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Train timetable during the end-of-service period is crucial for passenger accessibility and operation cost in urban rail transit networks. Existing studies have investigated the last train timetabling problem for improving passenger accessibility. This study investigates a train timetabling problem for the end-of-service period, which concentrates on the coordination of the service ending time on different lines and the last several train timetables. A mixed-integer linear programming model based on a space–time network is proposed to determine the number of train services provided in the end-of-service period while coordinating the timetables of both last and non-last trains, of which the objective function minimizes the number of inaccessible passengers and operation costs. To address the computational challenges, a Benders decomposition algorithm is developed and enhanced with dedicated acceleration strategies. A dual solution algorithm is proposed to efficiently generate the optimal dual solution of the subproblems. A reformulation and update strategy is proposed for the Benders cuts, and a relax-and-fix heuristic is developed to improve solving efficiency of the master problem. Small-scale numerical experiments demonstrate the optimality and efficiency of the proposed Benders decomposition algorithm. Large-scale experiments in the Wuhan network show that the proposed model and algorithm can improve passenger accessibility by 6.8% without additional operation cost, and by 38.7% with a 28.4% increment in operation cost. • A train timetabling problem for the end-of-service period is investigated to determine the service ending time and trains' departure time. • A MILP model based on a space–time network is proposed to optimize the balance between passenger accessibility and operational costs. • A Benders decomposition algorithm is designed and enhanced with several acceleration techniques. [ABSTRACT FROM AUTHOR]

To addreess the challenge of overcrowding in the urban rail transit system, this paper proposes a novel joint optimization strategy that optimizes the timetable and the passing facility's working status (PFWS) simultaneously according to the passenger demands. To this end, a mixed-integer nonlinear programming (MINLP) model is formulated to jointly minimize overcrowding on trains and platforms, as well as the passenger travel time. The passing facility setting and the passenger flow activities depiction are particularly taken into account by the rigorous constraints. Subsequently, we design a simulation-based hybrid variable neighborhood search (SHVNS) algorithm to efficiently generate near-optimal solution. This algorithm incorporates a variable neighborhood search (VNS) algorithm, a randomly reset strategy, and a simulation-based algorithm. The VNS algorithm includes five neighborhood operators to enhance search efficiency. Finally, various experiments with the real-world data from Chongqing rail transit line 6 in China are tested to prove the applicability and the performance of our proposed model and algorithm. The computational results show that the joint optimization strategy outperforms a current operation strategy in terms of the overcrowded situation on trains and platforms, often by more than 60%, and some management implications and theoretical support can be obtained for the urban rail transit operator. [ABSTRACT FROM AUTHOR]

Highly utilized railway networks require regular infrastructure maintenance. Different track sections often need to be closed for entire days to carry out engineering works, which makes the regular timetables no longer feasible and thus adjusted railway services and temporary alternative services need to be planned. We introduce the Multimodal Alternative Services for Possessions (MASP) problem to support the planning of alternative services, from the passenger and transport operator points of view, including an adjusted train timetable, bus-bridging services and extra train services. The MASP problem is formulated based on the Service Network Design Problem and the Vehicle Routing Problem. To solve it efficiently, we develop a solution framework that incorporates heuristics based on the column and row generation with mixed-integer linear programming. The developed framework provides the optimized alternative service routes, schedules and passenger flows routing. We demonstrated the performance of the MASP solution framework on the real-life Dutch railway network. The results show that the MASP framework is capable of efficiently generating alternative services to route passenger flows affected by possessions with a very limited increase in the total passenger costs compared to a scenario with no link closures. High computational efficiency is observed even for highly disrupted networks. • Integration of the train timetable adjustment problem and the bus-bridging problem. • A new mathematical model to design alternative services for managing possessions. • An extended multimodal approach with bus-bridging services and extra train services. • A solution framework combining multi-column and row generation techniques. • A real-life case study in the Dutch railway network. [ABSTRACT FROM AUTHOR]

Highlights • Introduction of new methodology for autonomous shuttle bus service (ASBS). • Determine of optimal public transport (PT) timetable integrated with vehicle scheduling. • Analysis based on the deficit function (DF) graphical concept. • Treating a single-depot bidirectional circle ASBS route using the DF as a multi-decision choice model. • Use of binary-variable iteration method for genetic algorithm. Abstract The development of new technologies that allow us to know more precisely real-time public transport (PT) passenger demand enables the introduction of new methodologies to improve autonomous shuttle bus service (ASBS) from the perspective of both the user and the operator. This work develops a new methodology to determine the optimized PT timetable integrated with vehicle scheduling, including the possibility of using the skip-stop tactic based on real-time passenger demand. The consideration of a skip-stop operation allows for a reduction in the passengers' total travel time and in the number of autonomous shuttle vehicles in use. The analysis is based on the deficit function (DF) graphical concept and considers the constraints of the vehicle with regard to capacity. The methodology is developed for a single-depot bidirectional circle ASBS route using the DF as a multi-decision choice model. Because of the complexity involved in large-size genetic algorithm problems, a binary-variable iteration method is applied to attain efficient solutions. A case study in Auckland, New Zealand, is employed to assess the new model. The case study shows a reduction of 1.83% in total passenger travel time and 8.11% in the number of vehicles as compared to solutions that do not consider the skip-stop tactic. Moreover, it is shown that the advanced DF-based methodology could be used to develop fully autonomous PT in a network in the future. [ABSTRACT FROM AUTHOR]

