train timetabling model by considering the synchronization events of flight-train and the train circulation plan. Then, this model is reformulated as a relaxed non-linear programming (NLP) model. . A multimodal nomad algorithm (MNA) is proposed to solve it. The train circulation plan solves by the Gurobi solver. A numerical experiment based on data of the operation of the Jinnan–Binzhou HSR is implemented to demonstrate the efficiency and performance of our proposed model and algorithm.

Integrated optimization of train route plan and timetable with dynamic demand for the urban rail transit line

ABSTRACT In the urban rail transit system, train timetabling according to the dynamic passenger demand is important to offer high-quality service. Timetable optimization with the predetermined train route plan cannot synchronously consider the spatial and temporal characteristics of demand. Based on the Automated Fare Collection (AFC) data, this study proposes the integrated optimization (IO) to make route plan and timetable. A mixed-integer nonlinear programming (MINLP) model is formulated with the aim of reducing passenger penalty travel time and operation penalty cost. An improved non-dominated sorted genetic algorithm-II (Improved NSGA-II) is applied to deal with the bi-objective problem. A numerical experiment is used to prove the effectiveness and efficiency of the model and the algorithm. Then, the IO approach is applied in a bi-directional urban rail transit line. The results show that the IO performs the best compared with two other feasible strategies, namely the current optimization (CO) and phased optimization (PO).

Train timetabling for a double-track urban rail transit line under dynamic passenger demand

Train timetable is of critical importance for an urban rail transit line, chiefly because it is the primary factor determining passenger perception of service quality. As it not only delivers efficient transit service to users but also significantly contributes to operator profitability, the train timetabling problem has been a widely studied subject in academic circles. Still, the existing models in the literature, for the most part, fail to sufficiently take into account train capacity, fleet size, and vehicle circulation. As a contribution to bridging this research gap, this study mainly focuses on the train timetabling problem in a congested urban rail corridor to adapt to dynamic behavior of passenger demand subject to operational and resource constraints. A nonlinear programming model is formulated to devise timetables with a view to minimizing the average waiting time per passenger. In the model, the congestion is represented by some passengers who may not be able to take the first incoming train due to limited train capacity. To evaluate the effectiveness of the proposed approach, a case study is performed on a metro line in Istanbul. According to study results, the optimized demand-oriented train timetable proved to be more advantageous when compared to its periodical counterpart prepared by traffic planners. Finally, a sensitivity analysis is conducted to attain the best trade-off between passenger satisfaction and operation cost.

A modelling approach to the train timetabling problem using adaptive headways for dynamic passenger demand

ABSTRACT Rail systems are preferred to find sustainable solutions to traffic problems in cities with high population density. To increase the use of public transport without reducing service quality, it is essential to construct a demand-based timetable. In this study, a mathematical model that meets the passenger demand in cases of over and under-saturation, considers structural-operational constraints, aims minimum energy consumption and machinist costs is presented. Passenger demands are forecasted using four popular techniques. In both over and under-saturated situations, it is possible to meet passenger demand by using adaptive headways and determining train specifications as coupled or decoupled. Moreover, a comfort coefficient is incorporated in the model to adjust the service quality of the trip. To demonstrate the performance of the proposed MILP model, Kayseri Ulasim A.S. timetabling problem is solved. The effect of different passenger demand levels, over and under-saturated cases, on headways and train types is analysed.

Multi-Objective Timetabling Optimization for a Two-Way Metro Line Under Dynamic Passenger Demand

In metro systems, the train passenger load is an important parameter that reflects both the utilization level of the trains provided by the operator and the comfort level of passengers in terms of crowdedness. In addition to minimizing the energy consumption and passengers' time cost, the train passenger load should also be optimized in order to maintain a high utilization rate of trains and an adequate level of comfort for passengers. In this paper, a multi-objective train timetable optimization procedure is proposed to minimize the total energy consumption, the average waiting time, and the average maximum load deviation. Case studies on the Beijing Yizhuang line show that the proposed approach could effectively reduce the total energy consumption, the average waiting time, and the average maximum load deviation, thus ensuring a high service quality and a low operational cost for the metro system.

