Transit Schedule Research Articles

Accessibility derivative: Measuring the accessibility contribution of public transit routes

Accessibility is one of the most essential objectives of public transit systems as the transit service’s useability and service quality. The accessibility of transit systems as a whole is well understood; however, it is still unclear how each route contributes to the system-wide accessibility. Meanwhile, with a higher risk of disruptions and more uncertainties from climate change and other disruptions, there is an urgent need to systematically study the impacts of service change with the contribution of each route to general accessibility. To address this gap, we introduce the accessibility derivative, a model-agnostic measure of the contribution of each route in a transit system. We define the derivative of a route as the systemwide change in accessibility after removing the route from the system. We demonstrate how to calculate the derivative numerically from widely available public transit schedule and automated passenger count data. The measure reflects the inherent structure of a transit system and reveals the impacts of potential route-level service changes. The results provide firsthand evidence on public transit assessment and planning, including performance assessment, schedule redesign, and planning transfers.

Enhancing Public Transit System Through AI and IoT

The paper investigates the synergy between AI and IoT in revolutionizing public transit systems, emphasizing their role in addressing existing challenges and improving overall efficiency. It explores the application of IoT devices in creating a smart infrastructure that enables real-time data collection, monitoring, and management of transit operations. The research delves into the realm of predictive maintenance, showcasing how AI algorithms, powered by IoT data, can anticipate potential issues in transit vehicles. By analyzing sensor data, transit authorities can proactively address maintenance needs, minimizing downtime, reducing repair costs, and ensuring a more reliable and sustainable public transit service. Route optimization emerges as another crucial aspect of the study, highlighting how AI algorithms leverage historical and real-time data to recommend the most efficient transit routes. Factors such as traffic patterns, weather conditions, and passenger demand are considered to enhance overall system efficiency and reduce travel time for passengers. The paper introduces the concept of dynamic scheduling, illustrating how AI-driven algorithms adapt transit schedules in real-time based on changing passenger needs and external factors. This dynamic approach aims to provide more responsive services, ultimately reducing wait times and improving overall user satisfaction. Passenger information systems are explored as a pivotal component, illustrating how AI and IoT technologies enhance the passenger experience. Real-time communication through mobile apps, digital displays, and other channels ensures that passengers have accurate and timely information about arrival times, delays, and alternative routes, empowering them to make informed decisions. The researchers also delve into fare optimization, examining how AI algorithms analyze data on passenger demographics, travel patterns, and economic factors to create fair and affordable fare structures. This approach aims to encourage ridership, increase revenue, and improve the financial sustainability of public transit systems. The abstract presents a comprehensive overview of how the integration of AI and IoT technologies in public transit systems transforms urban mobility. The findings suggest that leveraging real-time data, predictive analytics, and dynamic solutions can significantly enhance the reliability, accessibility, and sustainability of public transit. As cities continue to explore innovative solutions, the abstract serves as a roadmap for developing smarter, user-friendly, and efficient urban transportation networks, ultimately contributing to improved quality of life for residents.

Accessibility of Opioid Treatment Programs Based on Conventional vs Perceived Travel Time Measures

Transportation barriers have long been associated with poorer health outcomes; this burden is especially acute for individuals with opioid use disorder (OUD), a chronic disease often associated with low socioeconomic status. Conventional travel time analyses may not fully account for experiential components of travel, thereby understating the true travel burden and overstating treatment accessibility to opioid treatment programs (OTPs). To develop a metric of feels-like accessibility for those using public transit to access OTPs that accounts for the realistic travel burden on individuals with OUD. This cross-sectional study integrated high-resolution transit schedules and operating hours of OTPs to measure feels-like accessibility. Feels-like accessibility considers the differential outcomes of out-of-vehicle travel components and more realistically reflects individuals' transportation burden than conventional accessibility measures. Gini indices and spatial regression models were used to investigate inequities in accessibility. Geocoded data for residential addresses of 1018 overdose fatalities in Connecticut in 2019 were used as a proxy for the treatment needs of individuals with OUD. Data were analyzed between May and August 2023. Conventional and feels-like accessibility scores. Fluctuations in public transit frequencies over the course of the day and the limited operating hours of the OTPs. Of the 1018 individuals in the study, the mean (SD) age at death was 43.7 (12.6) years, 784 individuals (77%) were men, 111 (11%) were African American, and 889 (87%) were White, with other racial and ethnic categories including 18 individuals (2%). A total of 264 individuals in the sample (26%) could not access an OTP within 180 minutes. For those who could access these facilities, the average 1-way travel time was 45.6 minutes, with individuals spending approximately 70% of their trip duration on out-of-vehicle travel components. The conventional accessibility metric underestimates individuals' travel burden to OTPs as well as the inequity in accessibility compared with the feels-like accessibility metric. For example, the median (range) conventional accessibility score, defined as the number of OTPs within 120 minutes of transit travel time, was 5.0 (0.0-17.0); the median (range) feels-like accessibility score, defined as the number of OTPs within 120 minutes of transit travel time weighted to account for in- and out-of-vehicle segments, was 1.0 (0.0-10.0). There is a considerable temporal variation in travel time and accessibility depending on the departure times. In this cross-sectional study of travel burdens, the calculated feels-like accessibility scores, which consider the differential outcomes of out-of-vehicle travel components (eg, walking and waiting), could better and more realistically reflect passengers' transportation burden. Policy recommendations derived from the conventional accessibility metric could be misleading, and decision-makers should use feels-like accessibility metrics that adequately capture individuals' travel burdens. In the context of access to OTPs, the findings from this study suggest that opening new OTP sites to address gaps in access due to distance to services or extending hours of operation at existing sites may ameliorate the travel burden for individuals.

