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Public transport service reliability is crucial for all stakeholders, including users, operators, and society. Bus bunching, where two or more buses on the same route travel closely together, significantly undermines service reliability. This paper reviews bus bunching, its causes and consequences, and control strategies from demand, supply, and decision-making perspectives. It identifies gaps in the literature, emphasising the need for realistic evaluations of control methods and real-world applications. The paper reveals that most bunching solutions prioritise operators over public transport users, and the trade-offs posed by these methods require further examinations. Hybrid methods combining holding with other measures have outperformed standalone holding methods but need real-world testing. User-centric approaches, such as encouraging and incentivising passengers to choose less crowded vehicles or wait, have demonstrated some potential in alleviating service bunching. However, their effectiveness in real-world applications present important research directions. In summary, the practical classification and framework presented in this review can assist policymakers in making informed and optimised decisions by considering various variables and performance measures involved in the process, and in finding balanced solutions for passenger and operator. [ABSTRACT FROM AUTHOR]

Real-time control strategies deal with the day's dynamics in bus rapid transit systems. This work focuses on minimizing the number of buses of the same line cruising head-to-tail or arriving at a stop simultaneously by implementing bus holding times at the stops as a control strategy. We propose a new mathematical model to determine the bus holding times. It has quadratic constraints but a linear objective function that minimizes the bus bunching penalties. We also propose a beam-search heuristic to reduce computational solution time to solve large instances. Experimental results on a bus rapid transit system simulation in Monterrey, Mexico, show a bus bunching reduction of 45% compared to the case without optimization. Moreover, passenger waiting times are reduced by 30% in some scenarios. For real-world instances with 60 buses, the beam-search approach provides solutions with an optimality gap of less than 5% in less than 3 s. [ABSTRACT FROM AUTHOR]

Due to the inherent uncertainties of the bus system, bus bunching remains a challenging problem that degrades bus service reliability and causes passenger dissatisfaction. This paper introduces a novel deep reinforcement learning framework specifically designed to address the bus bunching problem by implementing dynamic holding control in a multi-agent system. We formulate the bus holding problem as a decentralized, partially observable Markov decision process and develop an event-driven simulator to emulate real-world bus operations. An approach based on deep Q-learning with parameter sharing is proposed to train the agents. We conducted extensive experiments to evaluate the proposed framework against multiple baseline strategies. The proposed approach has proven to be adaptable to the uncertainties in bus operations. The results highlight the significant advantages of the deep reinforcement learning framework across various performance metrics, including reduced passenger waiting time, more balanced bus load distribution, decreased occupancy variability, and shorter travel time. The findings demonstrate the potential of the proposed method for practical application in real-world bus systems, offering promising solutions to mitigate bus bunching and enhance overall service quality. [ABSTRACT FROM AUTHOR]

Regarding tools and systems from artificial intelligence (AI), chat-based ones from the area of generative AI have become a major focus regarding media coverage. ChatGPT and occasionally other systems (such as those from Microsoft and Google) are discussed with hundreds if not thousands of academic papers as well as newspaper articles. While various areas have considerably gone into this discussion, transportation and logistics has not yet come that far. In this paper, we explore the use of generative AI tools within this domain. More specifically, we focus on a topic related to sustainable passenger transportation, that is, the handling of disturbances in public transport when it comes to bus bunching and bus bridging. The first of these concepts is related to analyzing situations where we observe two or more buses of the same line following close to each other without being planned deliberately and the second is related to the case where buses are used to replace broken connections in other systems, such as subways. Generative AI tools seem to be able to provide meaningful entries and a lot of food for thought while the academic use may still be classified as limited. [ABSTRACT FROM AUTHOR]

A common problem in public transport systems is bus bunching, characterized by a negative feedback loop between service headways, number of boarding passengers and dwell times. In this study, we examine whether providing real-time crowding information (RTCI) at the stop regarding the two next vehicle departures can stimulate passengers to wait for a less-crowded departure, and thus alleviate the bunching effect. To this end, we leverage on results from own stated-preference survey and develop a boarding choice model. The model accounts for the presence of RTCI and is implemented within dynamic public transport simulation framework. Application to the case-study model of a major bus corridor in Warsaw (Poland) reveals that RTCI can induce a significant probability (30–70%) of intentionally skipping an overcrowded bus and waiting for a later departure instead. This behaviour, in turn, results in significantly lower vehicle headway and load variations, without deteriorations in total waiting utility. Overall, journey experience improves by 6%, and crucially—the prevalence of denial-of-boarding and excessive on-board overcrowding is substantially reduced, by ca. 40%. Results of our study indicate that the willingness to wait induced by RTCI can be a potential demand management strategy in counteracting bunching, with benefits already attainable at limited RTCI response rates. [ABSTRACT FROM AUTHOR]

In this paper, we focus on controlling multiline buses operated in networks with curbside bus stops. In such networks, both bus bunching and bus queueing, which often result in passenger inconvenience as well as bus waiting delays, are frequently observed during bus operations. To address the adverse influences of these two phenomena, we propose a mixed integer programming (MIP) model to provide guidance on real-time bus cruising speeds based on the real-time state of the whole system. The proposed model can avoid bus bunching by coordinating bus cruising speeds and alleviate bus queueing congestion by restricting the number of bus arrivals at each stop. Specifically, to address bus bunching, the model has a quadratic objective function that minimizes the total expected passenger waiting time; while for bus queueing, the model has big-M and time-indexed constraints that restrict the number of bus arrivals in each time interval of length g based on the waiting capacity Q s of each stop s. Simulation experiments are conducted with different sizes of virtual networks, and the corresponding results show that the proposed model can lead to both a shorter average passenger waiting time and less bus congestion at stops. The improvement with respect to bus waiting delay is more significant: the percentage decrease can reach 46.9%. Moreover, the results of the average computing time show that the control model can be solved before a bus finishes service in most cases, which means decisions can be fed back to drivers in a timely manner; therefore, the proposed model can meet the requirements of real-time control. A sensitivity analysis with respect to parameters Q s and g is also performed. These two parameters are shown to only affect control performance with respect to bus waiting delays at stops, and shorter bus waiting delays can be achieved with relatively small Q s and large g. Further experiments are conducted within a real network, and the experimental results show that our method is suitable for implementation in practice. • We consider to control multiline buses operated in urban transit networks. • We propose a MIP model which can alleviate bus bunching and queueing simultaneously. • We propose two crucial parameters and discuss their effects on multiline bus control. • Experimental results show that the model is suitable for practical implementation. [ABSTRACT FROM AUTHOR]

