Bus Timetables Research Articles

Alternative service network design for bus systems responding to time-varying road disruptions

In practice, road disruptions occur frequently, interrupting multiple bus routes at the same time and causing widespread passenger delays. Typically, these disrupted roads are repaired sequentially and then gradually put into service. In response to such time-varying road disruptions, this paper aims to assist bus operators in developing effective alternative service networks for passengers. The proposed approach involves the joint optimization of service-based route adjustments, bus timetables, and passenger assignment to minimize the total passenger cost and weighted bus operation time. Specifically, a novel service-based adjustment strategy is introduced to flexibly adapt each bus service to time-varying road disruptions. An integer programming model is built for the studied problem based on the set of passengers’ time-space itineraries. To efficiently generate these time-space itineraries and solve models for large-scale problems, this paper develops a hierarchical solution framework. The framework consists of three key parts: (1) a column generation procedure to iteratively explore passengers’ spatial paths; (2) a customized extension algorithm to extend these spatial paths to time-space itineraries; and (3) a tailored adaptive large neighbourhood search heuristic to solve the final itinerary-based model. After that, the overall methodology is tested with both an illustrative example and a real-world example in Beijing. Experimental results show that our methodology produces a high-performance solution with only 7.3% of unserved passengers. Besides, compared to the two benchmark adjustment strategies, our service-based adjustment strategy reduces the average itinerary cost for all passengers by 27.0% and 43.3%, respectively.

Using genetic algorithm for optimal sizing of stand-alone hybrid energy system

When planning a hybrid energy system (HES) that incorporates both renewable and non-renewable energy sources—those that rely on fossil fuels—the primary considerations are the total cost of the system and the CO? emissions. In this paper, we will investigate the typical hybrid energy system (HES) that incorporates both renewable and non-renewable energy sources involving a detailed simulation process that may require specific inputs, models, and data. Then, we employed dual optimization methods: genetic algorithm (GA) and particle swarm optimization (PSO). The consequences of GA and PSO execution in the bus timetabling problem depict that the GA algorithm is better at finding the optimal solution in terms of accuracy and iteration. Additionally, the GA algorithm is also superior to the straightforwardness of the techniques used. So, in this work, we employed a Genetic Algorithm Optimization (GA)–-based optimal sizing technique for HES configurations that include sustainability wind turbines (WTs), battery storage (BS), and diesel generators (DGs). HES improved power delivery to a rural community in the Wasit Province, Iraq, situated at 46° - 36° and 32° - 31° in the country's southeastern central region. Throughout the project's 25-year lifespan, the optimization primarily aims to minimize the total cost (CT) and total CO? emissions (ECO2T). The outcomes demonstrate that the GA algorithm may, with continuous electricity supply, minimize the objectives while meeting the load demand.

Optimizing the Three-Dimensional Multi-Objective of Feeder Bus Routes Considering the Timetable

To optimize the evacuation process of rail transit passenger flows, the influence of the feeder bus network on bus demand is pivotal. This study first examines the transportation mode preferences of rail transit station passengers and addresses the feeder bus network’s optimization challenge within a three-dimensional framework, incorporating an elastic mechanism. Consequently, a strategic planning model is developed. Subsequently, a multi-objective optimization model is constructed to simultaneously increase passenger numbers and decrease both travel time costs and bus operational expenses. Due to the NP-hard nature of this optimization problem, we introduce an enhanced non-dominated sorting genetic algorithm, INSGA-II. This algorithm integrates innovative encoding and decoding rules, adaptive parameter adjustment strategies, and a combination of crowding distance and distribution entropy mechanisms alongside an external elite archive strategy to enhance population convergence and local search capabilities. The efficacy of the proposed model and algorithm is corroborated through simulations employing standard test functions and instances. The results demonstrate that the INSGA-II algorithm closely approximates the true Pareto front, attaining Pareto optimal solutions that are uniformly distributed. Additionally, an increase in the fleet size correlates with greater passenger volumes and higher operational costs, yet it substantially lowers the average travel cost per customer. An optimal fleet size of 11 vehicles is identified. Moreover, expanding feeder bus routes enhances passenger counts by 18.03%, raises operational costs by 32.33%, and cuts passenger travel time expenses by 21.23%. These findings necessitate revisions to the bus timetable. Therefore, for a bus network with elastic demand, it is essential to holistically optimize the actual passenger flow demand, fleet size, bus schedules, and departure frequencies.

