Transition Operator Research Articles

Rearrangement and breakup amplitudes from the solution of Faddeev-AGS equations by pseudo-state discretization of the two-particle continuum

The AGS equations for rearrangement transition operators in the three-particle problem are turned into a set of effective multi-channel two-body equations using the pseudo-state discretization of the two-particle resolvent. The resulting effective equations are LS-type integral equations in the spectator degrees of freedom, much like the LS equations of multichannel inelastic scattering. In particular, the effective potential matrix is real, energy-independent and non-singular, while the propagator matrix has only simple poles. Difficulties associated with the moving singularities of the effective potential matrix in the usual separable-T approach to AGS equations are avoided. After regularization of the kernel via subtraction procedures well known from two-particle scattering, the set of coupled LS-type equations in the spectator momenta are solved rather straightforwardly by the Nyström method. Solutions of effective two-body equations are then used to calculate the breakup amplitudes using the well-known relationship between rearrangement and breakup amplitudes. Calculations using a local momentum-space basis on a benchmark model of the n+d collision show that rather accurate results for elastic and breakup amplitudes can be obtained with rather small bases.

Plan Your System and Price for Free: Fast Algorithms for Multimodal Transit Operations

We study the problem of jointly pricing and designing a smart transit system, where a transit agency (the platform) controls a fleet of demand-responsive vehicles (cars) and a fixed line service (buses). The platform offers commuters a menu of options (modes) to travel between origin and destination (e.g., direct car trip, a bus ride, or a combination of the two), and commuters make a utility-maximizing choice within this menu, given the price of each mode. The goal of the platform is to determine an optimal set of modes to display to commuters, prices for these modes, and the design of the transit network in order to maximize the social welfare of the system. In this work, we tackle the commuter choice aspect of this problem, traditionally approached via computationally intensive bilevel programming techniques. In particular, we develop a framework that efficiently decouples the pricing and network design problem: Given an efficient (approximation) algorithm for centralized network design without prices, there exists an efficient (approximation) algorithm for decentralized network design with prices and commuter choice. We demonstrate the practicality of our framework via extensive numerical experiments on a real-world data set. We moreover explore the dependence of metrics such as welfare, revenue, and mode usage on (i) transfer costs and (ii) cost of contracting with on-demand service providers and exhibit the welfare gains of a fully integrated mobility system. Funding: This work was supported by the National Science Foundation [Awards CMMI-2308750, CNS-1952011, and CMMI-2144127]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.0452 .

Identification of Risk Factors for Bus Operation Based on Bayesian Network

Public transit has been continuously developing because of advocacy for low-carbon living, and concerns about its safety have gained prominence. The various factors that constitute the bus operating environment are extremely complex. Although existing research on operational security is crucial, previous studies often fail to fully represent this complexity. In this study, a novel method was proposed to identify the risk factors for bus operations based on a Bayesian network. Our research was based on monitoring data from the public transit system. First, the Tabu Search algorithm was applied to identify the optimal structure of the Bayesian network with the Bayesian Information Criterion. Second, the network parameters were calculated using bus monitoring data based on Bayesian Parameter Estimation. Finally, reasoning was conducted through prediction and diagnosis in the network. Additionally, the most probable explanation of bus operation spatial risk was identified. The results indicated that factors such as speed, traffic volume, isolation measures, intersections, bus stops, and lanes had a significant effect on the spatial risk of bus operation. In conclusion, the study findings can help avert dangers and support decision-making for the operation and management of public transit in metropolitan areas to enhance daily public transit safety.