Abstract Traction energy is the main component of railway operation energy, and a timetable that predefines the running time of train operation can be used to determine the traction energy consumption. This study proposes a bi-level model that optimizes timetables to achieve the energy-saving control of railway systems. The upper level of the model ensures the relative stability of the timetable while maintaining railway safety constraints, which makes train operations more convenient for the railway sector as well as passengers; while the lower level of the model optimizes the arrival and departure time among intermediate stations to minimize the energy consumption of each train. Then, a unified iterative optimization algorithm combining particle swarm is developed to solve the model, and a timetable that ensures energy consumption optimizations is thus obtained. A case study using actual operation data from the Beijing-Shanghai high-speed railway is developed to illustrate the proposed method. Results show that the total energy consumption is reduced by more than 7.6%, and the average adjustment time for each distance interval is approximately 1 min, which maintains the stability of the original timetable. Highlights • A bi-level model is developed to optimize railway energy and passenger convenience. • Energy saving, timetable stability, and train tracking constraints are investigated. • Spare time of timetable are optimally distributed by an iterative-loop algorithm. • Train optimal energy-saving operation strategies are proposed and verified by a case. • The model is applied in a real case saving 7.6% energy consumption. [ABSTRACT FROM AUTHOR]

Highlights • A mixed integer linear model is developed to optimize multi-period tram timetables. • Priorities of improving tram operational efficiency and timetable adherence are considered. • Arterial signal timings are resynchronized when optimizing scheduled tram trajectories. • Tram performance is improved without sacrificing vehicular mobility. Abstract Modern trams run on exclusive rail lanes along urban streets, but they usually share the right of way with general traffic at intersections and often get interrupted by traffic signals. To improve tram operation reliability, this paper develops a methodology to optimize a multi-period tram timetable by simultaneously adjusting bidirectional scheduled tram trajectories and traffic signal timings. The objective balances the operational priorities of minimizing tram running time and maximizing timetable adherence. The scheduled trajectories depict tram movements along the roads and dwell processes at stations. Arterial signal timings are resynchronized to favor tram movements. The proposed methodology was evaluated in a simulation of a real-world tram line. Compared with a traditional approach, the proposed methodology reduced tram running time, number of stops at intersections and schedule delay by 11.1%, 82.4% and 37.5%, respectively. The impact on general traffic could be assumed neutral since cycle lengths, green splits and vehicular bandwidths were kept unchanged. [ABSTRACT FROM AUTHOR]

Highlights • A MIP model is built to improve the OD accessibility for the last train services. • A timetable-based Dijkstra algorithm is designed to compute the OD accessibility. • The model and algorithm are tested in the real-life metro network. • The model outperforms the existing transfer model in OD accessibility optimization. Abstract In urban rail networks, passengers usually make transfers from one line to another during their trips. Toward the closure of daily service, certain destinations will become inaccessible for last trains as the connecting service may have already been closed when passengers arrive at the transfer station. This study focuses on timetable synchronization of last trains to improve the network accessibility. A mixed integer programming model is first proposed to determine the scheduled time of last trains. The objective of the model is to maximize the weighted sum of accessible origin-destination (OD) pairs for last train services on the network, which indicates the percentage of passengers using last trains at origins who can reach their destinations successfully. A simple network is used to highlight the difference of the proposed model from existing transfer models in the literature. To solve for large networks, a genetic algorithm combining with a timetable-based Dijkstra's algorithm is developed. A real-life metro network is applied to evaluate the proposed model and solution methodology in practice. The results indicate the proposed model and algorithm enhances the network accessibility, as well as the transfer connections. Comparison analysis shows that the proposed model significantly outperforms the transfer model in network accessibility optimization. [ABSTRACT FROM AUTHOR]

• Construct a unified model for integrating timetable, bus formation and vehicle scheduling problems. • Schedule autonomous modular vehicles (AMVs) in both directions simultaneously. • Design a decomposition-based iterative solution framework based on Alternating Direction Method of Multipliers (ADMM) algorithm to solve the origin model efficiently. • Solve the subproblem efficiently with a customized time-dependent shortest path algorithm. • Introduce AMVs into public transport systems can reduce overall system costs and increase vehicle utilization. This paper presents a joint optimization of the timetable, bus formation, and vehicle scheduling in a flexible public transport (PT) system that utilizes autonomous modular vehicles (AMVs). In this system, AMVs have the capability to detach or join with each other at intermediate stops along the route to dynamically adjust the bus formation (capacity). To increase vehicle utilization, a flexible scheduling strategy is proposed that allows AMVs to detach from one modular bus and join another modular bus in either direction of a bidirectional line. In particular, the penalty cost for each detachment or joining operation, as well as the limited number of available AMVs is explicitly considered. We formulate a unified model for the integrated optimization of the modular bus service (timetable and bus formation) and vehicle scheduling by introducing two types of decision variables. The objective is to minimize overall system costs, including passenger waiting time cost, operational costs, and detachment/joining penalty costs. The two types of decision variables are coupled by a vehicle resource consistency constraint, ensuring the conformity of the modular bus service and vehicle scheduling decisions. To tackle the complexity of our model, the Alternating Direction Method of Multipliers (ADMM) is employed to decompose it into two subproblems, which can be efficiently solved using a customized forward dynamic programming algorithm and a commercial solver. The model is validated using illustrative examples and a real-world instance from the Beijing Public Transport system, and it is compared with two benchmark models. Our results demonstrate the efficiency of the ADMM-based solution framework for solving the integrated optimization model. Furthermore, our findings indicate that the use of AMVs in PT systems can lead to reduced overall system costs and increased vehicle utilization. [ABSTRACT FROM AUTHOR]