Integrated Bus Timetabling and Scheduling with a Mutation-Based Evolutionary Scheme Maximizing Headway Quality and Connections

Public transport planning is a multi-level process that includes various complex tasks. These tasks are traditionally executed sequentially, and the result of each task serves as input for consecutive tasks. A simultaneous integrated consideration of multiple tasks may lead to an overall improved solution, but further increase the complexity of already hard-to-solve planning problems. This work focuses on timetabling and vehicle scheduling and evaluates synergies from the integrated optimization. We investigate an exact sequential, exact integrated, and heuristic approach to solve the combined problem for large public transport networks considering the interlining of vehicles, multiple vehicle types, or multiple depots while additionally aiming to maximize regular “clock-faced’’ headways and transfer connections. Compared to sequential optimization, an integrated approach significantly reduces nominal and operational costs while maintaining high service quality. However, an exact integrated approach is only able to compute solutions for problems of limited size in a reasonable time. We propose an adaptive modular evolutionary extendable scheme that effectively balances computational efficiency and solution quality. By utilizing various problem-specific mutation operators and adaptively applying them based on their impact, the heuristic can compute high-quality solutions for large real-world-inspired public transport networks in a reasonable time while considering short connecting times between lines and regular clock-faced headways.

Integrated Bus Timetabling, Vehicle Scheduling, and Crew Scheduling with a mutation-based evolutionary scheme

Public transport planning is a complex process that covers multiple interdependent planning tasks. Traditionally, these tasks are executed sequentially. However, an integrated approach to planning multiple tasks can improve the overall solution. This study focuses on the timetabling, vehicle scheduling, and crew scheduling problems and evaluates the benefits of integrated solution approaches. A mutation-based evolutionary scheme is proposed and applied to different real-world inspired instances to solve a complex integration of all three planning tasks. Integrated solving of all three problems significantly improves the solution quality compared to a sequential approach. In reasonable computational time, the full integration led to reduced vehicle and duty schedule costs and, as a result, reduced overall costs while keeping the service quality equally high.

Smart Public Transport: A Bi-Objective Model for Maximizing Synchronizations and Minimizing Costs in Bus Timetables

Modern cities heavily rely on public transport systems to enhance citizen access to urban services and promote sustainability. To optimize public transport, intelligent computer-aided tools play a pivotal role in decision making. This article tackles the complex challenge of bus timetabling, specifically focusing on improving multi-leg trips or transfers. It introduces a novel multi-objective Mixed-Integer Programming Linear (MILP) model that concurrently maximizes passenger transfers and minimizes budgetary costs, while also adhering to the minimum required quality-of-service constraints for regular (non-multi-leg) trips, and an exact resolution approach based on the ε-constraint method to obtain a set of efficient solutions is used. The competitiveness of the model is validated via a computational experimentation performed over real-world scenarios from the public transportation system of Montevideo, Uruguay. The findings evinced that the MILP model was able to compute a set of Pareto efficient solutions that explore the tradeoff between the number of successful transfers and the cost of the system. Moreover, the best tradeoff solutions surpass the current city timetable, excelling in both the number of transfers and cost efficiency.