Bus bunching refers to the phenomenon that several buses arrive at a station within a short period. It dramatically increases passengers’ waiting time and reduces the quality of transit service. Evaluating the features of bus bunching and identifying the causes are important to developing countermeasures. The primary of this study was to analyze the temporal-spatial features of bus bunching by conducting an in-depth analysis of empirical bus GPS trajectory data obtained in Nanjing, China. The GPS data were inputted into the ArcGIS to track the spatial map's bus trajectories. A data processing procedure was proposed to analyze the data, including data cleaning, trip cutting, each station's arrival and departure time estimation, and time headway calculation. Then the spatiotemporal trajectory picture was drawn for the bus route where the bus bunching was identified. The study also analyzed the headway features of consecutive buses at the different stations and evaluated the variation of time headway, indicating the severity of bus bunching. The results showed that there are significant differences in the spatiotemporal features of bus bunching between bus stations. When the bus bunching occurred, it persisted on downstream stations for a long time. The bunching severity dramatically increased at downstream stations, reducing bus arrival reliability on the whole bus line. We also identified that the bus bunching was primarily caused by the overlong bus dwelling time at a station and the different travel times of buses between stations. The study fills the gap by developing the methodology to investigate the bus bunching features and causes with point-by-point empirical GPS trajectory data. Findings of the study can also support the real-time prediction and warning of bus bunching in practical applications. [ABSTRACT FROM AUTHOR]

Bus bunching is a typical phenomenon observed in daily public transit operations and that significantly reduces the reliability and attractiveness of transit service. Although various control strategies, such as vehicle holding, speed guidance, and signal priority, have been proposed to eliminate or alleviate bus bunching, the impact of road traffic flow on bus bunching has not been well studied. To bridge this gap, this work proposes a new mesoscopic simulation model by incorporating the lattice Boltzmann model to simulate bus bunching considering the impacts of road traffic flow. Simulation results show that by utilizing the new simulation model, different phase diagrams can be observed. Under different conditions of traffic flow-density evolution, i.e., no oscillation, single oscillation, global oscillation, and irregular oscillation, the resulting bus trajectories are significantly different. In addition, an investigation of a real-world bus line in Beijing with global positioning system (GPS)-based vehicle location data shows that some results of the model are qualitatively consistent with the actual characteristics of the bus route. It shows that the proposed new simulation model has great potential for enhancing our understanding of the impacts of road traffic flow on bus bunching. [ABSTRACT FROM AUTHOR]

Signal intersection delays seriously affect the transportation efficiency and service reliability of the bus system. Bus priority control is an effective method to reduce the delay of buses at signal-controlled intersections. However, the efficiency of buses is mainly considered in current researches, rather than the bus bunching and queuing delay at downstream stations of intersections. A bus fleet speed control method was proposed based on the cooperative vehicle and infrastructure system(CVIS) environment, which makes the buses actively adapt to the signal phase in a cooperative fleet way. Furthermore, two access rules were introduced to the cooperative fleet, so that the cooperative fleet can meet the requirements of bus bunching prevention as well as the number of berths at downstream stations. The result of the case study shows that the proposed method can significantly reduce the delay of buses at signal-controlled intersections. And the phenomena of same route bus bunching and the queuing into stations are effectively avoided as well, which literally promoting the efficiency and reliability of urban bus operation. [ABSTRACT FROM AUTHOR]

Bus bunching occurring at stops has an unstable impact on bus travel time. In order to evaluate urban bus travel time effectively, the travel time reliability (TTR) addressing bus bunching is analyzed. This paper focuses on the delayed time caused by bus bunching in the dwelling process at bus stops and uses the coefficient of variation of time headway to evaluate the degree of bus bunching. Moreover, the travel time deviation (TTD) indicator and travel time on-time accuracy (OTA) model are proposed to evaluate the bus TTR. The proposed model is used to analyze 113 runs of a bus route in Xi'an city, China. Real-time GPS data are used to analyze the operation of each run from the origin to the destination stops. The results show that 74.34% of the runs are delayed. When the value of TTD is higher than |0.1|, 64.2% of runs are delayed with bus bunching. Based on the measuring of OTA in two situations, the value of TTR considering bus bunching is reduced by 20%. In addition, the number of stopping routes at peak periods has a significant impact on the occurrence of bus bunching. The research results would have practical implications for the operation and management of buses. [ABSTRACT FROM AUTHOR]

Bus bunching is a common phenomenon caused by irregular bus headway, which increases the passenger waiting time, makes the passenger capacity uneven, and severely reduces the reliability of bus service. This paper clarified the process of bus bunching formation, analyzed the variation characteristics of bus bunching in a single day, in different types of periods, and at different bus stops, then concluded twelve potential factors. A hybrid model integrating a genetic algorithm with elitist preservation strategy (eGA) and decision tree (DT) was proposed. The eGA part constructs the model framework and transforms the factor identification into a problem of selecting the fittest individual from the population, while the DT part evaluates the fitness. Model verification and comparison were conducted based on real automatic vehicle location (AVL) data in Shenzhen, China. The results showed that the proposed eGA–DT model outperformed other frequently used single DT and extra tree (ET) models with at least a 20% reduction in MAE under different bus routes, periods, and bus stops. Six factors, including the sequence of the bus stop, the headway and dwell time at the previous bus stop, the travel time between bus stops, etc., were identified to have a significant effect on bus bunching, which is of great value for feature selection to improve the accuracy and efficiency of bus bunching prediction and real-time bus dispatching. [ABSTRACT FROM AUTHOR]