This study solves the simultaneous planning problem of network design and timetabling for urban bus systems. An innovative mixed-integer programming (MIP) model is formulated and a parallel branch-and-price-and-cut (BPC) algorithm is proposed to solve the problem. The key idea of the model formulation and the solution algorithm is to represent a bus timetable with a route and a dispatch pattern. An aggregation and greedy algorithm is developed to efficiently solve the pricing subproblem. The cuts of disaggregate coupling inequalities are dynamically added to strengthen the lower bound. A computational study is conducted to evaluate the performance of the proposed methodology. The comparison with alternative solution approaches indicates that the parallel BPC algorithm is superior to solving the MIP formulations with the off-the-shelf MIP solver. Different values of model parameters are also tested, and various statistics of operators and passengers are reported for the cases. [ABSTRACT FROM AUTHOR]

Carbon mitigation effectiveness in the building sector profoundly determines the achievement of the "Dual carbon" target. However, the timetable and roadmap for the building sector to achieve such a target are still lacking. This study constructs a STIRPAT-PLS model framework to clarify the impact of the key factors from various dimensions on building carbon emissions across sub-sectors. Then, a dynamic scenario simulation model is established and applied in China to explore the dynamic evolutionary paths, and the timetable and roadmap are ultimately formulated. The results show that building sector will probably peak at 2.99 (± 0.09) Gt CO 2 in 2036 (± 1). Rural residential buildings will peak earliest in 2026 (± 1), followed by urban residential and commercial buildings: in 2036 (± 2) and 2038 (± 1). Achieving carbon neutrality will require the building sector to peak its carbon emissions in 2026 with 2.16–2.40 Gt CO 2. The remaining 0.56–0.81 Gt CO 2 by 2060 will be offset by negative carbon technologies. Dynamic sensitivity analysis shows that building floor space per capita and energy intensity significantly promote the emission peaks, and population and building floor space per capita markedly impact the peaking times. This study can promote the development of the theory and model for carbon emissions prediction. It can also offer a scientific basis for governments to set effective carbon-reduction targets and paths. [Display omitted] • Constructing a STIRPAT-PLS model to clarify the impact of critical factors on building carbon emissions. • Establishing a dynamic scenario simulation model by combining the Monte Carlo simulation and scenario analysis. • Building sector will probably peak at 2.99 (± 0.09) Gt CO 2 in 2036 (± 1). • Achieving carbon neutrality requires the building sector to peak its carbon emissions in 2026 with 2.16–2.40 Gt CO 2. • Building floor space per capita and energy intensity significantly promote the emission peaks. [ABSTRACT FROM AUTHOR]

This paper proposes a bi-level model to solve the timetable design problem for an urban rail line. The upper level model aims at determining the headways between trains to minimize total passenger cost, which includes not only the usual perceived travel time cost, but also penalties during travel. With the headways given by the upper level model, passengers’ arrival times at their origin stops are determined by the lower level model, in which the cost-minimizing behavior of each passenger is taken into account. To make the model more realistic, explicit capacity constraints of individual trains are considered. With these constraints, passengers cannot board a full train, but wait in queues for the next coming train. A two-stage genetic algorithm incorporating the method of successive averages is introduced to solve the bi-level model. Two hypothetical examples and a real world case are employed to evaluate the effectiveness of the proposed bi-level model and algorithm. Results show that the bi-level model performs well in reducing total passenger cost, especially in reducing waiting time cost and penalties. And the section loading-rates of trains in the optimized timetable are more balanced than the even-headway timetable. The sensitivity analyses show that passenger’s desired arrival time interval at destination and crowding penalty factor have a high influence on the optimal solution. And with the dispersing of passengers' desired arrival time intervals or the increase of crowding penalty factor, the section loading-rates of trains become more balanced. [ABSTRACT FROM AUTHOR]

This paper explores at the planning level the benefits of coordinating tram movements and signal timings at controlled intersections. Although trams may have dedicated travel lanes, they mostly operate in a mixed traffic environment at intersections. To ensure tram progression, pre-set signal timings at intersections are adjusted by activating Transit Signal Priority (TSP) actions, which inevitably add delays to the auto traffic. A mixed integer program is proposed for jointly determining tram schedules for a single tram line and modifying signal timings at major controlled intersections. The objective is to minimize the weighted sum of the total tram travel time and TSP’s negative impacts on other traffic. A real-world case study of Line 5 of the Shenyang Hunnan Modern Tramway shows that by extending the dwell time or link travel time we can significantly reduce the TSP’s negative impacts on the auto traffic while only slightly increasing tram travel times. [ABSTRACT FROM AUTHOR]

In passenger railway operations, unforeseen events require railway operators to adjust their timetable and their resource schedules. The passengers will also adapt their routes to their destinations. When determining the new timetable and rolling stock schedule, the railway operator has to take passenger behavior into account. The operator should increase the capacity of trains for which the operator expects more demand than on a regular day. Furthermore, the operator could increase the frequency of the trains that serve stations with an additional demand. This paper describes a real-time disruption management approach which integrates the rescheduling of the rolling stock and the timetable by taking the changed passenger demand into account. The timetable decisions are limited to additional stops of trains at stations at which they normally would not call. Several variants of the approach are suggested, with the difference in how to determine which additional stops should be executed. Real-time rescheduling requires fast solutions. Therefore a heuristic approach is used. We demonstrate the performance of the several variants of our algorithm on realistic instances of Netherlands Railways, the major railway operator in the Netherlands. [ABSTRACT FROM AUTHOR]