Joint optimal vehicle and recharging scheduling for mixed bus fleets under limited chargers

Owing to the high acquisition costs, maintenance expenses, and inadequate charging infrastructure associated with electric buses, achieving a complete replacement of diesel buses with electric counterparts in the short term proves challenging. A substantial number of bus operators currently find themselves in a situation where they must integrate electric buses with their existing diesel fleets. Confronted with the constraints of limited electric bus range and charging infrastructure, the primary concern for bus operators is how to effectively utilize their mixed bus fleets to adhere to pre-established bus timetables while maximizing the deployment of electric buses, known for their zero pollution and cost-effective travel. Consequently, this paper introduces the concept of the joint optimization problem for vehicle and recharging scheduling within mixed bus fleets operating under constrained charging conditions. To tackle this issue, a mixed integer linear model is formulated to optimize the coordination of bus schedules and recharging activities within the context of limited charging infrastructure. By establishing a set of feasible charging activities, the problem of electric buses queuing for charging at constrained charging stations is transformed into a linear optimization model constraint. Numerical simulations are conducted within the real transit network of the Dalian Economic Development Zone in China. The results indicate that the judicious joint optimization of vehicle and charging scheduling significantly enhances the service frequency of electric buses while reducing operational costs for bus lines. Notably, the proportion of total trips performed by electric buses rises to 80.4%.

Multi-route coordination for bus systems in response to road disruptions

Road disruptions frequently occur in practice, resulting in a productivity loss of bus services and widespread passenger delays. These negative impacts are significant, especially when multiple routes are influenced at the same time. In order to mitigate these impacts, this paper proposes a multi-route coordination approach that collaboratively adjusts multiple bus routes and optimizes bus timetables to provide effective alternative bus services for passengers. Three adjusting strategies are adopted for bus routes with varying passenger demand: detouring, short-running, and cancellation. To address the multi-route coordination problem, a column-generation-based two-stage framework is developed. Concretely, a column generation technique is utilized in the first stage to iteratively generate candidate adaptive bus routes and passenger paths. Following that, an integrated integer programming model is built in the second stage to simultaneously determine bus timetables and the combinations of those adaptive bus routes. After realizing the low computational efficiency for large-scale problems, this paper designs a customized decomposition algorithm based on set partitioning to solve the presented model and obtain near-optimal solutions efficiently. Finally, the proposed methodology is applied to an illustrative Sioux Falls network and a real-world bus network in Beijing to verify its validity and effectiveness. Three comparative analyses are conducted to discuss the advantages of the three adjusting strategies, to investigate the benefits of coordinating bus timetables, and to explore the applicability of different adjusting strategies, respectively.

Spatial and temporal access to warm spaces during the winter of 2022/2023

It is estimated that over half a million people visited one network of ‘warm rooms’ during the winter of 2022 in the UK, a figure that may rise to 2.5 million people if other networks are considered. As well as offering a means to try to limit exposure to cold temperatures and reduce household energy costs, these winter warm hubs also address wider concerns such as social isolation, loneliness and mental well-being as the cost-of-living bites. This graphic demonstrates how geospatial approaches can be used to explore access via public transport and walking to a network of warm spaces in the capital city of Cardiff, Wales. By accounting for site opening times in relation to existing bus timetables for those for whom walking may not be an option, we illustrate how such information can be included in three commonly applied access measures (floating catchment area, cumulative opportunity and shortest distance) to highlight potential spatio-temporal gaps in provision across the city.

Optimization of Bridging Bus Timetable and Vehicle Scheduling under URT Disruption

After the occurrence of a disruptive event in an urban rail transit (URT) network, passengers’ travel is affected, and a large number of passengers are stranded in the stations. These stranded passengers have to be evacuated urgently. With its flexible deployment, a bus bridging service has become an effective solution to evacuate stranded passengers. In order to avoid large passenger flow at stations, in addition to evacuating the static passenger flow stranded at the disrupted stations, the bridging buses need to focus on the dynamic passenger flow arriving at the turnover stations along the short-turning trains. In this paper, we propose a mathematical model to optimize the timetable and vehicle scheduling of bridging buses considering the adjustment of rail transit operations. The model aims to minimize passenger waiting time, the number of lost passengers, and the amount of bridging buses used. The model makes buses operate flexibly on different routes, taking the bus capacity and number of buses into account. By creating an improved ε-constraint method, the Pareto front of the problem is solved using the model with a commercial solver. Finally, the accuracy and validity of the model is verified by applying an example based on China’s Hangzhou rail transit line 4. The results show that the bridging bus timetable and scheduling plan generated by the model effectively solved the problem of large passenger flow at turnover stations. In addition, compared with bridging buses with an even headway timetable, the results demonstrate that bridging buses with an uneven headway timetable, which considers coordination with rail transit, could reduce the passenger waiting time and the number of lost passengers. The model has better performance with an uneven headway timetable in the face of large passenger demand. The computational experiment shows that the total passenger waiting time and the number of bridging buses was reduced when the bus capacity was increased. However, the effect on passenger waiting time and the number of lost passengers was limited when the number of buses available at bus depots was increased.

