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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.

We propose an optimal actuation of operational commands for regularizing bus headways. Assuming that a transit headway control system manages the bus operation by issuing reference arrival times at the next station for a bus, the problem is how to implement the control decisions for the bus in terms of three nonexclusive alternative actions: holding the bus at stops; varying bus speeds; and controlling traffic lights. Mathematical programming provides the basis of the approach. The constraints specify the bus trajectory model and the operator objectives are formulated as a multi-objective cost function solved by a lexicographic method. Results for a bus run on a single segment between two stops highlight the properties of the solution. A simulation study of an entire transit corridor in Quebec City, Canada, shows the advantage of the method over both headway control based on pure holding at stops and on one that combines holding and absolute transit signal priority.

In high-frequency electric bus services, bus operators strive to increase the service regularity by minimizing the deviation between the planned and actual headways. In this pursue, bus operators apply corrective control strategies, such as bus holding(s) at control point stops. This study expands the traditional headway-based, bus holding models to cater for the planned arrival times of electric buses at the respective charging points. To this end, this study models - for the first time - the bus holding problem for electric buses considering the scheduled charging times in the objective function. Additionally, it introduces an analytic solution that can return an optimal holding decision in real-time. Our approach is tested using realistic data from bus line 15 in Amsterdam demonstrating a significant reduction of charging delays with only a marginal increase of the average passenger waiting times when compared to existing holding strategies. Its closed-form expression is suitable for real-time holding control and can be applied to obtain a reliable solution or perform stochastic optimization in the case of travel time uncertainty. [ABSTRACT FROM AUTHOR]

In high frequency bus service lines buses often come irregularly at the stops, often in bunches, due to the uncertainty of the passenger demand and behavior and unexpected conditions on the roads. Vehicle holding is a commonly used strategy among a variety of control strategies in transit operation in order to reduce bus bunching and regulate bus headways. This paper investigates a control strategy of holding a group of buses at a single or multiple control point(s). By incorporating any passenger boarding activities during holding, a single control point problem is developed and extended to multiple control points to reduce the variance of headways for the downstream stops. The problem is a non-convex optimization problem with linear constraints that minimizes the total passenger waiting time both on-board and at stops. A heuristic is then developed that is easy and fast to implement, which makes it suitable for real-time implementation. The model is evaluated with a simulation case study by using the real-time bus operation data (i. e., Automatic Vehicle Location and Automatic Passenger Count Data) from the Chicago Transit Authority (CTA). The simulation results show that considering the boarding activities in the total waiting time, our model mitigates the error propagation and maintains steady performance, compared to the common models in the literature, which do not consider boarding while holding. © 2012 Springer-Verlag Berlin Heidelberg.

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]

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]

• 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]

• A decentralized DRL signal control for multi-modal traffic networks is introduced based on a microscopic environment. • Car traffic and bus performances are improved simultaneously and traded off. • The proposed method is applicable to different bus lane layouts and multiple bus lines. • The scalability and transferability of the model are verified. Managing traffic flow at intersections in a large-scale network remains challenging. Multi-modal signalized intersections integrate various objectives, including minimizing the queue length and maintaining constant bus headway. Inefficient traffic signals and bus headway control strategies may cause severe traffic jams, high delays for bus passengers, and bus bunching that harms bus line operations. To simultaneously improve the level of service for car traffic and the bus system in a multi-modal network, this paper integrates bus priority and holding with traffic signal control via decentralized controllers based on Reinforcement Learning (RL). The controller agents act and learn from a synthetic traffic environment built with the microscopic traffic simulator SUMO. Action information is shared among agents to achieve cooperation, forming a Multi-Agent Reinforcement Learning (MARL) framework. The agents simultaneously aim to minimize vehicles' total stopping time and homogenize the forward and backward space headways for buses approaching intersections at each decision step. The Deep Q-Network (DQN) algorithm is applied to manage the continuity of the state space. The tradeoff between the bus transit and car traffic objectives is discussed using various numerical experiments. The introduced method is tested in scenarios with distinct bus lane layouts and bus line deployments. The proposed controller outperforms model-based adaptive control methods and the centralized RL method regarding global traffic efficiency and bus transit stability. Furthermore, the remarkable scalability and transferability of trained models are demonstrated by applying them to several different test networks without retraining. [ABSTRACT FROM AUTHOR]