METS-R SIM: A simulator for Multi-modal Energy-optimal Trip Scheduling in Real-time with shared autonomous electric vehicles

We develop an agent-based simulator named METS-R SIM to support operational decisions for multi-modal shared autonomous vehicle (SAEV) services. Compared with existing traffic simulators, METS-R SIM offers several valuable features including: 1) A microscopic vehicle movement model for SAEV services, which allows us to explicitly model vehicular interactions and generate detailed speed and acceleration profiles for energy estimation. 2) An efficient implementation in which parallel computing is embedded in METS-R SIM which can update the state of different agents (e.g., vehicle locations in different links) simultaneously. 3) A modular and extensible framework as the simulator is built upon an agent-based modeling environment named Repast Simphony which is featured by its well-factored abstractions; in addition, a server-client structure is introduced to implement real-time operational algorithms such as energy-efficient routing and adaptive transit scheduling. 4) Open-source, reproducible with web-based visualization (METS-R SIM introduces these features to promote transparency). We validate METS-R SIM by matching the aggregated travel time and travel distance with the real observed ones obtained from New York City (NYC). We also compare the generated speed profiles qualitatively to the ones reported in published studies. We demonstrate the functionalities of our simulator by simulating SAEV services deployed to serve travel needs related to three main transportation hubs in NYC.

Factoring in temporal variations of public transit-based healthcare accessibility and equity

Access to healthcare services using public transportation (PT-based healthcare accessibility) is a crucial aspect in achieving healthcare equity as it affects individuals’ ability to receive healthcare. Previous research has focused on the spatial features of healthcare accessibility. However, less attention has been given to its temporal characteristics, which can be influenced by transit schedules, multimodal connectivity, congestion, and other factors. This study proposes a framework to better understand the impacts of temporally varying PT-based healthcare accessibility on healthcare equity. A case study of Shanghai, China is used to illustrate the temporal variation of healthcare accessibility, with a focus on hourly inter- and intra-regional disparities. These disparities are captured using the Gini coefficient and Theil index. Additionally, the study introduces bivariate local Moran’s I to identify healthcare shortage areas and evaluate the spatial autocorrelation between population density and healthcare accessibility. The findings of this study reveal that the accessibility to healthcare services experiences significant fluctuations throughout the day, leading to temporal variations in healthcare equity. Subway service quality contributes more to temporal variations than bus service quality. The lowest point of such equity is reached when PT operates at its full capacity. On a spatial level, individuals residing in newly developed regions, which surround the historical urban core or recently planned city subcenters, tend to experience decreased accessibility to healthcare via public transportation. Consequently, it results in a heightened reliance on motorized transportation in these areas. These findings provide insights that can inform the design of PT accessibility-based strategies, healthcare improvement plans and inclusive housing policies, to address healthcare equity issues in metropolitan areas. By considering both spatial and temporal factors, we can better understand the complex relationships between transportation and healthcare accessibility to promote equitable access to healthcare services and foster social equity.