Simulation-based optimization of bus departure scheme for large airport considering passenger evacuation

Purpose This study aims to optimize the traffic capacity allocation to solve the problem of low share of public transit in the landside system so as to get rid of the congestion trouble in landside traffic. The optimal timetable for airport buses can be searched by changing the departure interval of each line and evaluating the corresponding performance continuously. Design/methodology/approach This paper constructs a simulation model based on the real-world situation in Beijing Capital International Airport (BCIA), which simulates the whole process of airport bus schedules and analyzes the connections among multiple steps for transferring. The evaluation system is constructed by considering the benefits of passengers, airports and companies comprehensively. The optimal timetable for airport buses can be searched by changing the departure interval of each line and evaluating the corresponding performance continuously. Findings According to the experimental results, an excellent evacuation effect can only be achieved when the majority of departure intervals of airport buses are shortened to 50% of their original values, and some busy routes such as the Beijing Station line are supposed to be reduced to one-third of their original fixed intervals. As the airport bus passenger flow presents an obviously periodic variation over days, the timetable of the airport bus is supposed to be redesigned every day. A flexible bus timetable can not only meet the dynamic passenger flow but also enhance the attractiveness of public transit. Originality/value This paper constructs a simulation model based on the real-world situation in BCIA, which can not only model the complex scenes in the whole process of airport bus schedules but also reflect the intricate interaction between transferring passengers and vehicles caused by dense streamlines.

A reinforcement learning-based approach for online bus scheduling

Bus Scheduling Problem (BSP) is vital to save operational cost and ensure service quality. Existing approaches typically generate a bus scheduling scheme in an offline manner and then schedule vehicles according to the scheme. In practice, uncertain events such as traffic congestion occur frequently, which may make the originally planned bus scheduling scheme infeasible. This study proposes a Reinforcement Learning-based Bus Scheduling Approach (RL-BSA) for online bus scheduling. In RL-BSA, each departure time in a bus timetable is regarded as a decision point, and an agent makes a decision at the departure time to select a vehicle to depart at the time. The BSP is modeled as a Markov Decision Process (MDP) for the first time in literature. The state features are devised, which consist of real-time information of vehicles, including remaining working time, remaining driving time, rest time, number of executed trips and vehicle type. A reward function combining a final reward and a step-wise reward is devised. An invalid action masking approach is used to avoid the agent from selecting vehicles not meeting constraints. The agent is trained by interacting with a simulation environment and then the trained agent can schedule vehicles in an online manner. Experiments on real-world BSP instances show that RL-BSA can significantly reduce the number of vehicles used compared with the manual scheduling approach and Adaptive Large Neighborhood Search (ALNS). Under uncertain environment, RL-BSA can cover all departure times in the timetable without increasing the number of vehicles used.

Feeder Bus Timetabling Optimization for High-Speed Railway Station with Uneven Departure Interval

This paper proposes a bus timetable with uneven departure interval, which is mainly used to optimize the bus timetable at high-speed railway stations. The railway comprehensive transportation hub is an important node for the connection between the internal and external transportation of the city. Efficient transfer efficiency can not only improve the travel satisfaction of passengers, but also enable public transport enterprises to retain passenger flow in the competition with rail enterprises. Therefore, this paper analyzes the travel time distribution law of railway passenger transfer to public transport, constructs a timetable optimization model that adapts to the passenger flow law, and uses genetic algorithm to solve it. The optimization results show that, without changing the departure frequency, the waiting time of passengers in peak hours using the uneven departure interval mode is reduced by 29.6%, and the waiting time in average peak hours is reduced by 16.2%. If the departure frequency is changed, the waiting time of passengers in the uneven departure interval mode will also be shorter than that in the equal time departure mode.

