Bus Bridging Service Research Articles

Analysis of multi-modal public transportation system performance under metro disruptions: A dynamic resilience assessment framework

The well-functioning multi-modal public transportation systems play crucial roles in reducing traffic congestion, alleviating environmental pollution, and improving mobility. There are variants of disruptions that may impede the smooth functioning of public transportation systems and challenge their normal operations. It is essential to develop resilient multi-modal public transportation systems, and a reasonable resilience assessment framework serves as the foundation for developing such systems. In this paper, we propose a resilience assessment framework based on performance-based measurement metrics. We develop a dynamic simulation procedure that considers the impacts of disruptions on passenger choices of path and departure time. By incorporating these features into the simulation procedure, we can effectively model the variations of passenger flow under disruptions. Finally, to demonstrate the proposed resilience assessment framework and dynamic simulation procedure, the multi-modal public transportation system in Beijing is considered as a case study. The results reveal that the system exhibits good resistance and recovery capabilities, but it lacks robustness. Additionally, we discuss the effects of downtime, bus frequency, bus bridging services, and proportions of commuters on resilience, which lead to several valuable policy implications.

Collaborative optimization of passenger flow control and bus-bridging services in commuting metro lines

With the advantages of high speed and punctuality, urban rail transit has become the preferred choice for many commuters. However, overcrowding of urban rail transit lines during peak hours is a common problem in megacities owing to the excessive passenger demand. To address this problem, this study proposes an integrated optimization method that combines passenger flow control and bus-bridging services. An integer nonlinear optimization model is developed to minimize the weighted passenger waiting time and operating cost of bus-bridging services by considering the coupling relationships between passenger movements on both the metro and buses. Then, the proposed model is equivalently transformed into a linear form with better mathematical properties, and variants of this model are further formulated to extend the usability. Finally, real-world case studies based on the operational data of the Beijing Metro Batong line are conducted to verify the effectiveness of the proposed methods. The computational results indicate that the proposed approach can effectively alleviate overcrowding and reduce passengers' waiting time, thereby improving the operational efficiency and safety of the urban rail transit system.

A stochastic programming model for designing bus bridging services under metro disruptions

ABSTRACT With the growing reliance on urban metro networks, any accidental disruption can lead to rapid degradation and significant economic losses. Bus bridging services are common and efficient ways to minimize such adverse impacts. In this study, we investigate the problem of designing bus bridging services in response to unexpected metro disruptions, and propose a routing strategy with multiple bridging routes. In particular, to respond to uncertain factors such as passenger arrivals and bus travel times in the disruption environment, we develop a two-stage stochastic programming model for the collaborative optimization of bus bridging routes, schedules, and passenger assignments. To solve the computational challenges arising with the proposed model, a tailored tabu search algorithm is developed. Finally, several sets of numerical experiments are conducted and experimental results reveal that our proposed routing strategy can effectively improve the service level for the affected passengers during metro disruptions.

Urban rail transit disruption management based on passenger guidance and extended bus bridging service considering uncertain bus running time

Disruptions occurring at an urban rail transit (URT) system can severely affect its normal operations, and an effective bus bridging service (BBS) is able to help to reduce the negative effects. Transit operators usually arrange BBS to depart from the disrupted stations to evacuate the stranded passengers. However, the overload of passengers at the disrupted stations, especially at turnover and transfer stations, may incur the secondary operation disruptions such as stampede accidents. To mitigate the negative effects of disruptions and reduce the number of passengers stranded at the disrupted stations, the strategy based on the passenger guidance and extended BBS (E-BBS) is introduced in this paper. Different from the widely applied standard BBS running within the disrupted links, E-BBS runs among the normal operating stations or between the normal operating stations and the disrupted stations. A mixed integer linear programming model is developed in this paper to guide the stranded passengers and design an optimal E-BBS solution to transport them. Considering the bi-directional running trains along the disrupted links, a dynamic decision framework is developed to manage the disruptions. Given the impacts of the high uncertainty on bus running time which could affect the performance of E-BBS, a robust model is proposed to obtain more reliable travel guidance and E-BBS schemes. Numerical experiments based on Chengdu subway system in China are conducted. The results indicate that the proposed model can obtain optimal travel guidance and E-BBS solutions in a timely manner. When the uncertainty on bus running time is ignored, the total travel cost for affected passengers is reduced 14.20 % on average with the aid of the optimal travel guidance and E-BBS solutions. Moreover, the number of passengers gathering at the disrupted stations decreases by 36.80 %. The robust model can obtain more reliable travel guidance and E-BBS schemes in consideration of uncertain bus running time. The proposed model shows great potential to effectively mitigate the negative effects of disruptions and help to enhance the capability of a URT system to respond to disruptions.