Bus bunching in public transport is the concentration of similar buses having different schedules to a common time point. The reason for this phenomenon is variations existing in the bus operation as earliness and lateness. Bus bunching has the consequence of reduced service reliability concerning both passengers and operators. A zero bunching state is vital for enhancing the usage of public transport where the buses operate with utmost schedule adherence. Two generally adopted strategies for solving bus bunching are a schedule-based strategy which provides slack time in a timetable to address late running and fixed departure time for the early operations, and a headway-based strategy that maintains headway between buses. Bus bunching due to multiple origins is a special case in which common tactics cannot effectively control a bunching tendency that arises at the entry point. The operation schedules of multiple origins must be so designed that a state of zero bus bunching can be ensured while buses from different origins reach the entry points. This article presents a model of a multiple-origins public transport network as a combination of origins, routes and entry points, developed in the search for achieving a zero bunching state in the operation beyond an entry point. The origins are modelled based on the entry-point variables. The routes are modelled based on the running time, departure time, arrival time, and dwell time. The entry points are modelled based on route and entry-point variables. Redesigning route schedules based on the entry-point characteristics and an appropriate slack time implementation are proposed and observed to be suitable for overcoming bunching in a multiple-origins bus operation. [ABSTRACT FROM AUTHOR]

An efficient urban bus control system has the potential to significantly reduce travel delays and streamline the allocation of transportation resources, thereby offering enhanced and user-friendly transit services to passengers. However, bus operation efficiency can be impacted by bus bunching, a problem originating from uncertain travel times between stops and time-varying passenger demand rates. This problem is notably exacerbated when the bus system operates along a signalized corridor in the face of unpredictable travel demand. To mitigate this challenge, we introduce a multi-strategy fusion approach for the longitudinal control of connected and automated buses. The approach is driven by a physics-informed deep reinforcement learning (DRL) algorithm and takes into account a variety of traffic conditions along urban signalized corridors. Taking advantage of connected and autonomous vehicle (CAV) technology, the proposed approach can leverage real-time information regarding bus operating conditions and road traffic environment. By integrating the aforementioned information into the DRL-based bus control framework, our designed physics-informed DRL state fusion approach and reward function efficiently embed prior physics and leverage the merits of equilibrium and consensus concepts from control theory. This integration enables the framework to learn and adapt multiple control strategies to effectively manage complex traffic conditions and fluctuating passenger demands. Three control variables, i.e., dwell time at stops, speed between stations, and signal priority, are formulated to minimize travel duration and ensure bus stability with the aim of avoiding bus bunching. We present simulation results to validate the effectiveness of the proposed approach, underlining its superior performance when subjected to sensitivity analysis, specifically considering factors such as traffic volume, desired speed, and traffic signal conditions. • A multi-strategy fusion approach based on distributed DRL is presented for dynamic bus operation control. • Uncertainties in bus operation systems are considered, and a practical bus control environment is designed. • An efficient DPPO-based learning procedure is developed, demonstrating remarkable solution efficiency and convergence. • A physics-informed DRL state fusion approach and a tailored reward function are utilized to achieve multi-agent consensus. • Principles from multi-agent control theory and equilibrium states within bus operations are incorporated in the framework. [ABSTRACT FROM AUTHOR]

In high-frequency bus services, maintaining the service regularity is a critical issue. The service regularity is directly related to the excessive waiting times (EWT) of passengers at bus stops. In a regular service, the EWT is minimized resulting in even headways between consecutive buses of the same line. In this study, we propose the combined use of rescheduling and bus holding to improve passengers' excessive waiting times. We model the dynamic rescheduling and bus holding problem as an integer nonlinear program (INLP) and we prove its NP-hardness. Our model considers the constraints of the original timetable – an issue that is usually neglected from most dynamic control methods. Given the NP-hardness of our mathematical program, we introduce a problem-specific heuristic to explore efficiently the solution space. The convergence rate of the proposed heuristic is tested against other solution methods, including simulated annealing with linear cooling, hill climbing and branch and bound with multi-start sequential quadratic programming. In addition, simulations with the use of actual operational data from a major bus operator in Asia Pacific demonstrate an up to 35% potential EWT improvement for a minor increase of 6% to the travel times of onboard passengers.

The problems of bus bunching mitigation and the energy management of groups of vehicles have traditionally been treated separately in the literature and been formulated in two different frameworks. The present work bridges this gap by formulating the optimal control problem of the bus line eco-driving and regularity control as a smooth, multi-objective nonlinear program. Since this nonlinear program has only a few coupling variables, it is shown how it can be solved in parallel aboard each bus, such that only a marginal amount of computations need to be carried out centrally. This procedure leverages the structure of the bus line by enabling parallel computations and reducing the communication loads between the buses, which makes the problem resolution scalable in terms of the number of buses. Closed-loop control is then achieved by embedding this procedure in a model predictive control. Stochastic simulations based on real passengers and travel times data are realized for several scenarios with different levels of bunching for a line of electric buses. Our method achieves fast recoveries to regular headways as well as energy savings of up to 9.3% when compared with traditional holding or speed control baselines. [ABSTRACT FROM AUTHOR]