Integrated electric bus timetabling and scheduling problem

Vehicle timetabling and scheduling in a public transit system are usually performed separately, with the output of timetabling serving as the input of scheduling. An obvious drawback of this sequential planning method is that the trade-off between bus timetables and vehicle schedules may be neglected when determining solutions, which in turn results in that the obtained solutions may be inferior to those produced using an integrated framework. For example, a well-planned timetable may result in a schedule that requires a large vehicle fleet size with more operational cost, while a well-planned schedule may reduce the quality of a bus timetable by limiting the use of vehicles. In this paper, we introduce a time-space network-based framework for integrating electric bus timetabling and scheduling, with minimum and maximum headway times, depot requirements, deadheading and vehicle battery capacities considerations. The underlying time-space network is constructed with well-designed inventory arcs that represent multiple operations a bus may execute, thus decreasing the network size. Using the constructed network, we formulate the considered problem with a multi-commodity network flow model and develop a Lagrangian relaxation heuristic that consists of three phases, including generating relaxed solutions, making relaxed solutions feasible, and improving feasible solutions, to solve the integrated model. Tests on a set of instances confirm that the proposed integrated solution method can efficiently produce bus timetables and schedules with valid bounds, indicate that the integrated method can produce better solutions where the profit is increased by 5.29%–20.28%, and show how the headway times, service trip profit and operating cost settings affect the solution.

Multi-Objective Bus Timetable Coordination Considering Travel Time Uncertainty

This paper proposes a timetable coordination method for transfer problems in a bus transit system. With a given bus network, a stochastic mixed-integer linear programming (MILP) model has been formulated to obtain coordinated bus timetables with the objective of minimizing a weighted sum of the average value of total waiting time and its average absolute deviation value, allowing for random bus travel time. The vital decision variable is the terminal departure offset time of each target bus trip within a certain off-peak period. The robust MILP model can also be used to solve the first-bus transfer problem with the introduction of several new linear constraints. A solution method based on the Monte Carlo simulation has been developed to solve the MILP model. Numerical experiments have been conducted for different scenarios. The results indicate that bus timetables coordinated by the developed model are capable of substantially reducing waiting time for transfer and non-transfer passengers. In addition, the feasibility of simplifying a common sub-route into a single transfer stop in a timetable coordination problem has been explored based on numerical experiments.

Designing boarding limit strategy by considering stop-level fairness amid the COVID-19 outbreak

Bus operators have to make trade-offs between transporting more passengers and maintaining social distancing to reduce ridership congregation amid Corona Virus Disease 2019 (COVID-19) outbreak. The traditional bus boarding mode could easily lead passengers fully occupy the bus available capacity at one stop, and it would prevent subsequent passengers from boarding. It is crucial to establish a new operating mode and strategy to ensure all passengers have opportunities to ride and to collaboratively optimise the bus timetable. In this paper, the boarding limit strategy that considers the fairness of passenger boarding probability is proposed to address the inequitable problem with minimise the passenger travel time and the number of stranded passengers. The coupling relationship between bus dwell time and passenger flow is used to collaboratively optimise the bus timetable. Case studies are conducted to illustrate the performance of the boarding limit strategy in improving passenger boarding equity.