Bus Rescheduling for Long-Term Benefits: An Integrated Model Focusing on Service Capability and Regularity

Unplanned disruptions, such as vehicle breakdowns, in a public transportation system can lead to severe delays and even service interruptions, preventing the successful implementation of subsequent plans and the overall stability of transit services. A common solution to address such issues is implementing a bus bridging service using an experience-based response strategy, involving the deployment of spare buses to continue affected services. However, with this approach, it becomes impractical and challenging to generate a feasible and rational rescheduling scheme for the remaining transit services when spare buses are insufficient or widespread disruptions occur. In response to this challenge, we propose an innovative model that integrates service capability and regularity, aiming to minimize rescheduling costs through timetable adjustments and scheduling reassignments. We apply dynamic programming to comprehensively consider the hysteresis effects of disruptions and achieve a long-term optimal rescheduling scheme. To efficiently solve the proposed model, the large neighborhood search algorithm is improved by incorporating operational rules. Finally, several experiments are conducted under an actual transit operation scenario in Shenzhen. The results demonstrate that our method significantly reduces trip cancellations and, simultaneously, diminishes the increase in the departure interval resulting from the adjusted schedule by 23.27%.

Modelling and accelerating the passenger evacuation process in a bi-modal system with bus and e-hailing modes after mass gathering events

After mass gathering events, passenger trip demand surges immediately within a small area. While organized bus bridging services would be usually offered in such circumstances to speed up passenger evacuation, many people prefer the more comfortable e-hailing service to leave the area. However, the use of e-hailing services for speedy passenger evacuation is a double-edged sword. On the one hand, e-hailing vehicles supplement to buses by offering more transportation supplies; on the other hand, the large inflows of e-hailing vehicles and the time-consuming passenger-driver (offline) searching process would lead to a huge vehicle accumulation within the area, thus lower vehicle speed and reduce bus evacuation efficiency. This paper proposes a mathematical model to depict the dynamic passenger evacuation rates and traffic conditions in a bi-modal system with both bus and e-hailing services for passenger evacuation. Numerical examples show that e-hailing service could significantly deteriorate the evacuation process when the arrival rates of e-hailing vehicles are high. Thus we further propose two feedback based perimeter control strategies that control the total inflow rates of e-hailing vehicles and background traffic, based on the vehicle accumulation and the number of parked vehicles within the area respectively. As shown by simulation experiments, both perimeter control strategies can effectively improve evacuation efficiency in the presence of e-hailing vehicles, especially when bus frequency is low, passenger demand is high, and/or the number of parking spaces is limited.

Enhancing resilience assessment and bus bridging service design for large‐scale rail transit systems under disruptions

AbstractThis paper proposes a more computationally efficient approach for resilience assessment of rail transit system under disruptions. An improved linear programming model is developed to depict commuter flows and estimate system statuses. To address the computational challenge caused by the complexity of system, a four‐step approach is proposed based on the proposed commuter flow model. In the first step, Origin‐Destination (OD) pairs are divided into smaller groups and their flows under normal conditions are estimated by the proposed model separately, with the assumption that the railway capacity is sufficient relative to demand. Next, overall system statuses under normal conditions, including commuters on each train and spare capacities of each train are calculated by integrating results obtained in the first step. In the third step, system statuses under disruptions are estimated. In this step, we assume that unaffected commuters will not change their routes and flows of all affected commuters are estimated by a modified commuter model with given spare space of trains. Based on these outputs, several critical measures are introduced and calculated to quantify the resilience, resistance, and recovery ability of rail network systematically. We also demonstrate how our approach could be used to facilitate design and evaluation of bus bridging service. The proposed approach is demonstrated on the core part of Hangzhou rail transit network.