This paper demonstrates timetabling visualizations – timetables, transport timetables, multi-project schedules. These visualizations present an allocation of system resources. The visualization of high-school timetable demonstrates a timetable of student groups. The visualization of transport timetable shows arrivals/departs across stations and lines. The visualization of multi-project schedule includes Gantt chart and an allocation of system resources. These visualizations are provoked a new approach to timetable optimization. The timetabling problems can be solved efficiently by two-stage algorithm developed in database system. The first, a set of demands must be developed as initial timetable. A set of local and global resources are available for carrying out the activities of the systems. The solutions obtained by the first stage algorithm with the best resource allocation rule are used as a baseline to compare those obtained by the latter. The second, the initial timetable must be optimized. The basic criterion for optimization operations is demanded as criterion of resource equability. The latter is equal a root-mean-square deviation from a middle value. [ABSTRACT FROM AUTHOR]

The article is devoted to the study of metaheuristic method for scheduling problems solution. The article describes genetic algorithm successfully applied to solve the problems. The article considers the model of a problem of an optimal timetable development, describes genetic algorithm applied to the problem. The results of the algorithm are provided. [ABSTRACT FROM AUTHOR]

• An integrated model is developed to optimize the timetable, train formation plan and rolling stock circulation under time-dependent passenger demand. • Variable running times, variable dwell times and coupling/decoupling operations are taken into account. • The multi-objective MINLP model is reformulated into a single-objective MILP model by linearizing and fuzzy programming. • A multi-stage model and an integrated model are formulated into a unified framework. Timetable, train formation plan and rolling stock circulation are the key operational issues for efficient railway operation. The three issues are optimized sequentially based on the order of the operational plan. Sequential optimization manner cannot balance the costs of the three stages effectively and could create an infeasible solution for a later stage when the resources are limited. In addition, because of the computational complexity, multiple variable elements, such as the variable running times, variable dwell times and the coupling/decoupling operations, of a transportation system are ignored. This paper focuses on optimizing timetable, train formation plan and rolling stock circulation simultaneously to minimize costs and meet passenger demand. The key to solving the problem is to determine operation times (i.e., arrival times, departure times, running times and dwell times), the formation type of each train service and rolling stock connections (including the turnaround operations and the coupling/decoupling operations) between these train services. Considering the passenger costs and operator costs, a multi-objective mixed-integer nonlinear programming (MINLP) model is proposed to minimize the total passenger waiting time (TWT), the number of rolling stocks (NR), the number of formations (NF) and the number of coupling/decoupling operations (NC) based on a time–space network. The multi-objective MINLP model is further reformulated into a single-objective mixed-integer linear programming (MILP) model by logical linearizing, piecewise linearizing and fuzzy programming. A numerical example is used in which the exact solution of MINLP obtained by the BARON solver is compared with the approximate solution of MILP obtained by the CPLEX solver to verify the effectiveness of the piecewise linearization. Finally, the model is tested on a real-world case study of the Jinshan Line in Shanghai. The CPLEX solver can efficiently produce the approximate solution within a given computation time in acceptable gaps. The results demonstrate that the integrated model can reduce the number of rolling stocks and improve the utilization rate of rolling stocks. Furthermore, the integrated model can effectively resolve the shortage of rolling stocks when only one depot has rolling stocks or the number of available rolling stocks is limited. In addition, considering the multiple variable elements have a significant effect on the improvement of all the objectives and reduce both the passenger costs and the operator costs. [ABSTRACT FROM AUTHOR]

The Shinkansen, the first high-speed rail (HSR) service in the world, started operations in 1964 in Japan, where the world's first long-distance intercity magnetic levitation (maglev) line will open in 2027. In light of this, the study evaluated time-series changes in railway accessibility in Japan. The impact of opening the maglev line on accessibility was investigated by comparing it to Shinkansen. Accessibility was measured by modifying a daily accessibility model to include the concept of distance decay. Daily accessibility significantly increased between 1961 and 2000 with Shinkansen's development. However, after 2000, this trend weakened, and accessibility did not increase much in most cities. Comparing accessibility changes from 1961 to 1980 and those projected for 2020 to 2040 suggests that the impact on accessibility from maglev services will be smaller than that of Shinkansen for two main reasons. First, the reduction in travel time will be smaller because many Shinkansen lines will already be operating between large cities when the maglev line opens. Second, most of the positive effects of reduced travel time from the maglev line are negated by countrywide depopulation and a population concentration in metropolitan areas. The maglev line's effects are offset by depopulation. Therefore, parallel policies to increase the maglev line's effects must be implemented. In the rare case of Japan, where the HSR network has already expanded and the population is declining, the cost-effectiveness of maglev will be small. However, in many countries where such conditions do not apply, maglev lines are expected to be more effective. [ABSTRACT FROM AUTHOR]

In this paper, a “by transit accessibility (BTA)” measure to evaluate the impacts of travel distance and transfer tolerance on the convenience of commuting by transit on a regional scale is proposed. Considering the spatiotemporal factors for commuting efficiency evaluation, the timetable-dependent passenger carrying capacity of the transit station and the time-varying passenger demand at originating sites have been formulated into the BTA model. Moreover, the proposed BTA measure could reflect the commuting trip demand elasticity, which is caused by travel distance and transfer tolerance. In the meantime, this BTA measure can provide an important basis for transit timetable adjustment in the study area during different time periods. The proposed measure is tested on a small transit network to display its function, and finally, it is applied to an empirical case to draw practical findings. [ABSTRACT FROM AUTHOR]