Comprehensive optimization of urban rail transit timetable by minimizing total travel times under time-dependent passenger demand and congested conditions

The comprehensive optimization of the timetables of urban rail transit systems under more realistic conditions is essential for their practical operation. Currently, most time-dependent timetabling models do not adequately consider train capacity and variable operation parameters. To bridge this gap, this study mainly investigates the timetable design problem of the urban rail transit system so as to adapt to time-dependent passenger demand under congested conditions by considering the variable number of trains, train running time, and train dwell time. Two nonlinear non-convex programming models are formulated to design timetables with the objective of minimizing the total passenger travel time (TTT) under the constraints of train operations, and passenger boarding and alighting processes. The difference between the two models is that one is a train-capacity unconstrained model and the other is a train-capacity constrained model. The proposed models are examined through real-world cases solved by the adaptive large neighborhood search algorithm. The results show that the first model can minimize passenger TTT under dynamic passenger demand, whereas the second can comprehensively optimize passenger TTT and meantime keep the train load factor within a reasonable level. Accordingly, it is concluded that the proposed models are more realistic.

Dynamic passenger demand oriented metro train scheduling with energy-efficiency and waiting time minimization: Mixed-integer linear programming approaches

In the daily operation of metro systems, the train scheduling problem aims to find a set of space-time paths for multiple trains that determine their departure and arrival times at metro stations, while train operations are in charge of selecting the best operational speed to satisfy the punctuality and operation costs. Different from the most existing researches that treat these two problems separately, this paper proposes an integrated approach for the train scheduling problem on a bi-direction urban metro line in order to minimize the operational costs (i.e., energy consumption) and passenger waiting time. More specifically, we simultaneously consider (1) the train operational velocity choices that correspond to the energy consumption of trains on each travelling arc, and (2) the dynamic passenger demands at each station for the calculation of total passenger waiting time in the planning horizon. By employing a space-time network representation in the formulations, this complex train scheduling and control problem with dynamic passenger demands is rigorously formulated into two optimization models with linear forms. The first model is an integer programming model that jointly minimizes train traction energy consumption and passenger waiting time. The second model, which is formulated as a mixed-integer programming model, further considers the utilization of regenerative braking energy on the basis of the first model. Due to the computational complexity of these two models, especially for large-scale real-world instances, we develop a Lagrangian relaxation (LR)-based heuristic algorithm that decomposes the primal problem into two sets of subproblems and thus enables to find a good solution in short computational time. Finally, two sets of numerical experiments, involving a relatively small-scale case and a real-world instance based on the operation data of Beijing metro are implemented to verify the effectiveness of the proposed approaches.

The sightseeing bus schedule optimization under Park and Ride System in tourist attractions

This paper proposes a sightseeing bus schedule optimization method for Park and Ride System in tourist attractions. The optimization method can provide a high-quality tourism experience by decreasing passenger waiting time. The optimization method consists of two fundamental steps. First, modal split for self-drive tourists is proposed based on a logit function. Then, the sightseeing bus schedule considering dynamic passenger demand is designed based on the sightseeing bus time-expanded network. The numerical results show that the sightseeing bus schedule optimization method can decrease passenger waiting time efficiently and can be applied to more realistic tourism attractions.

Optimization of Urban Single-line Metro Timetable for Total Passenger Travel Time under Dynamic Passenger Demand

This paper studies the optimization of an urban single-line metro timetable for total passenger travel time adapted to dynamic passenger demand, which arises in an urban metro service and is a common problem in major cities. After analyzing the components of the total passenger travel time, a model is presented with the aim of minimizing total passenger travel time. An S-pattern function is proposed to represent the cumulative demand function for each pair of origin and destination in an urban single-line metro. Furthermore, a spatial branch and bound algorithm that is applicable to the model is presented. The advantages of designing a timetable that optimizes the total passenger travel time adapted to dynamic passenger demand are depicted through extensive computational experiments on several cases derived from a real urban single-line metro. An extensive computational comparison of a regular timetable, a timetable optimizing average waiting time, and a timetable optimizing total passenger travel time timetable are performed.