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.

Integrated optimization of bus bridging service design and passenger assignment in response to urban rail transit disruptions

As the urban rail transit (URT) system plays an increasingly important role in supporting large cities’ mobility around the world, service disruptions have become more prevalent, potentially resulting in severe economic losses and passenger safety issues. It is imperative to investigate effective response strategies to mitigate the effects of such disruptions. In response to URT service disruptions, this paper systematically investigates the bus bridging service design (BBSD) problem, which concerns the integration of bus bridging route design, frequency determination, and passenger assignment in the integrated URT and bus network. The problem is formulated as a path-based integer linear programming (ILP) model with the goal of simultaneously minimizing operator-oriented and passenger-oriented costs. A column generation-based approach is proposed to solve this model efficiently, allowing nonintuitive bus routes to be freely generated on the network dynamically. Our method has been tested with two different case studies based on real data from the Hong Kong Mass Transit Railway (MTR). Experiments demonstrate that our proposed approach can assist public transit (PT) operators in developing efficient emergency response plans for various potential disruption situations in advance. Even in the face of unexpected disruptions that necessitate a quick response, our approach can generate high-quality solutions in a matter of minutes.

An Optimization Approach considering Passengers’ Space-Time Requirements for Bus Bridging Service under URT Disruption

Rapid urbanization and growth of population in megacities generate severe pressures on urban rail transit (URT) system. The quantity and frequency of disruptive events have increased significantly, which might have obvious adverse impacts. A large number of passengers are stranded at disrupted URT station when a disruptive event occurs. One essential solution for passenger evacuation is the bus bridging service. This paper is aimed at addressing the passenger evacuation problem caused by a disruptive event in the URT network, by proposing a bus bridging service model considering the passengers’ space-time requirements. The model is proposed to minimize the waiting time of passengers and considers factors including bus service capacity limitations, bus stop parking capacity, and the maximum bridging time limit of a single bus. Buses are assumed to provide bridging service on either the local bus route or the direct bus route. The optimal routes and scheduling plans of bridging bus are designed. The model is applied to an example of a disruptive event in Shanghai URT line 9. The results of this example show that the proposed model is capable of reducing the waiting time of passengers and the number of buses used by 3.2% and 24.7%, compared with the traditional bus bridging service. Further analysis of the example shows that it is not a cost-effective solution to reserve a large number of buses for URT disruption. Decision-makers should comprehensively trade off between passengers’ space-time demands and monetary costs of bus bridging service.

Real-time dispatching of operating buses during unplanned disruptions to urban rail transit system

Unplanned disruptions to urban rail systems can result in widespread confusion and severe delays, and running bus bridging service is a common solution. Currently, transit operators usually adopt experience-based response strategy in such a way that spare buses from bus terminals and parking lots are used to run bus bridging services. Such a response approach can be effective when there are spare buses available at nearby terminals/parking lots. However, in case spare buses are not available or enough, it could be beneficial to dispatch running buses from nearby operating bus lines to ensure efficient response while incurring minimal inconvenience to on-board passengers. While this approach could reduce metro users’ delays, it causes extra delays and dissatisfaction to affected bus riders. In this study, we investigate the optimal bus dispatching problem for responding to unplanned disruptions of urban rail transit system with two bus fleet sources: (1) spare buses at terminals and parking lots, and (2) running buses from nearby operating bus lines. To obtain the optimal dispatching scheme, we develop an integer programming model, which achieves a balance between the delays of metro users and that of bus riders. Considering of the high uncertainty of bus headways which could affect the performance of the above deterministic model, we further develop a robust optimization model to obtain more reliable bus dispatching schemes. Case studies based on the data sets in Shanghai are conducted. The results demonstrate that our approach can be carried out in real-time, and employing running buses from operating bus lines shows great potential in reducing affected users’ delays. In addition, the robust model offers a more reliable and competitive solution when the headway varies widely.