The integrated timetable and speed profile optimization model has recently attracted more attention because of its good achievements on energy conservation in metro systems. However, most previous studies often ignore the spatial and temporal uncertainties of train mass, and the variabilities of tractive force, braking force and basic running resistance on energy consumption in order to simplify the model formulation and solution algorithm. In this paper, we develop an integrated metro timetable and speed profile optimization model to minimize the total tractive energy consumption, where these real-world operating conditions are explicitly considered in the model formulation and solution algorithm. Firstly, we formulate a two-phase stochastic programming model to determine the timetable and speed profile. Given the speed profile, the first phase determines the timetable by scheduling the arrival and departure times for each station, and the second phase determines the speed profile for each inter-station with the scheduled arrival and departure times. Secondly, we design a simulation-based genetic algorithm procedure incorporated with the optimal train control algorithm to find the optimal solution. Finally, we present a simple example and a real-world example based on the operation data from the Beijing Metro Yizhuang Line in Beijing, China. The results of the real-world example show that, during peak hours, off-peak hours and night hours, the total tractive energy consumptions can be reduced by: (1) 10.66%, 9.94% and 9.13% in comparison with the current timetable and speed profile; and (2) 3.35%, 3.12% and 3.04% in comparison with the deterministic model. [ABSTRACT FROM AUTHOR]

The growth of worldwide environmental awareness has prompted numerous countries to focus on developing energy-conservation and carbon-reduction technology. The advancement of such technology enables the emergence of low-noise, low-polluting alternatives for bus systems, such as hybrid-electric, battery-electric, and fuel-cell electric buses (e-buses). For such buses to serve the existing schedules and lines operated by their conventional counterparts, reorganizing bus transportation systems is a major challenge and entails construction costs that comprise the costs of e-buses, battery capacity, chargers, and bus scheduling. To facilitate the development of environmentally friendly public transportation, this study proposes a model for simulating the operation and battery charging schedule of plug-in e-buses on the basis of an existing schedule and line network. The model was used to estimate the overall construction cost of converting the existent bus transportation system into an all plug-in e-bus one. Focusing on the bus transportation system in Penghu, an archipelago of Taiwan, this case study examined the effects of day- and nighttime charging requirements on the construction cost of an e-bus transportation system to improve the practicability of e-buses. It also applied a genetic algorithm to determine the minimum construction cost, which varied depending on the number of e-buses, level of battery capacity, number of chargers, and electricity costs. The optimized parameters involved the hourly residual battery capacity and battery charging times during the daytime operating hours. The results showed that although daytime charging involved electricity uses during peak hours and thus incurred additional costs, it contributed to the use of e-buses and an overall reduction in the construction cost. In summary, the proposed optimization method would successfully reduce the construction cost of the Penghu e-bus transportation system. [ABSTRACT FROM AUTHOR]

An airport bus service, which is newly introduced in a multi-airport region, commonly leads to a gradually increasing market share of airports until a new state of equilibrium is reached. With the goal of speeding up and enlarging the increase in market share, this paper proposes a timetable optimization model by incorporating reactions of airport-loyal passengers to bus service quality. The simulation part of the model, which uses cumulative prospect theory to formulate discrete airport choices, results in predicted passenger demand needed in the optimization part. Then a genetic algorithm for multi-objective optimization problems called NSGA-II is applied to solve the model. To illustrate the model, the “Lukou airport-Wuxi” airport bus in China is taken as an example. The results show that the optimized timetables shorten the cultivation period and impel the market share to grow rapidly. [ABSTRACT FROM AUTHOR]

To further improve the utilization rate of railway tracks and reduce train delays, this paper focuses on developing a high-efficiency train routing and timetabling approach for double-track railway corridors in condition that trains are allowable to travel on reverse direction tracks. We first design an improved switchable policy which is rooted in the approaches by Mu and Dessouky (2013), with the analysis of possible delays caused by different path choices. Then, three novel integrated train routing and timetabling approaches are proposed on the basis of a discrete event model and different dispatching rules, including no switchable policy (No-SP), Mu and Dessouky (2013)’s switchable policy (Original-SP) and improved switchable policy (Improved-SP). To demonstrate the performance of the proposed approaches, the heterogeneous trains on Beijing–Shanghai high speed railway are scheduled by aforementioned approaches. The case studies indicate that in comparison to No-SP and Original-SP approaches, respectively, the Improved-SP approach can reduce the total delay of trains up to 44.44% and 73.53% within a short computational time. Moreover, all of the performance criteria of the Improved-SP approach are usually better than those of other two approaches. [ABSTRACT FROM AUTHOR]

Understanding the cascade dynamics of delay propagation under inclement weather is crucial to proactive railway management. In this paper, we proposed a Switching Max-Plus System (SMPS) to model the delay propagation on railway networks, which extends the conventional MPS by incorporating multiple system matrices to capture the dynamic impacts of inclement weather. An algorithm based on the All-Paired Critical-Path (APCP) graph was developed to solve the SMPS, which calculates secondary delays without backtracking the precedent events. The proposed model and its solution algorithm were validated using discrete-time simulations on both artificial and empirical networks. The robustness of railway services was also analyzed using the concepts of vulnerability and diffusivity. [ABSTRACT FROM AUTHOR]

In the urban subway transportation system, passengers may have to make at least one transfer traveling from their origin to destination. This paper proposes a timetable synchronization optimization model to optimize passengers’ waiting time while limiting the waiting time equitably over all transfer station in an urban subway network. The model aims to improve the worst transfer by adjusting the departure time, running time, the dwelling time and the headways for all directions in the subway network. In order to facilitate solution, we develop a binary variables substitute method to deal with the binary variables. Genetic algorithm is applied to solve the problem for its practicality and generality. Finally, the suggested model is applied to Beijing urban subway network and several performance indicators are presented to verify the efficiency of suggested model. Results indicate that proposed timetable synchronization optimization model can be used to improve the network performance for transfer passengers significantly. [ABSTRACT FROM AUTHOR]