Development of a hybrid fuzzy genetic algorithm model for solving transportation scheduling problem

There has been an increasing public demand for passenger rail service in the recent times leading to a strong focus on the need for effective and efficient use of resources and managing the increasing passenger requirements, service reliability and variability by the railway management. Whilst shortening the passengers’ waiting and travelling time is important for commuter satisfaction, lowering operational costs is equally important for railway management. Hence, effective and cost optimised train scheduling based on the dynamic passenger demand is one of the main issues for passenger railway management. Although the passenger railway scheduling problem has received attention in operations research in recent years, there is limited literature investigating the adoption of practical approaches that capitalize on the merits of mathematical modeling and search algorithms for effective cost optimization. This paper develops a hybrid fuzzy logic based genetic algorithm model to solve the multi-objective passenger railway scheduling problem aiming to optimize total operational costs at a satisfactory level of customer service. This hybrid approach integrates genetic algorithm with the fuzzy logic approach which uses the fuzzy controller to determine the crossover rate and mutation rate in genetic algorithm approach in the optimization process. The numerical study demonstrates the improvement of the proposed hybrid approach, and the fuzzy genetic algorithm has demonstrated its effectiveness to generate better results than standard genetic algorithm and other traditional heuristic approaches, such as simulated annealing.

Learning Management Systems (LMS) and e-learning management: an integrative review and research agenda

There has been an increasing public demand for passenger rail service in the recent times leading to a strong focus on the need for effective and efficient use of resources and managing the increasing passenger requirements, service reliability and variability by the railway management. Whilst shortening the passengers’ waiting and travelling time is important for commuter satisfaction, lowering operational costs is equally important for railway management. Hence, effective and cost optimised train scheduling based on the dynamic passenger demand is one of the main issues for passenger railway management. Although the passenger railway scheduling problem has received attention in operations research in recent years, there is limited literature investigating the adoption of practical approaches that capitalize on the merits of mathematical modeling and search algorithms for effective cost optimization. This paper develops a hybrid fuzzy logic based genetic algorithm model to solve the multi-objective passenger railway scheduling problem aiming to optimize total operational costs at a satisfactory level of customer service. This hybrid approach integrates genetic algorithm with the fuzzy logic approach which uses the fuzzy controller to determine the crossover rate and mutation rate in genetic algorithm approach in the optimization process. The numerical study demonstrates the improvement of the proposed hybrid approach, and the fuzzy genetic algorithm has demonstrated its effectiveness to generate better results than standard genetic algorithm and other traditional heuristic approaches, such as simulated annealing.

Single-line rail rapid transit timetabling under dynamic passenger demand

Railway planning is a complex activity which is usually decomposed into several stages, traditionally network design, line design, timetabling, rolling stock, and staffing. In this paper, we study the design and optimization of train timetables for a rail rapid transit (RRT) line adapted to a dynamic demand environment, which focuses on creating convenient timetables for passengers. The objective is to minimize the average passenger waiting time at the stations, thus focusing on passenger welfare. We first propose two mathematical programming formulations which generalize the non-periodic train timetabling problem on a single line under a dynamic demand pattern. We then analyze the properties of the problem before introducing a fast adaptive large neighborhood search (ALNS) metaheuristic in order to solve large instances of the problem within short computation times. The algorithm yields timetables that may not be regular or periodic, but are adjusted to a dynamic demand behavior. Through extensive computational experiments on artificial and real-world based instances, we demonstrate the computational superiority of our ALNS compared with a truncated branch-and-cut algorithm. The average reduction in passenger waiting times is 26%, while the computational time of our metaheuristic is less than 1% of that required by the alternative CPLEX-based algorithm. Out of 120 open instances, we obtain 84 new best known solutions and we reach the optimum on 10 out of 14 instances with known optimal solutions.