Node Importance Evaluation of Urban Rail Transit Based on Signaling System Failure: A Case Study of the Nanjing Metro

Assessing the importance of nodes in urban rail transit systems helps enhance their ability to respond to emergencies and improve reliability in view of the fact that most of the existing methods for evaluating the importance of rail transit nodes ignore the disturbance effect of signaling system failures and are unable to objectively identify critical stations in specific disturbance scenarios. Therefore, this paper proposed a method for evaluating the importance of urban rail transit nodes in signaling system failure scenarios. The method was based on the research background of the signaling system failure that occurs most frequently and analyzed the network failure mechanism after the occurrence of a disturbance. The node importance evaluation indices were selected from the network topology and network operation performance in two aspects. The variation coefficient–VIKOR method was employed to comprehensively assess the significance of urban rail transit stations during signaling system failures. The Nanjing Metro network was also used as an example to evaluate the importance of network stations. The results showed that under the attack method of signaling system failure, most ECC and interlocking stations experienced significantly higher network performance losses compared to the original attack method, and a few interchange stations showed smaller performance losses. The critical stations identified based on the proposed method are mainly distributed in the passenger flow backbone of the Nanjing Metro and were constructed in the early stage; of these, 85% are ECC stations or interlocking stations, which are easily neglected in daily management, in contrast to interchange stations with heavy passenger flow. The results of this study can provide an important reference for the stable operation and sustainable construction of urban rail transit.

Capacity of infinite graphs over non-Archimedean ordered fields

In this article we study the notion of capacity of a vertex for infinite graphs over non-Archimedean fields. In contrast to graphs over the real field monotone limits do not need to exist. Thus, in our situation next to positive and null capacity there is a third case of divergent capacity. However, we show that either of these cases is independent of the choice of the vertex and is therefore a global property for connected graphs. The capacity is shown to connect the minimization of the energy, solutions of the Dirichlet problem and existence of a Green's function. We furthermore give sufficient criteria in form of a Nash-Williams test, study the relation to Hardy inequalities and discuss the existence of positive superharmonic functions. Finally, we investigate the analytic features of the transition operator in relation to the inverse of the Laplace operator.

Resilience of socio-technical transportation systems: A demand-driven community detection in human mobility structures

Existing scholarship on transportation resilience analysis has primarily focused on engineering resilience, often overlooking the intricate socio-technical dimensions. This oversight underscores the necessity for a more comprehensive understanding of the dynamic interplay between social, including travel behaviors, and technical infrastructure components within transportation systems. This article delves into the impact of “social shocks” on transportation systems, which are defined as disturbances affecting the social subsystem without yet affecting the technical subsystem. Drawing inspiration from C.S. Holling’s ecological resilience, which signifies a system’s ability to cope with change by adapting its structure and functionality, we propose a multi-level resilience assessment framework. It encompasses four mobility-related indicators: entropy (measuring network-level complexity), stationarity (assessing community compositional changes at the cluster level), and two node-level metrics — within-module degree and weighted participation coefficient — capturing location connectivity. These indicators proxy for evaluating the mobility structure and node functionality within the social subsystem. In a case study, we analyze historical smart card data to examine the mobility pattern’s structural changes within Hong Kong, a rail-oriented metropolis, during a prolonged and city-wide protest. The framework and associated indicators provide an alternative perspective for transit planners and operators, allowing them to assess both the overall system and individual stations, moving beyond traditional assessments of service supply and patronage changes.

Helicity evolution at small x: quark to gluon and gluon to quark transition operators

We include the quark to gluon and gluon to quark shock-wave transition operators into the small Bjorken-x evolution equations for helicity in the flavor-singlet channel derived earlier in [1–3]. While such transitions do not affect the large-Nc version of the evolution equations for helicity, the large-Nc & Nf equations are affected. (Nc and Nf are the numbers of quark colors and flavors, respectively.) We derive the corresponding corrected large-Nc & Nf equations for the polarized dipole amplitudes contributing to the flavor-singlet quark and gluon helicity distributions in the double-logarithmic approximation (DLA), resumming powers of αs ln2(1/x) with αs the strong coupling constant. We solve these equations iteratively and extract the polarized splitting functions up to four loops. We show that our splitting functions agree with the fixed-order perturbative calculations up to and including the existing three-loops results [4–7]. Similar to the large-Nc helicity evolution in the shock-wave approach [8], our large-Nc & Nf small-x splitting functions agree with those obtained in the infrared evolution equations framework from [9, 10] up to three loops, but appear to slightly disagree at four loops.