This paper discusses the formulation of crowding in public transport and its implications for pricing, seating capacity and optimal scheduling. An analytical model is used to describe the user equilibrium and the optimal equilibrium for different stylized conditions. For the one OD pair case with identical desired arrival time, we derive the optimal dynamic pricing and optimal share of seats. For the uniformly distributed desired arrival times case, we derive the optimal time table and the optimal pricing. Next we generalize the results to the case of a small network with several stations, stochastic choice and allocation of seats. [ABSTRACT FROM AUTHOR]

As more and more governments are planning or constructing their high-speed rail (HSR) systems, the central control mechanism of such systems, i.e., train timetables, should be investigated more in order to cope with various disturbances due to disasters. Several optimization-based approaches have been successfully utilized for generating stable and reliable train timetables; however, few researchers have considered train circulation issues, especially for HSR systems, even though it could be such a way to reschedule the timetable against disturbances. This research proposed a scheduling optimization model that has the capability to accommodate not only basic requirements but train circulation as well for Taiwan HSR system. The sensitivity analysis was applied in order to identify how disturbances propagate in the original timetable and which actions to be taken in order to mitigate the impact instead of cancelling trains. With proper enhancement, the proposed model could be a good simulation tool to help predict the effect of disruptions on the timetable without doing real experiments. [ABSTRACT FROM AUTHOR]

Timetable design is crucial to the metro service reliability. A straightforward and commonly adopted strategy in daily operation is a peak/off-peak-based schedule. However, such a strategy may fail to meet dynamic temporal passenger demand, resulting in long passenger waiting time at platforms and over-crowding in trains. Thanks to the emergence of smart card-based automated fare collection systems, we can now better quantify spatial–temporal demand on a microscopic level. In this paper, we formulate three optimization models to design demand-sensitive timetables by demonstrating train operation using equivalent time (interval). The first model aims at making the timetable more dynamic; the second model is an extension allowing for capacity constraints. The third model aims at designing a capacitated demand-sensitive peak/off-peak timetable. We assessed the performance of these three models and conducted sensitivity analyzes on different parameters on a metro line in Singapore, finding that dynamical timetable built with capacity constraints is most advantageous. Finally, we conclude our study and discuss the implications of the three models: the capacitated model provides a timetable which shows best performance under fixed capacity constraints, while the uncapacitated model may offer optimal temporal train configuration. Although we imposed capacity constraints when designing the optimal peak/off-peak timetable, its performance is not as good as models with dynamical headways. However, it shows advantages such as being easier to operate and more understandable to the passengers. [ABSTRACT FROM AUTHOR]

Rail capacity is currently administratively allocated in Europe, whereas the economic literature has often contemplated the opportunity of introducing market mechanisms, auctions in particular, into this industry. This article tries to fill the gap between practice and theory. It first describes the properties of rail capacity (rigidity and non-homogeneity) and shows that because of its very nature, this capacity must be allocated through combinatorial auctions. As identified by the economic literature, using combinatorial auctions introduces a lot of complexity (winner determination and information burden) into the allocation process. To deal with this complexity, some form of centralized planning is necessary to design the right market mechanisms and to allocate capacity. This could have strong consequences on the current deregulation process. [ABSTRACT FROM AUTHOR]

Highlights: [•] An optimization method is developed to improve the operations of metro rail system. [•] It gives quantitative analysis on net energy consumption. [•] It optimizes the scheduling and speed control to minimize the energy consumption. [•] It reduces the net energy consumption of Beijing Metro Yizhuang Line around 25%. [ABSTRACT FROM AUTHOR]

Abstract: This paper studies the disruption management problem of rapid transit rail networks. Besides optimizing the timetable and the rolling stock schedules, we explicitly deal with the effects of the disruption on the passenger demand. We propose a two-step approach that combines an integrated optimization model (for the timetable and rolling stock) with a model for the passengers’ behavior. We report our computational tests on realistic problem instances of the Spanish rail operator RENFE. The proposed approach is able to find solutions with a very good balance between various managerial goals within a few minutes. [Copyright &y& Elsevier]

Abstract: In the paper a study on the correlation among capacity, block sections length, typology of services and timetables for high density lines such as urban railway corridors is presented. The adopted methodology is explained as well as the use of simulation for the analysis of sensitivity. Stability and robustness of selected timetables are investigated. In particular, railway system’s performances are linked to timetable planning criteria, i.e. to the definition of appropriated recovery times and buffer times, which influence the definition of available capacity. The possibility to find a trade-off value among these parameters is described. In this context the differences between theoretical timetables (which are defined by technical features of infrastructure and rolling stock) and the adopted timetables (which include recovery and buffer times and are functional to a defined level of service) are explained. The estimation of correlations among capacity, block sections length, timetable and operational plan is conceived as a basis to provide guidelines to design new urban railways or to evaluate possible reliability effects of actions on block sections (often with changes on the adopted signalling) or timetables. [Copyright &y& Elsevier]

Abstract: In this paper, we review the main concepts and methods to perform capacity analyses, and we present an automated tool that is able to perform several capacity analyses. Capacity is extremely dependent on infrastructure, traffic, and operating parameters. Therefore, an in-depth study of the main factors that influence railway capacity is performed on several Spanish railway infrastructures. The results show how the capacity varies according to factors such as train speed, commercial stops, train heterogeneity, distance between railway signals, and timetable robustness. [Copyright &y& Elsevier]