Scheduling multimodal alternative services for managing infrastructure maintenance possessions in railway networks

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

Optimizing Disruption Tolerance for Rail Transit Networks Under Uncertainty

In this paper, we develop a distributionally robust optimization model for the design of rail transit tactical planning strategies and disruption tolerance enhancement under downtime uncertainty. First, a novel performance function evaluating the rail transit disruption tolerance is proposed. Specifically, the performance function maximizes the worst-case expected downtime that can be tolerated by rail transit networks over a family of probability distributions of random disruption events given a threshold commuter outflow. This tolerance function is then applied to an optimization problem for the planning design of platform downtime protection and bus-bridging services given budget constraints. In particular, our implementation of platform downtime protection strategy relaxes standard assumptions of robust protection made in network fortification and interdiction literature. The resulting optimization problem can be regarded as a special variation of a two-stage distributionally robust optimization model. In order to achieve computational tractability, optimality conditions of the model are identified. This allows us to obtain a linear mixed-integer reformulation that can be solved efficiently by solvers like CPLEX. Finally, we show some insightful results based on the core part of Singapore Mass Rapid Transit Network.

First train timetabling and bus service bridging in intermodal bus-and-train transit networks

Subway system is the main mode of transportation for city dwellers and is a quite significant backbone to a city's operations. One of the challenges of subway network operation is the scheduling of the first trains each morning and its impact on transfers. To deal with this challenge, some cities (e.g. Beijing) use bus ‘bridging’ services, temporarily substituting segments of the subway network. The present paper optimally identifies when to start each train and bus bridging service in an intermodal transit network. Starting from a mixed integer nonlinear programming model for the first train timetabling problem, we linearize and reformulate the model using the auxiliary binary variables. Following that, the bus bridging model is developed to cooperate with the first train operation for reducing long transfer waiting times. After realizing the low computational efficiency of solving the integrated model, a tailored algorithm is designed to optimally solve the first train timetabling and bus service bridging problems. The exact models and algorithms are applied to the Beijing subway network to test their effectiveness and computational efficiency. Numerical results show that our approaches decrease the total passenger waiting time by 53.4% by a combined effect of adjusting the first train departure times and operating 27 bridging buses on 7 routes.

Multi-disruption resilience assessment of rail transit systems with optimized commuter flows

This paper studies the resilient performance of urban rail transit systems by extending a linear programming optimization model, which can provide optimized commuter flows with contingency routing under multiple disruptions. The rail transit systems in Singapore and Chongqing (China) are selected as case studies, and the system resilience and the effectiveness of providing bus-bridging services are comparatively studied. Intuitively, failures of the interchange stations would inevitably lead to a significant loss of resilience due to deteriorated network connectivity. However, the Singapore case shows that attacking those interchange stations does not always result in an extensive resilience loss. Comparing with the Chongqing case, it is discernible that the position of interchange stations would affect the system resilience. The numerical simulations reveal that the positive effect of providing bus-bridging strategy, in terms of improving the system resilience, is heterogeneous in different systems, which varies from 14% to 30% on average. As demonstrated in the sensitivity on travel demands, this positive effect is robust, yet dynamic, indicating that there is no one-size-fits-all solution for designing transfer-based recovery strategies in disruption management of rail transit systems. The managerial implications for decision makers are also provided and discussed in terms of infrastructure planning.

Assessing the Bus Bridging Effectiveness on the Operational Resilience of the Subway Service in Toronto

Unplanned rail disruptions result in substantial delays to passengers and severe effects on the economy of a large city like Toronto. While bus bridging has been a widely adopted method to replace the subway service in such events, its effect on the operational resilience of the subway service is less often studied. This study assesses the resilience of the subway network of Toronto employing an optimal bus bridging strategy. First, subway incidents are categorized based on their characteristics using K-mean clustering analysis. The incidents are then grouped based on the performance of optimal bus bridging plans. Classification and regression tree analysis is used for this task, employing two metrics: the total user delay and total number of shuttle buses under the optimal bridging scenario. Queueing and optimization models developed previously by the University of Toronto are used to determine and simulate the optimal bus bridging plans of a sample of incidents. The severity of unplanned disruptions is finally demonstrated using a severity scale and the effect of incident duration uncertainty is analyzed. The results show that along the congested city alignments, where the capacity of the roads and stations is limited, the bus bridging service is often insufficient to replace the train service. However, it could be a good alternative in uncongested subway segments where the available street capacity is relatively high, allowing large bus volumes to serve the corridor. This model is easily applicable to different rail systems and it could assess other systems to produce better bridging plans.