In uncontrolled bus systems, buses tend to bunch due to the stochastic nature of traffic flows and passenger demand at bus stops. Although schedules and priori target methods introduce slack time to delay buses at control points to maintain constant headways between successive buses, too much slack required delay passengers on-board. In addition, these methods focus on regular headways and do not consider the rates of convergence of headways after disturbances. We propose a self-adaptive control scheme to equalize the headways of buses with little slack in a single line automatically. The proposed method only requires the information from the current bus at the control point and both its leading and following buses. This elegant method is shown to regulate headways faster than existing methods. In addition, compared to previous self-equalizing methods, the proposed method can improve the travel time of buses by about 12%, while keeping the waiting time of passengers almost the same. [ABSTRACT FROM AUTHOR]

Bus holding is a commonly used control strategy used in transit operations for the purpose of improving transit service reliability; its implementation requires dynamic decision-making in an interactive and stochastic system environment. This paper presents a distributed cooperative holding control formulation based on a multi-agent reinforcement-learning (MARL) framework to optimize real-time operations of public transport system. We use agent technology to model buses operation on a transit corridor. In the MARL framework, each bus agent is modeled as a coordinated reinforcement learner when it dwells at a stop for which the state, actions, reward function and operation constraints are defined. In the absence of coordination mechanisms for the multiple agent case, different agents may break these ties between multiple optimal joint actions in different ways, and the resulting joint may be suboptimal. Coordination Graphs (CGs) are thus applied in a cooperative holding action selection, which considers the holding action of bus agent depends on its backward and forward and edge-based decomposes the global payoff function into a linear combination of local payoff functions. Variable Elimination (VE) algorithms are proposed to obtain the best cooperative joint holding action due to the particularity of the sparsely structured graphs. The simulation results show the advantages of the MARL framework for distributed holding control. [ABSTRACT FROM AUTHOR]

Models are formulated to predict the added vehicle and person delays that can occur when a bus stop is located a short distance upstream or downstream of a signalized intersection. Included in the set of models are those that predict the expected delays that cars collectively incur when a bus blocks one of multiple lanes while loading and unloading passengers at the stop. Others in this set predict the expected added delays incurred by the bus due to car queues. Each model is consistent with the kinematic wave theory of highway traffic, as is confirmed through a battery of tests. And each accounts for the randomness in both, bus arrival times at a stop, and the durations that buses dwell there to serve passengers. Though the models are analytical in form, solutions come through iteration. Hence model applications are performed with the aid of a computer. The applications presented herein show that bus delays can often be shortened by placing the bus stop downstream of its neighboring signalized intersection, rather than upstream of it. In contrast, car delays are often shortened by placing the stop some distance upstream of the intersection, rather than downstream. We further show how exerting a measure of control on bus arrivals can further enhance these benefits to cars without further delaying the buses. The models are also used to assess the net person delays collectively incurred by car- and bus-travelers. [ABSTRACT FROM AUTHOR]

This paper develops an infrastructure-enabled eco-approach specifically for transit systems, where a two-stage simulation approach is proposed to include the impact of bus stops, and can further quantify the effects of infrastructure-enabled eco-approach on transit operating and service. The developed system is then embedded into a well-developed simulation environment, i.e., Simulation of Urban Mobility (SUMO), and a series of real-world-based cases are designed to compare the proposed system with traditional method and non-control case at segment-, line-, and network-level service respectively. Results reveal that the proposed method outperforms the traditional eco approach and can significantly improve the energy efficiency and reduce CO 2 emission by up to 54.33%, where the environmental benefits are more clearly seen when more transit services are involved. In particular, it has the capability of marginalizing the speed fluctuations around the bus stop. [ABSTRACT FROM AUTHOR]