In order to alleviate bus bunching and improve the balance and punctuality rate of bus operation, a single-line real-time control strategy based on Intelligent Transportation System (ITS) was proposed. The strategy took three measures: controlling the cruising speed, dwell time, and the bus load rate to improve the stability of bus operations and to ensure its running speed. At the same time, the proposed strategy was compared with the literature on the traditional single-point control strategy based on timetable (S1 for short) and the multi-point control strategy based on time headway (S2 for short). Finally, the No. 245 bus line in Nanchang City, China, was selected as a case. It was modeled and simulated by Python programming software, and the control effects of the three control strategies were analyzed. Compared with the uncontrolled bus operations, the simulation results show that: under the control of S1, the bus operation stability is improved, but the bus operation efficiency is reduced; under the control of S2, the problem of S1 operation efficiency reduction can be solved, and the operation stability can be improved at the same time to achieve the effect of preventing bunching. For the real-time control strategy (S3 for short), the average bus travel time is the smallest, the distance between the buses is maintained the best, and the running stability is also the best, which avoids the bus bunching to the greatest extent. Among them, the average travel time is reduced by about 34% compared with the second strategy. This study provides a theoretical basis and strategy reference for bus operators to ensure balanced bus operation. [ABSTRACT FROM AUTHOR]

The most relevant issues related to headway variability in public transport planning, operations and quality of service are reviewed in this paper. We discuss the causes and consequences of headway variability, the alternative metrics that have been proposed to measure it, the preventive and reactive strategies to control headway variability in both research and practice, including the role of drivers and of present and future technology, and how service provision contracts might deal with headway variability through metrics and financial incentives. The most influential elements that explain headway variability along a route are the irregularity at which vehicles are dispatched, the scheduled frequency, the distance travelled or route length, the passenger demand and associated dwell times, and the number of stops. We conclude that there is a large gap between the state-of-the-art and the state-of-practice in terms of identification of headway variability issues, as well as in the development of mitigation and control measures. It is therefore paramount that future research will contribute to closing this gap by addressing organisational, contractual and technological barriers in the implementation of measures aimed at mitigating headway variability in public transport services. [ABSTRACT FROM AUTHOR]

The unreliable service and the unstable operation of a high-frequency bus line are shown as bus bunching and the uneven distribution of headways along the bus line. Although many control strategies, such as the static and dynamic holding strategies, have been proposed to solve the above problems, many of them take on some oversimplified assumptions about the real bus line operation. So it is hard for them to continuously adapt to the evolving complex system. In view of this dynamic setting, we present an adaptive holding method that combines the classic approximate dynamic programming (ADP) with the multistage look-ahead mechanism. The holding time, the only control means used in this study, will be determined by estimating its impact on the operation stability of the bus line system in the remaining observation period. The multistage look-ahead mechanism introduced into the classic Q-learning algorithm of the ADP model makes it easy that the algorithm gets through its earlier unstable phase more quickly and easily. During the implementation of the new holding approach, the past experiences of holding operations can be cumulated effectively into an artificial neural network used to approximate the unavailable Q-factor. The use of a detailed simulation system in the new approach makes it possible to take into account most of the possible causes of instability. The numerical experiments show that the new holding approach can stabilize the system by producing evenly distributed headway and removing bus bunching thoroughly. Compared with the terminal station holding strategies, the new method brings a more reliable bus line with shorter waiting times for passengers. [ABSTRACT FROM AUTHOR]

Some stops on busy bus lines regularly suffer from bus bunching, which refers to a bus arriving with a little headway to its predecessor. This phenomenon increases scheduling difficulties and has a negative impact on the passenger experience due to unreasonable scheduling. The conventional holding strategy aims to alleviate this problem by holding buses at control points. However, the holding strategy has the drawbacks of creating large deviations from the original schedule and prolonging passenger waiting time when confronted with traffic congestion. This study proposes an innovative short-turning strategy to alleviate bus bunching by the deliberate conversion of a few regular trips to short-turning trips. A nonlinear optimisation model is developed by rescheduling a set of trips using the short-turning strategy to minimise schedule deviation from the original schedule. The nonlinear short-turning model is then converted into a linear form that is solvable by CPLEX. Based on real data from the Yuntong 111 bus line in Beijing, China, the proposed short-turning strategy is deployed in a simulation experiment. The results show that the short-turning strategy is superior at alleviating bus bunching than the alternatives of no control strategy and the holding strategy. Compared with no control strategy, the short-turning strategy can achieve a more than 43.44% reduction in schedule deviation and significantly reduce total passenger waiting time by up to 8.99%. [ABSTRACT FROM AUTHOR]

Providing public transportation with quality service is critical to attracting more passengers to the system. However, high-demand routes are prone to the so-called bus bunching--a tendency of buses to group as a consequence of variations in travel times and demands. Bus holding is applied to overcome this effect. In this study, we present a novel method for bus holding in which the control law is based only on the buses' position using a computationally efficient rolling horizon approach. The method uses similar inputs as linear control approaches while not increasing significantly the computational time. On the other hand, the method overcomes a key weakness of the linear control approach thanks to the explicit constraint handling that always ensures the control action effectiveness. Simulation experiments in a validation case and a model-specific for a bus rapid transit line in Curitiba, Brazil, showed a reduced holding time and improved resilience, delivering more than 20% reduction in delay time accounting for the on-board and station delays. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyze an online, decentralized policy for dispatching vehicles in a multi-line public transit system. In the policy, vehicles arriving at a terminal station are assigned to the lines starting at the station in a round-robin fashion. Departure times are selected to minimize deviations from a certain target headway. We prove that this policy is self-organizing: given that there is a sufficient number of available vehicles, a timetable spontaneously emerges that meets the target headway of every line. Moreover, in case one of the vehicles breaks down, the remaining vehicles automatically redistribute over the network to re-establish such a timetable. We present both theoretical and numerical results on the time until a stable state is reached and on how quickly the system recovers after the breakdown of a vehicle. Experiments on three real-world transit systems show that our policy performs well, even if not all assumptions required for the theoretical analysis are met: if there are enough vehicles, the realized headways are typically close to the target headways. These promising results suggest that our self-organizing policy could be useful in situations where centralized dispatching is impractical or simply impossible due to an abundance of disruptions or the absence of information systems. • A simple decentralized policy for dispatching in a multi-line network is proposed. • We show analytically that the policy matches the performance of centralized control. • Numerical experiments using real networks confirm the good performance of the policy. [ABSTRACT FROM AUTHOR]