On representations and topological aspects of positive maps on non-unital quasi *- algebras

In this paper we provide a representation of a certain class of C*-valued positive sesquilinear and linear maps on non-unital quasi *-algebras, thus extending the results from Bellomonte (GNS-construction for positive C∗-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C^*-$$\\end{document}valued sesquilinear maps on a quasi ∗-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$*-$$\\end{document}algebra, Mediterr. J. Math., 21 166 (22 pp) (2024)) to the case of non-unital quasi *-algebras. Also, we illustrate our results on the concrete examples of non-unital Banach quasi *-algebras, such as the standard Hilbert module over a commutative C*-algebra, Schatten p-ideals and noncommutative L2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^2$$\\end{document}-spaces induced by a semifinite, nonfinite trace. As a consequence of our results, we obtain a representation of all bounded positive linear C*-valued maps on non-unital C*-algebras. We also deduce some norm inequalities for these maps. Finally, we consider a noncommutative L2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^2$$\\end{document}-space equipped with the topology generated by a positive sesquilinear form and we construct a topologically transitive operator on this space.

A sequential transit network design algorithm with optimal learning under correlated beliefs

Mobility service route design requires demand information to operate in a service region. Transit planners and operators can access various data sources including household travel survey data and mobile device location logs. However, when implementing a mobility system with emerging technologies, estimating demand becomes harder because of limited data resulting in uncertainty. This study proposes an artificial intelligence-driven algorithm that combines sequential transit network design with optimal learning to address the operation under limited data. An operator gradually expands its route system to avoid risks from inconsistency between designed routes and actual travel demand. At the same time, observed information is archived to update the knowledge that the operator currently uses. Three learning policies are compared within the algorithm: multi-armed bandit, knowledge gradient, and knowledge gradient with correlated beliefs. For validation, a new route system is designed on an artificial network based on public use microdata areas in New York City. Prior knowledge is reproduced from the regional household travel survey data. The results suggest that exploration considering correlations can achieve better performance compared to greedy choices and other independent belief-based techniques in general. In future work, the problem may incorporate more complexities such as demand elasticity to travel time, no limitations to the number of transfers, and costs for expansion.

Composite Accessibility Index: A Novel and Holistic Measure for Evaluating Transit Accessibility

The accessibility of public transport is a vital factor for the overall success of transit operations. It determines whether people choose to use and rely on public transport by assessing the ease of accessing opportunities. Accessibility, as a measure of the system’s performance, encompasses various travel segments and can be evaluated from different perspectives. Evaluating transit accessibility in data-constrained environments, particularly in developing countries, requires an optimal framework. The present study proposed a framework by modifying available accessibility measurement indices and trying to encompass all affecting variables in a single composite index. The integrated transit system comprising the bus rapid transit system and city bus in Surat city, India, is selected to demonstrate the proposed framework. The results of the ranked-based correlation coefficient test exhibit the comprehensive assessment capabilities of the proposed composite index in evaluating transit performance. Surat city’s transit network shows better coverage based on the gravity model theory, that is, moderate performance in local coverage offered capacity per population. However, it exhibits poor accessibility with respect to reaching destinations, resulting in below-average transit accessibility. Except for the city center and eastern part, 65% of the city area experiences inadequate accessibility of public transport. These findings align with the city’s low transit mode share of 2.5% and stagnant daily ridership of 0.25–0.28 million passengers in the last half decade. The composite index map serves as a planning tool for optimizing the utilization of available resources and guiding future policy implementations.