Abstract: Recently, as a means of forming global networks and improving operation efficiency, major air carriers have increasingly entered into alliances with other carriers. Fleet routing and flight scheduling are not only important in individual airline operations, but also affect the alliances. The setting of a good flight schedule can not only enhance allied airline operating performance, but can also be a useful reference for alliance decision-making. In this research, we develop several coordinated scheduling models, which will help the allied airlines solve for the most satisfactory fleet routes and timetables under the alliance. We employ network flow techniques to construct the models. The models are formulated as multiple commodity network flow problems which can be solved using a mathematical programming solver. Finally, to evaluate the models, we perform a case study based on real operating data from two Taiwan airlines. The preliminary results are good, showing that the models could be useful for airline alliances. [Copyright &y& Elsevier]

This article examines the nature of capacity on a railway network and identifies the key features of rail timetables and track access rights that need to be accommodated in any capacity allocation mechanism. It describes three basic allocation methodologies (administered/rule-based, cost-based and market-based) and how they have been applied on the UK rail network. It describes the current allocation mechanism which is a mixture of rule-based industry decision criteria, supplemented by cost-based capacity charges set at half the short-run congestion costs of operating additional trains. It does not anticipate a major role for auction-based approaches to allocating capacity in the near future due to their complexity and the role of the SRA in determining the demand for infrastructure capacity to meet social objectives. [Copyright &y& Elsevier]

The setting of timetables and bus routing/scheduling are essential to an inter-city bus carrier''s profitability, its level of service and its competitive capability in the market. In the past, carriers in Taiwan usually set their timetables and bus routes/schedules manually, which was inefficient. In this research we thus attempt to develop a model that will help Taiwan inter-city bus carriers in timetable setting and bus routing/scheduling. The model employs multiple time–space networks that can formulate bus movements and passenger flows and manage the interrelationships between passenger trip demands and bus trip supplies to produce the best timetables and bus routes/schedules. Mathematically, the model is formulated as a mixed integer multiple commodity network flow problem. An algorithm, based on Lagrangian relaxation, a sub-gradient method, the network simplex method, a Lagrangian heuristic and a flow decomposition algorithm, is developed to efficiently solve the problem. The results of a case study, regarding a major Taiwan inter-city bus operation, illustrate the model performance. [Copyright &y& Elsevier]

• Transfer coordination is critical for realising the 'seamless travel' vision. • A complex multi-criteria optimization problem at the tactical level. • Classify papers into 4 categories based on their solution approach and 3 extensions. • Recent trends include integration of planning phases and with passenger assignment. • Identify six promising future research directions. While transferring between public transport services has a negative impact on the level-of-service, it is an inevitable feature of public transport networks. Transfer coordination can help reduce passenger transfer waiting times and improve service connectivity. In this paper, we systematically review the literature on transfer coordination design in public transport systems. First, four solution approaches for solving the transfer coordination design problem (TCDP) are identified and reviewed in detail, namely heuristic rule-based, analytical modelling, mathematical programming, and simulation. We then identify and review three extensions of the TCDP, i.e., considering first or last train transfer optimization, integrating vehicle scheduling, and incorporating passenger demand assignment. Finally, following the synthesis of the literature, some promising future research directions are outlined. This paper provides comprehensive insights on how to better design coordinated transfers to provide a seamless travel experience and improve the service connectivity of public transport networks. [ABSTRACT FROM AUTHOR]

• Railway capacity is estimated in view of infrastructure and vehicle driven factors. • A hybrid time–space network is applied to describe timetable saturation problem. • The integrated optimization model is solved by a Lagrangian relaxation algorithm. • The intensity-based heuristic is used to compute high-quality saturated timetables. Railway capacity is a vague concept, related to the possibility to run a maximal transport performance given a set of available resources. While most approaches focus only on infrastructure resources (i.e. availability of train paths), we include both infrastructure and vehicle resources in a capacity estimation problem. We study the railway capacity estimation problem applying an associated timetable saturation method; in other words, the capacity is related to a timetable where no additional trains can be added. We use optimization methods to find such a timetable integrating explicitly variables and constraints from vehicle circulation. A hybrid time–space network describes the integrated timetabling and vehicles scheduling problem, based on which an integer programming model can be formulated, to maximize the overall transportation performance. A Lagrangian relaxation-based decomposition algorithm is proposed to solve the problem, and is shown able to scale to large instances efficiently. The integrated scheduling problem is decomposed into a timetabling sub-problem and a vehicle circulation sub-problem by dualizing the consistency constraints linking the two. A new heuristic, based on the concept of timetable intensity, is employed to improve the quality of the feasible (non-relaxed) solution found. The experimental result shows the benefit of the approach, which can evaluate transportation performance and relate it to various fleet sizes, vehicle depot locations, and minimum headways. [ABSTRACT FROM AUTHOR]

In metro systems, reducing traction energy consumption and increasing the use of regenerative braking energy (RBE) are two important methods of energy-saving optimization, which are closely related to the driving strategy and timetable of the trains. In order to minimize the net traction energy consumption (i.e., the difference between traction energy and feedback energy) of trains in a metro system, an energy-saving optimization strategy of multi-train metro timetable based on double decision variables is proposed. Considering the actual situation of the short distance between the stations of the Shanghai Metro Line One (SML1) pilot network, at the driving strategy level, two optimized driving strategies of acceleration-cruising-braking (ACRB) and acceleration-coasting-braking (ACOB) are considered respectively. At the timetable level, genetic algorithm (GA) is used to optimize the decision variables of the trains. The optimization of driving strategy and timetable balances the traction energy consumption and feedback energy to minimize the net traction energy consumption of the metro system. Finally, simulation experiments were conducted based on the pilot network of the SML1. The results show that the energy consumption of the proposed strategy can be reduced by 23.28%. • A model based on Shanghai Metro Line One is established. • An optimization strategy based on dual decision variables is proposed. • Energy-saving timetable is obtained. • The energy was consequently saved by 23.28% in total efficiency. [ABSTRACT FROM AUTHOR]