Efficient operation of bus networks is vital for urban centers. Unfortunately, factors such as uneven passenger loads and congestion hinder the adherence to posted schedules, leading to reliability issues. Most notably, bus bunching has been identified as a significant reliability problem, impacting both users and operators. Bus bunching is treated as a route-level problem in the relevant literature, while spatial patterns in explanatory factors are overlooked. Diverging from the typically performed route-level analysis, this study exploits Automatic Vehicle Location data to investigate factors affecting bus bunching at the network level, while taking into account their spatial variability. For this purpose, a Geographically Weighted Regression Model is applied to model bus bunching, using bus stop and network attributes as explanatory variables. Results for approximately 360 bus stops in Athens, Greece underline the superiority of the proposed model to Ordinary Least Squares Regression and corroborate the presence of spatial variability in the factors affecting bus bunching. Indeed, the number of traffic lanes at the stop level is positively associated with bunching in heavy traffic segments, whereas a higher number of lanes is negatively linked to bunching in less congested regions. Further, the number of bunching occurrences generally increases with the number of routes serving each stop, as well as with the distance from subway stops in the outer parts of the city. Such findings highlight the need to consider spatial structures in relevant models and can help improve their reliability and accuracy.

Bus bunching is a common phenomenon caused by irregular bus headway, which increases the passenger waiting time, makes the passenger capacity uneven, and severely reduces the reliability of bus service. This paper clarified the process of bus bunching formation, analyzed the variation characteristics of bus bunching in a single day, in different types of periods, and at different bus stops, then concluded twelve potential factors. A hybrid model integrating a genetic algorithm with elitist preservation strategy (eGA) and decision tree (DT) was proposed. The eGA part constructs the model framework and transforms the factor identification into a problem of selecting the fittest individual from the population, while the DT part evaluates the fitness. Model verification and comparison were conducted based on real automatic vehicle location (AVL) data in Shenzhen, China. The results showed that the proposed eGA–DT model outperformed other frequently used single DT and extra tree (ET) models with at least a 20% reduction in MAE under different bus routes, periods, and bus stops. Six factors, including the sequence of the bus stop, the headway and dwell time at the previous bus stop, the travel time between bus stops, etc., were identified to have a significant effect on bus bunching, which is of great value for feature selection to improve the accuracy and efficiency of bus bunching prediction and real-time bus dispatching.

This paper proposes a dynamic control method to overcome bunching and improve the regularity of fixed-route transit systems. The method uses a combination of dynamic holding and en-route driver guidance to achieve its objectives. It applies to systems with a mix of headway-based and schedule-based lines but it is evaluated for scheduled systems as this is the more challenging application. Improved schedule adherence is the goal. The method’s calculation complexity per piece of advice does not increase with system size. As a result, the method is scalable and can be used with large multiline systems, no matter how complex. When controled, each vehicle is mostly affected by exogenous disturbances (e.g. traffic) and very little by other vehicles. As a result, disruptions to a vehicle or group of vehicles caused by inattentive drivers or control equipment failures remain confined to the vehicles experiencing the problems. The control method effectively quarantines “disease”. The method is evaluated analytically and with simulations over a broad range of conditions, including schedules with zero slack. The method was also evaluated by observing the performance of a real world multi-line system that uses inexpensive on-board tablets to apply the control. The evaluation addresses driver compliance and equipment malfunction issues. It is found that the method is resilient and improves reliability considerably even under challenging conditions.

This study examines bus bunching along a common-line corridor, considering crucial factors underexplored in existing literature, such as stochastic travel times, passenger arrival patterns, and passenger transfer behaviours. We first develop a bus motion model that captures the interaction between bus trajectories and passenger movement. Then we formulate a reliability-based passenger arrival time choice and a transfer choice model to characterise passengers' behaviours. Afterwards, the bus motion model and the passenger choice models are integrated, and a Method of Successive Averages type iterative algorithm is developed to obtain stable passenger arrival patterns and transfer choices. Numerical experiments are carried out on a hypothetical network followed by a case with real-world data. Our findings demonstrate that a high transfer demand could amplify the propagation of bus bunching across lines along the common-line corridor. Meanwhile, a 50% increase in transfer demand leads to a 24%–30% rise in headway fluctuation. Furthermore, our results suggest that non-uniform passenger accumulation patterns can restore headway regularity as a result of coordinated passenger movement and bus motions, thus alleviating the persistent deterioration in bus bunching. • Development of a bus motion model with passenger arrival time and transfer choices. • Reliability-based models for passenger arrival time and transfer choices. • Integration of bus motion and passenger choice models using an MSA-type algorithm. • Numerical experiments of impacts of passenger arrivals and transfers on bus bunching. [ABSTRACT FROM AUTHOR]