Machine Learning for public transportation demand prediction: A Systematic Literature Review

Within the Intelligent Public Transportation Systems (IPTS) field, the prediction of public transportation demand is a key point for enhancing the quality of the services. These predictions can be exploited by transit operators, for service planning and management, as well as by passengers, for planning their trips. Hence, the public transportation demand prediction problem is being more and more investigated by the scientific community, with several different proposals in terms of Machine Learning (ML) techniques, employed sensors, considered external features, and so on. However, there is a lack of comprehensive reviews that summarize and organize the available proposals on this topic. Hence, researchers intending to propose novel ML solutions, and practitioners willing to implement such solutions, may be overwhelmed by the plethora and heterogeneity of scientific work.To support these kinds of profiles, in this paper, we provide a Systematic Literature Review on ML techniques for predicting public transportation demand. This review highlights a growing interest by the scientific community on this topic, but also the lack of open datasets (useful for benchmarking), and in general of reproducible studies. Moreover, while deep learning techniques are frequently favored for their potential in terms of accuracy, associated costs, interpretability, and energy consumption are often overlooked.

A Comprehensive Research Agenda for Integrating Ecological Principles into the Transportation Sector

The paper examines the integration of novel Transportation Ecology principles into transit operations, aiming to address the environmental impacts associated with surface services in urban areas and with the purpose of creating a comprehensive agenda for integrating ecological principles into transit planning and management. The research problem is to quantify the tangible benefits for transit operators, particularly in the context of mitigating wildlife-vehicle collisions and improving overall operational efficiency as a motivator for transit managers to adopt Transportation Ecology principles. The study design, after analyzing the regulatory requirements, implements scenario-based methodology, utilizing data from an average Italian bus fleet to estimate potential monetary savings and benefits. Key parameters, such as maintenance costs, insurance premiums, and collision-related expenses, are analyzed to provide a realistic assessment of the economic advantages of implementing Transportation Ecology measures. The findings reveal that significant cost reductions can be achieved by minimizing accidents involving wildlife, alongside other operational improvements. The scenario demonstrates that even a small fleet, when adopting these principles, can yield substantial financial benefits, thereby making a compelling case for broader implementation. The paper concludes that while the qualitative nature of the analysis necessitates conservative estimates, the results underscore the value of incorporating ecological considerations into transit planning and management. These insights are vital for transit operators and policymakers seeking to balance environmental sustainability with operational profitability and protect urban ecosystems. This also implies the need for a more holistic and interdisciplinary approach to transportation planning and management.

State-dependent multi-agent discrete event simulation for urban rail transit passenger flow

Urban rail transit passenger flow modeling is the foundation of urban rail transit planning, design, and operation. The motivation of this paper is to accurately and efficiently simulate passenger flow dynamics in urban rail transit systems. To this end, we propose a State-dependent Multi-agent Discrete Event Simulation (SdMaDES). The state-dependence (or congestion-dependence) means that the service abilities (or travel times) of bottleneck facilities (e.g. platform screen doors and transfer corridors) are not constant and they interact with the congestion dynamics. Specifically, we first establish a modular Multi-agent Discrete Event Simulation (MaDES), which includes four types of modules (passenger, train, station, and network modules) and three types of agents (passenger, train, and station agents). The logical connections and event-triggering modes between the modules are analyzed and defined, and thirty types of events are designed. The state-dependence is then captured by an Improved Social Force Model (ISFM), which adds an autonomous obstacle avoidance mechanism. The ISFM reproduces passenger movement behavior within bottleneck facilities of urban rail transit systems at the microscopic level. These state-dependent functions or general rules are explicitly formulated by fitting the results of ISFM and are subsequently applied to the proposed MaDES model, resulting in the SdMaDES. This integration aims to enhance the accuracy of the simulation. We conducted a real case from the Chengdu Metro network. Some interesting results are found. (a) The maximum number of boarding passengers in a train carriage is a complex nonlinear function that is dependent on the state (density inside the train carriage). This challenges the linear function commonly utilized in most studies. (b) Compared to the actual data, the proposed SdMaDES model shows a cumulative error of 9.85% after data smoothing, while the conventional MaDES model exhibits a much higher cumulative error of 21.9% after data smoothing. (c) As the overall traffic demand level increases, the gap between the two simulation models’ results is getting wider and wider due to the amplified nonlinear impact of congestion.