• Propose a flexible train scheduling to extend the narrow time limitations. • Design compact incompatibility constraints to augment and decompose the problem. • Develop a priority-based ADMM approach to solve the proposed model. In this study, we focus on how to optimize multi-type train scheduling problems in a practically available and computationally efficient manner. When solving the complicated train timetabling problem with overtaking operations for a congested high-speed rail corridor, a simplified approach is to predesignate a thin time interval from its origin station for each train. This setting is difficult and laborious in practice. What is more serious is that an imperfect setting may cause the expected solutions to be unreachable in many instances. To fundamentally get out of this thorny trouble, this study proposes a flexible scheduling framework that extends narrow time limitations to one-hour periods, which allows the trains to depart from any timestamp within the relaxed period. Further, a group of incompatibility constraints with a more compact form is formulated to mirror the coupling relation between train headway and regularity requirements. However, the relaxed time window increases the difficulty of obtaining the optimal or near-optimal solution under the standard Lagrangian-based decomposition framework. Therefore, an improved alternating direction method of multipliers (ADMM) approach is introduced for effectively eliminating the computational barriers that are due to its increased complexity. Specifically, a priority-based search sequence is employed by applying the associated dual costs during the solution of train-level path subproblems individually. Finally, a set of numerical experiments is conducted to demonstrate the effectiveness and availability of the proposed approach. [ABSTRACT FROM AUTHOR]

Railway capacity allocation in a deregulated market requires planners to solve a mathematically complex optimization problem while simultaneously arbitrating the wants and needs of different stakeholders. This paper analyses timetable quality from the perspective of timetable planners working for the Swedish infrastructure manager Trafikverket. Seven quality aspects are discussed : feasibility, disturbance resistance, competition management, capacity safeguarding, application fulfilment, attractiveness and compatibility with surrounding planning areas. Each aspect is introduced, including references to legal documents, development projects, and research literature. Further, an interview study with eight practitioners gives insight into the current state of practice in Sweden. The practitioners consider feasibility to be both most important and easiest to handle. Capacity safeguarding is considered least important, despite its prevalence in legal documents and envisioned process developments, and is also considered hardest to handle. In general, formal rules and guidelines seem important for emphasising the importance of a quality aspect in the planning process. To better support the planners in their arbitrating role, timetable planning tools based on mathematical optimization models could be implemented. For example, support tools could be used to analyse different solutions, and could unburden the planner from working with feasibility aspects by providing automatic conflict identification and resolution. • Railway timetable planners solve a complex optimization problem while simultaneously arbitrating the needs of various actors. • Eight practitioners from the Swedish infrastructure manager are interviewed about different timetable quality aspects. • There is a gap between the wanted state and the current state of practice in Sweden. • Quality aspects relating to operability are considered most important and easiest to handle by the practitioners. • Capacity safeguarding is considered least important and hardest to handle by the practitioners. [ABSTRACT FROM AUTHOR]

• Develop integrated model to optimize the train stop plan and timetable under time-dependent passenger demand. • Improves passenger travel efficiency and reduces train running costs. • The number of trains and stops can be changed freely, oversaturation is permitted. • Improved extended adaptive large neighborhood search approach for solving. Train stop plans and timetables play key roles in railway operation. Previous research has demonstrated that their integration can significantly improve the quality of a train timetable, especially for commuter railways with flexible service frequencies and multiple stop plans. However, solving the dilemma of the mathematical tractability and practicality of the model is still an open challenge. To obtain a high-quality timetable and simultaneously consider more realistic conditions, an integrated combination optimization model of both train stop plans and timetables under time-dependent passenger demand is proposed in this article. More realistic conditions, such as no predefined schedule, a variable total number of trains and oversaturation, are taken into account. The problem is modeled as a mixed-integer nonlinear programming problem (MINLP) to optimize passenger travel efficiency and mainly consists of (1) the total waiting time at stations, (2) the delay time for trains due to a train stop, and (3) the minimization of the total train running time. An extended adaptive large-scale neighborhood search (ALNS) algorithm is developed to solve the problem. A numerical experiment is designed to test the validity of the model and the algorithm. Then, the integrated approach is applied in a real-world case. The results show that the proposed approach can simultaneously reduce the passenger total waiting time and delay time as well as the train running time within a short computation time and demonstrate the effectiveness of the model and the approach. [ABSTRACT FROM AUTHOR]

In both Stockholm and Tokyo, small dwell time delays of at most 5 min make up around 90% of the total delays for commuter trains. To understand these disturbances, we use high resolution data on dwell times and passenger counts from both countries over the last several years. We find that trains in Tokyo are much more congested than in Stockholm, and that the exchange of passengers is modest at most stations in the latter city. In both cities, the range of dwell time delays is quite narrow, with between 40 and 50 s separating the 5th and 95th percentiles. Most delays are thus very small, and even small adjustments to dwell times can make a big difference overall. We find that the data on passengers explain about 40% of this variation in dwell time delays, if we account for non-linear and interaction effects, which is thus a ballpark estimate for how much the exchange of passenger contributes to delays for these trains. We also produce simple, linear models which can be used in practice to assign more appropriate dwell times. To facilitate such improvements, key stakeholders and practitioners have been closely involved with the research in both countries. • We analysed commuter trains in Stockholm and Tokyo, morning peak 2011–2017. • Small dwell time delays make up c. 90% of all delay time in both cities. • Passenger count data can explain up to c. 40% of these dwell time delays. • The non-linear and interaction effects are large and significant. • Dwell times can be adjusted to take account of passenger flows, reducing delays. [ABSTRACT FROM AUTHOR]