The conventional bus propagation modeling process has two main shortcomings: bus bunching and extra energy consumption caused by idling at signalized intersections and unexpected speed variation along the route. To overcome these problems simultaneously, an extended bus propagation model and anti-bunching control are proposed in this paper. To extend the time-based bus propagation model, the authors used a finite state machine and an intelligent driver model to establish a spatial-temporal based bus propagation model accounting for dynamic bus motion and passenger swapping behavior between bunched buses. To mitigate bus bunching and improve fuel economy in a connected environment, an anticipated average speed plan was used to improve headway regularity and reduce the chance of encountering a red signal. Then, predictive control accounting for state and control constraints was used to generate a smooth trajectory for connected buses to follow the commands given by anticipated average speed planning. This ensured that connected buses traversed signalized intersections and approached downstream stops efficiently. Simulations show that the proposed model can imitate passenger swapping behavior when bus bunching occurs, and the anti-bunching control can mitigate bus bunching and guide connected buses to traverse signalized intersections and reach downstream stops with less delay. [ABSTRACT FROM AUTHOR]

The objective of this paper is to identify hot spots of bus bunching events at the network level, both in time and space, using Automatic Vehicle Location (AVL) data from the Athens (Greece) Public Transportation System. A two-step spatio-temporal clustering analysis is employed for identifying localized hot spots in space and time and for refining detected hot spots, based on the nature of bus bunching events. First, the Spatio-Temporal Density Based Scanning Algorithm with Noise (ST-DBSCAN) is applied to distinguish bunching patterns at the network level and subsequently a k++means algorithm is employed to distinguish different types of bunching clusters. Results offer insights on specific time periods and route segments, where bus bunching events are more likely to occur and, also, on how bus bunching clusters change over time. Further, headway deviation analysis reveals the differences in the characteristics of the various bunching event types per line, showing that routes running on shared corridors experience more issues while underlying causes may vary per line. Collectively, results can help guide practice toward more flexible solutions and control strategies. Indeed, depending on the type of spatio-temporal patterns detected, appropriate improvements in service planning and real-time control strategies may be identified in order to mitigate their negative effects and improve quality of service. In light of emerging electric public transport systems, the proposed framework can be also used to determine preventive strategies and improve reliability in affected stops prior to the deployment of charging infrastructure. [ABSTRACT FROM AUTHOR]

• An injection stochastic model based on the headway distribution second moment is proposed. • An expression for the optimal headway threshold triggering the injection is proposed. • A model to determine when a bus should be injected within the headway was developed. • We identify at which moment within the headway a bus should be injected. • Simulations with real data are used to test the proposed model, proving its accuracy. Randomness affecting the operation of public transport systems generates significant increments in waiting times. A strategy to deal with this randomness is bus injection, in which buses are kept in specific points along the route ready to be dispatched when an event such as an extremely long headway occurs. In this work, a stochastic model based on the second moment of the headways distribution is developed to determine if one or more buses are worth reserving for injection in a public transport service. A single stop approach is initially used to determine an expression for the optimal headway threshold triggering the injection. Then, a model for the complete service is developed and used to determine when the empty bus should be injected within the headway once the decision to inject it has been taken. We show that the bus should be injected approximately when 57% of the headway has passed. Simulations with real data are used to test the proposed model, proving its accuracy in terms of measuring the impact on waiting times. The results show that reserving a bus to be injected can be better than operating the entire fleet continuously. [ABSTRACT FROM AUTHOR]

This work proposes a periodic bus holding control method where the bus holding times of all running trips are computed simultaneously within each optimization time period; thus, increasing the coordination among running buses for avoiding bus bunching. This paper considers the adverse effects of the bus holding control in the in-vehicle travel times of on-board passengers and performs holistic bus holding decisions by modelling the bus holding problem as a discrete, nonlinear, constrained optimization problem. Given the computational complexity of the bus holding problem, an alternating minimization approach is introduced for computing the optimal holding times at each optimization instance. The performance of the periodic control method is evaluated against the performance of event-based control methods using 5-month automated vehicle location and automated passenger count data from bus line 1 in Stockholm for contacting simulation-based experiments. [ABSTRACT FROM AUTHOR]

In an uncontrolled bus line, buses tend to bunch due to the stochastic nature of traffic flow and passenger demand at bus stops. Although bus holding has been shown to effectively prevent bus bunching, this control method often fails when disturbances are large and frequent. A coordinated control method combining two control means (bus holding and stop-skipping) is proposed instead of using only one control means. Bus holding and stop-skipping are integrated with the concept of predictive control. Considering the conciseness and convenience in applications, herein, we propose an analytical method to automatically equalize bus headways in a single line by analyzing bus headways between both its leading and following buses, as well as the number of waiting passengers at the bus stops. Numerical tests conducted in a simplified scenario and random scenario show that the proposed coordinated control method performs better in terms of headway convergence rate and resisting random disturbance than using bus holding only. Moreover, a set of simulation tests based on an actual bus route showed better performance of the proposed coordinated control method with increasing demand in terms of regulating the bus headway, saving the total travel time, and providing reliable service for passengers. [ABSTRACT FROM AUTHOR]

This paper presents a multi-modal framework for modelling and analysing different headway control strategies for improving bus service regularity. The interaction between buses and their surrounding traffic is captured in a multi-modal system through a Hamilton–Jacobi formulation of kinematic wave model. This paper further presents a set of signal-based strategies which regulate bus headway through adjusting signal timing plans. The results reveal that the capability of regulating bus headway disturbances through utilising traffic signals is important for maximising bus service regularity and coordinating the bus dynamics with surrounding traffic. This study generates new insights on managing bus reliability and multi-modal traffic in busy urban networks. [ABSTRACT FROM AUTHOR]