Distributed Multiagent Deep Reinforcement Learning for Multiline Dynamic Bus Timetable Optimization

As a primary countermeasure to mitigate traffic congestion and air pollution, promoting public transit has become a global census. Designing a robust and reliable bus timetable is a pivotal step to increase ridership and reduce operating cost for transit authorities. However, most previous studies on bus timetabling rely on historical passenger count and travel time data to generate static schedules, which often yield biased results in these uncertain scenarios, such as demand surge or adverse weather. In addition, acquiring real-time passenger origin/destination from a limited number of running buses is not feasible. This article considers the multiline dynamic bus timetable optimization problem as a Markov decision process model to address the aforementioned issues, and proposes a multiagent deep reinforcement learning framework to ensure effective learning from the imperfect-information game, where the passenger demand and traffic condition are not always known in advance. Moreover, a distributed reinforcement learning algorithm is applied to overcome the limitation of high computational cost and low efficiency. A case study of multiple bus lines in Beijing, China, confirms the effectiveness and efficiency of the proposed model. The results demonstrate that our method outperforms heuristic and state-of-the-art reinforcement learning algorithms by reducing 20.30% of operating and passenger costs compared with actual timetables.

Integrated solution for electric bus timetabling and vehicle scheduling combined with choices of charging locations

This paper presents a novel mathematical model, integrating timetabling and vehicle scheduling problems for electric buses. The objective is to minimize the number of buses while satisfying constraints concerning routing and charging, including design choices for where to install charging stations. The aim of the paper is to illustrate and discuss the effects of solving the timetabling and vehicle scheduling of electric buses (including where to install charging infrastructure) separately, compared to solving them jointly in one single step. For that purpose, we perform tests with: i) given timetable, that is, solving only the vehicle scheduling problem, ii) fixed headways for each line, and iii) variable headways. A small test case based on actual bus lines from Västra Frölunda, Gothenburg, Sweden, is used. From the numerical experiments, we verify that combining the two planning steps can significantly reduce the number of vehicles needed.

Shuttle Bus Timetable Adjustment in Response to Behind-Schedule Commuter Railway Disturbance

Shuttle bus connection is a valid technique to handle unplanned problems and promote sustainable transportation. The study describes tools that facilitate the shuttle bus timetable adjustment responding to a disturbance resulting from behind-schedule trains on a commuter railway. This behind-schedule disturbance is divided in four stages allowing for different delay ranges. The problem and its solution involve different elements, such as shuttle bus route selection, stop location, and timetable adjustment. We propose a nonlinear integer programming model, in which the objective function is based on the waiting, travelling, and walking costs for passengers as well as the operation cost of the route chosen. Vehicle capacity constraints and precise passengers’ waiting times are considered. A genetic algorithm and a simulated annealing algorithm combined with a priori decomposition are used to derive an efficient solution. A case study of a shuttle bus serving the Jinshan Railway in Shanghai, China, is tested to validate that, compared to the no-planning timetable, the total cost of the optimized timetable is reduced by 7.6%, especially including a dramatic reduction in the cost of passenger waiting time by 49.1%.

Deep Reinforcement Learning based dynamic optimization of bus timetable

Bus timetable optimization is a key issue to reduce operational cost of bus company and improve the transit service quality. Existing methods optimize the timetable offline. However, in practice, the short-term passenger flow may change dramatically from time to time. Timetables generated offline cannot be adjusted in real time to handle the changed passenger flow. In this paper, we propose a Deep Reinforcement Learning based bus Timetable dynamic Optimization method (DRL-TO). In DRL-TO, the problem of bus timetable optimization is formulated as a Markov Decision Process (MDP). A Deep Q-Network (DQN) is applied as the agent to decide whether a bus departs at each minute during the service period. Therefore, departure intervals of bus services are determined in real time in accordance with passenger demand. We identify several new and useful state features for the DQN agent, including the load factor, the carrying capacity utilization rate, passengers’ waiting time and the number of stranded passengers. Considering the interests of both the bus company and passengers, a reward function is designed, which includes metrics of full load rate, empty load rate, passengers’ waiting time, and the number of stranded passengers. Experiments demonstrate that, in comparison to the timetable generated by offline optimization approaches and the manual method, DRL-TO can dynamically determine the departure intervals based on the real-time passenger flow, and generate a timetable with less departure time points (i.e., operational cost) and shorter passengers’ waiting time (i.e., higher quality of service).