Abstract: Bus stops are often placed short distances upstream of signalized intersections. Buses that dwell at one of these so-called near-side stops can impede queued cars upstream from discharging through the intersection during green times. Residual car queues can form at the intersection as a result. The smaller the distance between a stop and its intersection, the greater the problem can be. Models are formulated to address this problem using kinematic wave theory. The models can be used to determine where to place a near-side stop to achieve a target level of residual car queueing. In addition, the models are used herein to develop a scheme for mitigating residual car queues by briefly detaining some buses from reaching the stop. The scheme can be applied selectively, so that the times that detained buses depart from the stop are not postponed. The buses are therefore not delayed over the longer run. Analysis indicates that this bus-holding scheme can significantly reduce car delays and queueing. Our models for placing stops and holding buses are shown to be robust to systematic and random changes in car flow. [Copyright &y& Elsevier]

A distributed control approach based on multiagent negotiation is presented, wherein stops and buses act as agents that communicate in real-time to achieve dynamic coordination of bus dispatching at various stops. The negotiation between a Bus Agent and a Stop Agent is conducted based on marginal cost calculations. We present optimality conditions for the formulated problem, using a negotiation algorithm, which we derive, to coordinate bus holding at various stops. A comparison between the negotiation algorithm and other simple bus control strategies such as on-schedule and even-headway strategies made through simulations verifies the robustness and efficiency of our negotiation strategy to different transit environments, involving both stationary passenger arrivals as well as a variety of nonstationary passenger arrivals. [ABSTRACT FROM PUBLISHER]

To solve the problems of bus bunching and large gaps, this study combines bus holding and speed adjusting to alleviate them respectively considering the characteristics of passenger's perceived waiting time. The difference between passenger's perceived waiting time at stops and actual time is described quantitatively through the expected waiting time of passengers. Bus holding based on a threshold method is implemented at any stops for bunching buses, and speed adjusting based on a Markovian decision model is implemented at limited stops for lagging buses. Simulations based on real data of a bus route show that the integrated control strategy is able to improve the service reliability and to decrease passengers' perceived waiting time at stops. Several insights have been uncovered through performance analysis: (1) The increase of holding control strength results in improvement of the headway regularity, and leads to a greater perceived waiting time though; (2) Compared to traveling freely, suitable speed guidance will not slow down the average cruising speed in the trip; (3) The scale of passenger demand and through passengers are the two key factors influencing whether a stop should be selected as a speed-adjusting control point. [ABSTRACT FROM AUTHOR]

• Analytic solution for the single variable bus holding problem considering capacity limits. • The holding time of a vehicle can be determined in real time. • Significant reduction of stranded passengers in the expense of a slight regularity deterioration. • The service regularity performance is relatively insensitive to demand variations. This study focuses on single variable optimization approaches which determine the holding time of a vehicle when it is ready to depart from a bus stop. Up to now, single variable optimization methods resort to rule-based control logics to equalize the inter-departure headways or adhere to the target headway values. One of them is the two-headway-based control logic which determines the holding time of a bus based on its headway with its preceding and following bus without addressing other implications, such as overcrowding. To rectify this, we introduce a new model for the single variable bus holding problem that considers the passenger demand and vehicle capacity limits. Then, we reformulate this problem to an easier-to-solve program with the use of slack variables and introduce an analytic solution that can determine the holding time of a vehicle at the respective bus stop. Our analytic solution does not add a computational burden to the two-headway-based control logic and can be applied in real time. The operational benefit of our bus holding approach compared to other analytic solutions that do not consider the vehicle capacity is investigated using actual data from bus line 302 in Singapore. [ABSTRACT FROM AUTHOR]