Human Trafficking Awareness Training and Response Procedure Template for Transit Agencies

As the frontline eyes on communities, transit operators are uniquely positioned to recognize suspicious activities and report them to authorities. Training is necessary to inform and empower transit agencies in the fight against human trafficking. Human trafficking is modern day slavery, which the U.S. Department of Justice defines as a crime that involves the exploitation of a person for labor, services, or commercial sex. Human trafficking is a worldwide criminal industry that the denies freedom of 25 million people around the world. This heinous crime often targets the most vulnerable populations and preys on their needs, weaknesses, and insecurities as a strategy to control their victims through force, fraud, and coercion. This paper reviews the resources available for transit agencies to train their employees on the signs of human trafficking that they should be on the lookout for. Truckers Against Trafficking’s Busing on the Lookout program has shared success stories related to transit employees recognizing situations and saving human trafficking victims. However, the existence of transit agency policies and associated procedures is a recognized resource gap in the transit industry. The available training materials direct trainees to refer to their agency policy on how to report suspicious activity. However, as noted, many transit agencies do not have a formalized policy or procedures in place to dictate how to report suspected human trafficking activity. This paper provides agencies with valuable human trafficking awareness training resources and a response procedure template as tools to improve the awareness and reporting procedures in their agency.

ANALYSIS OF THE IMPLEMENTATION OF ISAK 16 - SERVICE CONCESSION AGREEMENTS AND ITS IMPLICATIONS FOR THE COMPANY'S FINANCIAL STATEMENTS

This research is qualitative research with data collection techniques through literature studies and field studies. Literature studies were obtained from scientific journals, accounting standards, government regulations, agreements and business studies related to the implementation of light rail/Light Rail Transit, while field studies were carried out through interviews with informants who understand the implementation of light rail/LRT. The company that is the object of research is PT Jakarta Propertindo (Perseroda) which is a company assigned by the DKI Jakarta Provincial Government to provide infrastructure and facilities for Light Rail Transit Corridor 1 Phase 1 (Kelapa Gading Velodrome). The aim of the research is to analyze appropriate accounting policies for companies related to the Light Rail Transit Infrastructure and Facilities Agreement for Corridor 1 Phase 1 (Kelapa Gading Velodrome) which is the scope of ISAK -16 Services Concession Agreement, implementation of ISAK 16 and implications of implementing ISAK 16 to the financial statements. The results of the research conclude that accounting policies related to the Implementation of Light Rail Transit Infrastructure are within the scope of ISAK 16: Service Concession Agreements so that the implications for financial statements are that companies must record LRT Infrastructure Assets as Intangible Assets, while for the Operation of Light Rail Transit Facilities Rail Transit is within the scope of PSAK 16: Fixed Assets so companies must record LRT Facilities Assets as Fixed Assets.

Effect of multiscale metro network-wide attributes on peak-hour station passenger and flow balancing

Analyzing the balance of station passenger and passenger flow is essential for understanding jobs-housing balance and built environment in station areas and network-wide range as well as for enhancing the efficiency of urban rail transit operations. Taking the Shanghai rail transit network as a case study, this paper defines the Multiscale Subnetwork (MSSN) based on a specific spatial scope. By extracting the network features and built-environment elements of the stations and the MSSN, this study analyzes the factors affecting the peak-hour station passenger and the imbalance of regional network passenger flow. The research suggests that the small MSSN analysis, within 6-8 km from a station, can provide valuable results from a network-wide perspective, rather than solely focusing on individual station areas or the entire network. The regional attributes of jobs-housing balance and the transportation conditions in the MSSN range have great impact on both station passengers and flow imbalance. This research provides theoretical insights for urban planners and policymakers to formulate effective strategies for urban rail transit networks.