Measuring route diversity in spatial and spatial-temporal public transport networks

Route diversity is a pivotal metric for evaluating the redundancy of transportation networks, a fundamental aspect of system resilience. This study provides a comprehensive exploration of route diversity in multimodal public transport systems, specifically considering the unique characteristics of bus networks. Our research introduces a two-pronged approach to measuring route diversity within spatial public transport networks, delving into service-based and infrastructure-based perspectives. The former assesses redundancy against transit service disruptions by factoring in transit line overlaps, while the latter evaluates redundancy against infrastructure-related interruptions by considering overlapping road segments on which transit lines rely. In addition, the study advances by modelling public transport systems as multilayer spatial-temporal networks, integrating time-variable service frequency and travel time uncertainty, which enables us to derive route diversity for origin-destination (O-D) pairs across different time periods.We present a case study of the multimodal public transport network in Jiading District, Shanghai, revealing a power-law distribution of the route diversity. The results unveil O-D pairs with lower route diversity, underscoring their lack of resilience against various disturbances. Lower service-based route diversity suggests the necessity of enhancing service frequency and bolstering cross-line combined transit scheduling, while lower infrastructure-based route diversity could warrant the design of road-diversified transit lines, especially within bus corridors. Besides, relative route diversity between the two indices highlights specific O-D pairs with notable disparities in service and infrastructure redundancy. This difference is correlated with the distance between O-D pairs and the road network's configuration. This analysis underscores the method's potential to offer more relevant insights to public transport planners and operators for adjusting transit lines and schedules through a resilience-focused lens.

Semi-flexible demand responsive transit scheduling based on ALNS-TS algorithm

Semi-flexible demand responsive transit scheduling based on ALNS-TS algorithm

Effeciency assessment of IoT devices control with Teletraffic theory

In connection with the global decarbonization program until 2050, the transition to clean green energy, the growth of the Internet of Things (IoT) number, and energy distribution and control across the load are being raised. The relevance of the work is confirmed that there has been significant growth of the industrial IoT for years, significantly changing the mechanism of industrial enterprise management programs. The object of the research is the IoT device control system for efficient energy distribution using a Queuing Theory, namely the Teletraffic Theory. The novelty of the work is that the Teletraffic Theory, which deals with the mathematical modeling and analysis of traffic patterns in communication networks, can be explicitly applied to IoT device control. The authors developed a mathematical model of IoT control using the Teletraffic Theory and, based on it, created a simulation model of a network router and a transition schedule in the "GPSS World" software. The obtained results of the work were 16 states and a balance equation in which all probabilities were found. Probabilities were used to calculate nodes and network characteristics. 100,000 requests from IoT devices coming to two routers were simulated. The study results showed that the first node's load is 63.2 % with an average processing time per transaction of M=1.436 sec., and the load of the second node is 32 % with M=0.914 sec. The created network router model worked with minimal losses during transactions. Accordingly, the IoT control system developed in this study has shown its effectiveness and is applicable for practical use in controlling IoT devices in Smart Grid. It is planned to research the possibility of using Teletraffic Theory in energy distribution control systems in Smart Grids

Design of thrust augmentation control schedule during mode transition for turbo-ramjet engine

A thrust augmentation control schedule was designed for turbo-ramjet engine during mode transition process to achieve high thrust performance. First, a mathematical model of turbo-ramjet engine was established, analyzing the reason for the existence of an insufficient thrust working range under conventional mode transition control schedule. On this basis, a thrust augmentation control schedule was devised for the thrust insufficient range considering the matching between the air inlet available airflow and the engine demand airflow. The control schedule could increase the flow capacity of the engine and reduce the overflow drag of air inlet by opening the ramjet bypass while keeping the turbofan components working at the maximum state, which could improve the maximum installation thrust performance of the engine and achieve a better air inlet/engine matching. By further designing the optimal regulation rule for the rear variable area bypass injector (RVABI), the installed thrust of the engine could be increased by more than 37.93% at most, while simultaneously reducing the fuel consumption by 0.16%. Finally, the turbo-ramjet engine was simulated along the isobaric flight path. The simulation results revealed that under conventional mode transition control schedule, the thrust insufficient occurred when Mach number is above 2.7. The designed thrust augmentation control schedule could effectively improve the maximum thrust of the thrust drop zone and provide sufficient thrust margin for engine during the whole working process. At the same time, considering the smooth thrust and thrust augmentation requirements, a compromise mode transition control schedule between the thrust augmentation control schedule and the conventional mode transition schedule is proposed. This control schedule could address the problem of insufficient thrust at high Mach numbers while the smoothness transition of engine total thrust could be guaranteed.