Integrated optimization of bus bridging routes and timetables for rail disruptions

A rail disruption may lead to rapid degradation of the public transportation system. In response to rail disruptions, this study focuses on bus bridging service design considering a routing strategy that combines express and short-turn routes. An integrated optimization framework is proposed to jointly optimize the bus bridging routes and timetables under time-varying demand. A brute-force search method is developed to identify all candidate bus bridging routes. A mixed integer linear programming model is then formulated to solve the route selection, bus deployment, and bus timetabling problem simultaneously. To handle the arising computational challenges in solving this large-scale problem, a tabu search-based heuristic with LP rounding is developed. Numerical studies based on Cranbourne Line, Melbourne, demonstrates the applicability of the proposed approach in practice. The results indicate that the proposed framework can generate high-quality bus bridging solutions in a reasonable time, which allows quick response to rail line disruptions. The bus bridging strategy with multiple routes outperforms the standard bridging route in terms of bus line capacity and passenger travel time.

Railway disruption management: Designing bus bridging services under uncertainty

In this paper, we study the rail transit disruption recovery problem under uncertainty, considering features of public transit network and commuters’ behavior in disruption. To be specific, our work highlights that spare capacities of operating rail and bus lines can provide complementary services to disrupted commuters and should be taken into consideration in disruption recovery plan. To this end, an integrated network is constructed, which consists of remaining available rail lines, existing operating bus lines and newly introduced bridging bus lines. Based on this network, alternative traveling routes for disrupted commuters are generated from a multimodal k-shortest path model. The model captures the fact that commuters can have several alternative routes in practice. They usually select one from them rather than insist on the shortest path. In addition, commuters may transfer between different lines when rerouting their travel. Based on the outputs of the aforementioned models, a stochastic programming model is developed for the design of bus bridging services plan within bus resource limit. The objective of the model is to minimize the expected unsatisfied commuter demand under rail transit disruptions, considering uncertainties in commuter demand and spare capacities of existing rail and bus lines. The proposed models are demonstrated on the core part of the Singapore Mass Rapid Transit network.

A social equity lens on bus bridging and ride-hailing responses to unplanned subway disruptions

During subway disruptions, commuters are often left stranded while they wait for bus bridging services. Some are able to change their mode of transport midway through their trip, often by requesting a ride-hailing service like Uber or Lyft if they are affordable. Many agencies use in-service buses to provide bus bridging services during subway disruptions, leading to reduced levels of service for other bus riders. Bus bridging policies and the affordability of ride-hailing raise questions regarding the equitable distribution of transit capacity during subway disruptions. After analyzing 78 major subway disruptions in Toronto, we found that bus routes serving disadvantaged populations were more likely to be negatively impacted by diversions for subway disruptions, than routes operating in more affluent areas of the city. We also found that ride-hailing demand increased during subway disruptions, but not in the more disadvantaged neighbourhoods. The research points to inequalities in how transit riders are impacted by subway disruptions, and further identifies how ride-hailing actually serves to reinforce these inequalities, rather than ameliorate them.

Evacuating metro passengers via the urban bus system under uncertain disruption recovery time and heterogeneous risk-taking behaviour

The bus-bridging service has always faced problems in severe emergencies or catastrophes that require the large-scale evacuation of passengers. This paper provides an alternative evacuation scheme which uses the urban bus network in the case of common metro service disruptions; this is modeled by minimizing the total cost of the affected metro passengers, through jointly selecting the bus lines and frequencies. The uncertain recovery time of the service disruption and the heterogeneous risk-taking behavior of the affected metro passengers are incorporated in the scheme. Therefore, we build a linkage between the evacuation service design and the risk-taking behavior of passengers. A heuristic algorithm is proposed to calculate the optimal evacuation scheme. A numerical experiment using a real-world network is conducted to illustrate the validity of the model and algorithm.