• Speed adjustment strategy proposed to resist bus bunching. • Various speed adjustment schedules in the dedicated bus lane are considered. • Multi-CTP looking-ahead mechanism is used to determine the regulating speed. • The stability of a bus line is improved with the reduced waiting and riding times of passengers. Bus bunching and the unevenly dispersed buses along a bus line commonly appear in an unstable high-frequency bus line system. They will lead to unreliable transit service and long waiting times for many passengers. To resist bus bunching and improve the stability of a bus line, researchers proposed some methods of adjusting the cruising speeds of buses. But their methods generally need to adjust the speeds in all road segments included in the bus line and sometimes need to coordinate the speeds of successively cruising buses. These requirements impede their implementations in practice. This paper presents a new strategy to overcome the above obstacles by adjusting the speeds of buses in the dedicated bus lanes. The regulating speed will be determined by looking multiple critical time points ahead to estimate the influence of the chosen speed. Numerical experiments show that the new strategy can not only stabilize a strongly unstable bus line but also shorten the waiting and riding times of passengers. Several insights have also been uncovered during numerical analyses. a. The set of regulating speeds used by an effective speed adjustment strategy should include refined elements and has a wide range for the values of its elements. b. Only with nonnegative elements in the above set, the strategy will be out of work. c. The more dedicated bus lanes in a bus line, the more effective the strategy becomes. The negligible computational time to supply the proper regulating speed makes the implementation of our strategy practical. [ABSTRACT FROM AUTHOR]

Autonomous Modular Buses (AMBs) with in-motion transfer capability can be more effective in preventing bus bunching than strategies available with conventional buses, such as bus-holding and/or stop-skipping. We previously proposed bus-splitting , a novel alternative to stop-skipping that directs a modular bus to decouple into individual units when it experiences a longer than normal headway. Despite outperforming stop-skipping, bus-splitting alone cannot eliminate bunching completely since it cannot increase short headways. Therefore, we now propose an integrated strategy that combines bus-splitting with bus-holding so that headways that are both shorter or longer than required can be corrected. We conduct a macroscopic simulation based on a bus route in Hangzhou, China, to compare our combined strategy with standalone bus-splitting as well as stop-skipping combined with bus-holding. Our strategy outperforms the others in terms of reducing both the average travel cost and its variation, limiting the overhead of bus bunching to below 10% under realistic system utilization levels. A bus service adopting the proposed strategy would therefore be more cost-effective, reliable, and attractive for commuters, potentially increasing its ridership and reducing the mode share of private vehicles. • Develops hybrid splitting+holding strategy to mitigate bus bunching. • Evaluates proposed strategy against standalone splitting and skipping-based strategy. • Conducts case study of a route in Hangzhou, China. • Proposed strategy significantly reduces average and variability of travel cost. • Even naïve AMB-based strategies outperform refined conventional strategies. [ABSTRACT FROM AUTHOR]

Bus bunching is a long-standing problem in transit operation and ruining the regularity of transit service. In a typical urban transit network setting of multiple lines with a shared corridor, bus bunching becomes more frequent as there is more uncertainty inside the shared corridor. While multi-agent reinforcement learning (MARL) has been a promising scheme for learning efficient control policy in a multi-agent system, few studies have explored its applicability in multi-line transit control scenarios. In this study, we focus on a basic transit network where there are two bus lines with a shared corridor. An efficient MARL framework is proposed to learn multi-line bus holding control to avoid bus bunching. Specifically, we design observation and reward functions that incorporate multi-line information. In addition, a preference weights producer is introduced to update the objective weights towards a good trajectory evaluation during daily transit operation. In this way, we handle the multi-objective issue in multi-line control. In experimental studies, we validate the superiority of the method in real-world bus lines. Results show that the state and reward augmented with multi-line information benefit MARL in multi-line bus control. Besides, by updating preference weights towards less passenger waiting time, the regularity of transit service is further improved. • We are the first to design a multi-agent reinforcement learning framework for multi-line bus control with shared corridor. • We address the multi-objective problem of multi-line control in multi-agent reinforcement learning. • Extensive experimental analyses are conducted to validate the performance of the proposed method. [ABSTRACT FROM AUTHOR]

This paper presents a real-time integrated holding and priority control strategy for bus rapid transit (BRT) and high-frequency segregated transit systems, in a network approach (considering the whole transit circuit). The integrated control strategy implements simultaneously the required bus headway corrections and the bus priority through signalized intersections with the objective of minimizing the total delay of passengers that are onboard and at stops. The developed model, in the form of a mathematical programming problem, presents peculiarities for describing the behavior of BRT and transit systems such as bus capacity, differentiation between passenger boarding and alighting processes in single stops, terminals and stations, and bus priority at signalized intersections. The iterative procedure proposed for solving the optimization problem brings about simplicity and efficiency for real-time applications. The results obtained by simulation for a transit scenario of the trunk line 10 of the city of Blumenau, Santa Catarina, Brazil, show the efficiency of the proposed strategy and potential of practical application. [ABSTRACT FROM AUTHOR]

• Bus substitution strategy with pooled standby fleet to control schedule deviations in multiline systems. • Stochastic dynamic program based on bus operation dynamics and substitution decisions • Approximate dynamic programming algorithm with offline simulations and estimation • Multi-period dynamic program to address fleet management in time-varying systems • Numerical examples demonstrate the performance and applicability of the proposed strategy Traditional bus bunching control methods (e.g., adding slack to schedules, adapting cruising speed), in one way or another, trade commercial speed for better system stability and, as a result, may impose the burden of additional travel time on passengers. Recently, a dynamic bus substitution strategy, where standby buses are dispatched to take over service from late/early buses, was proposed as an attempt to enhance system reliability without sacrificing too much passenger experience. This paper further studies this substitution strategy in the context of multiple bus lines under either time-independent or time-varying settings. In the latter scenario, the fleet of standby buses can be dynamically utilized to save on opportunity costs. We model the agency's substitution decisions and retired bus repositioning decisions as a stochastic dynamic program so as to obtain the optimal policy that minimizes the system-wide costs. Numerical results show that the dynamic substitution strategy can benefit from the "economies of scale" by pooling the standby fleet across lines, and there are also benefits from dynamic fleet management when transit demand varies over time. Numerical examples are presented to illustrate the applicability and advantage of the proposed strategy. The substitution strategy not only holds the promise to outperform traditional holding methods in terms of reducing passenger costs, they also can be used to complement other methods to better control very unstable systems. [ABSTRACT FROM AUTHOR]