Numerical Simulation Study on the Hydrothermal Characteristics and Dynamic Response of the Embankment–Bridge Transition Zone in Cold Regions

The chain reaction of bridge abutment structure caused by frost heave of the embankment–bridge transition zone filler in cold regions has a great impact on the smoothness of railway lines, which will bring great challenges to the normal operation, safety, and maintenance of rail transit in cold regions under the action of long-term dynamic load. In this paper, the hydrothermal model and dynamic analysis model of the embankment–bridge transition zone are established, and the frost heave deformation rule and dynamic response characteristics of the embankment–bridge transition zone under frost heave conditions are studied. The results show that the effect of the bridge abutment structure on vertical frost heave is mainly concentrated in the range of the bridge abutment, and the vertical frost heave near the abutment is much smaller than other parts away from the abutment. The dynamic response and wheel–rail contact force of the embankment–bridge transition zone are significantly different under non-frost heave and frost heave conditions. Frost heave may cause a higher risk of derailment. This study provides a scientific reference for the design, construction, and safe operation and maintenance of embankment–bridge transition zones in cold regions, and has certain practical engineering significance.

Earth-catalyzed detection of magnetic inelastic dark matter with photons in large underground detectors

Inelastic dark matter with moderate splittings, O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(few to 150) keV, can upscatter to an excited state in the Earth, with the excited state subsequently decaying, leaving a distinctive monoenergetic photon signal in large underground detectors. The photon signal can exhibit sidereal-daily modulation, providing excellent separation from backgrounds. Using a detailed numerical simulation, we examine this process as a search strategy for magnetic inelastic dark matter with the dark matter mass near the weak scale, where the upscatter to the excited state and decay proceed through the same magnetic dipole transition operator. At lower inelastic splittings, the scattering is dominated by moderate mass elements in the Earth with high spin, especially 27Al, while at larger splittings, 56Fe becomes the dominant target. We show that the proposed large volume gaseous detector CYGNUS will have excellent sensitivity to this signal. Xenon detectors also provide excellent sensitivity through the inelastic nuclear recoil signal, and if a future signal is seen, we show that the synergy among both types of detection can provide strong evidence for magnetic inelastic dark matter. In the course we have calculated nuclear response functions for elements relevant for scattering in the Earth, which are publicly available on GitHub.

Good practices on transit operation design: bus drivers’ perspective

Understanding which aspects can have the greatest influence on the performance, comfort and safety of a public transport system can be of great help in improving its operation and promoting more sustainable mobility. To find out more about these aspects, a survey was carried out among more than 180 drivers of urban bus transport systems in seven medium-sized cities in Spain. The drivers' perspective has been insufficiently taken into account in previous research, despite the fact that these workers have a high and direct knowledge of the operation and problems directly affecting the service. The data collected through this survey have been analysed using descriptive statistics and an Ordered Probit model. The results have allowed us to detect specific aspects to improve the performance and comfort of users and drivers such as the correct location and length of bus stops and enforcing regulation to ensure that buses have priority in traffic and that illegal parking does not interfere with their operations. In addition, bus lanes were seen as important by drivers to improve the comfort and safety of the service. Other factors related to safety were generally highly rated and there was little dispersion in the responses about their importance, although aspects such as proper visibility, avoiding illegal parking, and campaigns to encourage bus users to be aware of their surroundings stood out in the answers. Finally, the payment system was highlighted as very relevant to ensure the performance and comfort of users and drivers during the operation at bus stops. Improving this system was identified as the measure that could have the greatest impact on the performance of the service as a whole.

Determining capacity flexibility of the urban transit network under different transit operation conditions

This paper proposes the capacity flexibility models of transit networks to describe the ability of urban transit networks to accommodate the changes in passenger demands. In order to keep the variations of the average passenger travel time in a reasonable way, the concept of coefficient of variation (CoV) is introduced to measure and limit the deviation from a baseline time of the average passenger travel time. The CoV could transform the capacity flexibility values to non-dimensional form in order to compare the capacity flexibility characteristics of different scale transit networks on an equal basis. The genetic algorithm with deep search (GA-DS) for this problem is proposed to find the approximating optimal solution of the capacity flexibility models more effectively. The algorithm has been tested with benchmark problems reported in the existing literature. The optimal solution of the flexibility models shows that the flexibility values are further improved by reducing the number of stops for transit routes under different transit operation conditions. At last, the influence factors of the capacity flexibility of transit systems are discussed to address reliable transit services.