Bunching is an operational problem, in bus transit systems with high service frequency, that can lower capacity and affects user satisfaction. The headway (i.e. amount of time between transit vehicle arrivals at a stop) is intrinsically unstable, such that minor disturbances can cause divergence from the scheduled service. In this paper, a bus route is modelled using a one-dimensional cellular automata to investigate the effects of variations in passenger demand on headway instability and the bus bunching phenomenon. Unlike previous research, this study utilizes a typical route design approach, rather than obtaining a phase diagram from random passenger demand and service frequency. The results show that a one-second decrease in boarding and alighting times per passenger can significantly reduce bunching formation. Such a reduction can be achieved by adopting in-station fare collection methods as opposed to onboard ones, and/or using low-floor buses with wider/multiple doors/channels. In addition, an active mitigation strategy is proposed to prevent the formation of bunching. It is shown that limiting the waiting time for the delayed bus at stops has a great effect on regulating headways and mitigating bunching. Further, to compare different bunching situations, a new index is proposed to evaluate bunching severity (i.e. the number of buses involved in bunching) and intensity (i.e. the overall deviation from the scheduled headway). Using the developed index, it is found that a high Peak-Hour Coefficient acts like an uncontrolled traffic light that regulates the bus flow, resulting in less severe bunching, regardless of the subsequent total delay in the service. [ABSTRACT FROM AUTHOR]

• A dynamic control point selection algorithm for bus holding strategy is proposed. • A rolling-horizon performance model predicts bus operational states. • A cooperative game model with Myerson value ranks control points. • Passenger waiting time and headway variation are reduced by simulation tests. Bus holding is a widely used control method to regularize bus headways and reduce bus bunching. The method works in such a way by delaying buses at control points if their departure times or headways deviate from the planned ones. However, it may result in reduced bus commercial speeds and increased passenger onboard travel time. To avoid this problem, researchers have suggested that control points be spaced cautiously along the route such that only a few are needed. This study proposes a predictive headway-based bus holding strategy with dynamic control point importance ranking and selection based on the cooperative game theory. The framework considers not only individual control points' impact but also the collective group control effects. Specifically, the proposed framework consists of two components: a performance model and a cooperative game model. The performance model predicts headway performances of all running buses when different control point combinations are in effect. Dynamic bus running times and passenger demands are reflected in the model. Then, these headway performances are passed to the cooperative game model with control points being players and improvements in headway performances compared with that under no holding control being the utility function. The game is solved by Myerson value, a concept that extends Shapley value used for the normal cooperative game and considers the cooperation structure and potential worth of coalitions. We use Myerson value to rank the importance of control points on regularizing headways, as it measures the average marginal utility contribution of a control point to all possible coalitions that exclude that point. We prove that Myerson value lies in the Ω-core of the game and thus satisfies allocation efficiency, individual and coalition rationality. The proposed framework is applied to target headway control and two-way-looking self-equalizing headway control. Simulation results show that the framework can significantly reduce passenger waiting time and bus headway variation. [ABSTRACT FROM AUTHOR]

Bus bunching is a well-known phenomenon for operators, users and regulators of high-frequency bus services. Bus operations are usually affected by increasing differences in the time intervals (headways) between consecutive buses. The effect of this variability is that buses tend to group into bunches of two or more, which severely affects the quality of service and the operational efficiency. The aim of this paper is to analyze which factors are associated to the phenomenon, using massive data from high-frequency services available in Santiago (Chile) and common-route services in Gatineau (Canada). The data is obtained from the bus GPS and AFC systems and are processed to obtain headways between buses. Using data from one week, we develop models to explain the variation of the continuous and discrete indicators of bus bunching as a function of variables related to the operation, variables related to the demand structure, and variables related to the infrastructure. Some of the factors that contribute to increase bus bunching are: stops located toward the end of the route, high scheduled frequency, irregular bus dispatch headways, non-homogeneous fleet, high demand, and high variability of demand. The results are useful for the design of quality indexes to measure bunching in bus operations, and for the design and operation of bus routes, taking into consideration the potential bus bunching problems. [ABSTRACT FROM AUTHOR]

Highlights • A dynamic bus motion model with delay disturbances and demand uncertainties is developed. • Robust dynamic control mechanism is designed to improve both schedule adherence and headway regularity. • The formulated nonlinear optimal control problem is converted to a convex optimization problem. • The proposed method significantly reduces the bus bunching and improves the schedule adherence of bus service lines. Abstract This paper proposes a robust dynamic control mechanism for bus transit system, taking account of variations in congestion delays and passenger demand, and combines bus holding and operating speed control strategies. By using a prespecified uncertainty set, we propose a state space model for bus motion with delay disturbances and passenger demand uncertainties. According to the Lyapunov function analysis method, we design a robust dynamic control based on the state-feedback scheme as the bus control to achieve the robust stability of the bus transit system, which effectively reduces the bus bunching phenomenon. Furthermore, we formulate a nonlinear optimal control problem to design the robust optimal bus control, which not only reduces the bus bunching, but also improves the schedule adherence and headway regularity of bus service lines. To handle the complexity of the nonlinear optimal control problem with uncertain parameters and disturbances, we reduce it to a convex optimization problem by the minimization of an upper bound on the objective function. The problem is solved in a polynomial time and satisfies the practical real time requirement. Numerical examples are presented to validate the effectiveness of the model and control methods. [ABSTRACT FROM AUTHOR]