Resolving the accessibility dilemma: Comparing cumulative and gravity-based measures of accessibility in eight Canadian cities

There is a lack of agreement regarding the theoretical framework that practitioners should use for accessibility assessment – a measure of transport and land-use systems performance. Cumulative measures are simple and easy to interpret, while gravity-based measures are more sophisticated, resourceful, and less intuitive approaches. As such, this study aims to investigate whether the estimates of a simple cumulative opportunity measure are significantly different from those made using advanced gravity-based measures to understand if the former can be a substitute for the latter in practice and if a certain threshold of travel time can be recommended for different regions. We estimated cumulative and gravity-based accessibility using decay-probability density functions, decay-cumulative density functions, Gaussian, and a Log-Logistic decay-cumulative density functions using census commuting flows, car congested travel time and public transit schedules from eight metropolitan regions across Canada – Toronto, Montreal, Vancouver, Edmonton, Quebec City, Winnipeg, London, and Halifax. These measures of accessibility were tested for correlation, and we found that a coefficient of approximately 0.90 is reached when the threshold to calculate cumulative opportunities accessibility is set to the average commute time for both low- and non-low-wage jobs accessibility analyses by transit and motor vehicles. The paper provides evidence to support the reliability of cumulative accessibility, facilitates its broader adoption for evaluation of transport and land use interactions in North American cities, as well as opens opportunities to advance the equitable distribution of transport system benefits.

Integrated Robust Optimization of Scheduling and Signal Timing for Bus Rapid Transit

The unbalanced nature of passenger demand and the uncertainty of delay at intersections are considered critical factors in the efficiency of public transportation operations. Considering the controllable characteristics of the bus rapid transit system (BRT), an integrated optimization model that includes multi-mode transit scheduling and signal timing is proposed. The robust optimization model copes with the fluctuations in passenger demand and bus operation. A non-linear programming is developed to minimize the total passenger travel time and optimize the transit departure time, dwelling strategies at stations, and signal timings at intersections. The constraints on the signal control, degree of saturation, transit scheduling, and passenger waiting time at stations are intended to reflect real traffic conditions. A case study and extensive sensitivity analyses were conducted to evaluate the performance of the proposed model. The results show that the proposed integrated model can adjust the BRT dwelling strategies based on different passenger demands and coordinate transit departure time and signal timing adjustment to mitigate the passenger delay. Furthermore, experimental results demonstrate improvements of 5.3% and 8.1% in the mean and maximum values of passenger travel time, respectively, using the proposed model, compared to those obtained using the conventional operation strategy.

Changes in Traveler Stated Preference for Bus and Car Modes Due to Real-Time Schedule Information: A Conjoint Analysis

This paper reports a conjoint analysis that explored potential impacts of real-time transit schedule information on mode preference. Conjoint analysis is a stated-preference approach to choice modeling in which respondents are asked to rate hypothetical products or services described by a single level of each of a number of attributes. Respondent ratings are decomposed into “part-worths “ describing preferences for each attribute level. Subjects for the study were 500 randomly-sampled employees on the University of Michigan Medical Campus.The conjoint data indicate potential significance of real-time transit schedule information for circumstances under which modal choice decisions are made on a day-today basis. Stated mode preference is not, however, significantly affected by availability of such information when decisions are made on a month-by-month basis. These results should further motivate transit system designers to provide such information, with particular attention paid to developing a highly accessible method of information dissemination.

Understanding urban bus travel time: Statistical analysis and a deep learning prediction

Travel time reliability plays a key role in bus scheduling and service quality. Owing to various stochastic factors, buses often suffer from traffic congestion, delay and bunching, which leads to disturbances of travel time. Automatic vehicle location (AVL) could record the spatiotemporal information of buses, making it possible to understand the status of bus service. In this paper, we specifically analyze the statistical characteristics of travel time based on historic AVL data. Moreover, a Kalman filter-LSTM deep learning is proposed to estimate bus travel time. Numerical tests indicate that the travel time of bus routes shows a left-skewed and right-tail pattern with a good fit of the lognormal distribution. The bus service reliability fluctuates largely in the peak hours, especially the morning peak. Bus bunching and large bus time headway easily occur, and once it occurs, it will continue until destination. The Kalman filter-LSTM model outperforms the ensemble learning methods to predict travel time. This study could provide implications for transit schedule optimization to improve the bus service quality.

Transit Voronoi diagrams in multi-mode public transport networks

Network Voronoi diagrams (N-VDs) are effective geometric constructions for partitioning geographical space constrained by road networks. However, they are not applicable for urban areas with well-developed public transport systems. This study proposes new transit Voronoi diagram (T-VD) models for partitioning geographical space constrained by public transport networks. The proposed T-VD models explicitly consider the complexities of a public transport network, including transfers between different transport modes, dynamic transit schedules, changing network topologies, etc. To efficiently construct T-VDs, geo-computational algorithms are developed by modifying and integrating classical shortest-path algorithms in road networks and transit shortest-path algorithms in public transport networks. Case study results show significant differences between T-VDs and N-VDs, highlighting the need for using T-VDs in urban areas with well-developed public transport systems. The developed geo-computational algorithms efficiently constructed T-VDs in large-scale public transport networks within satisfactory computational times.

Integrated Optimization of Transit Networks with Schedule- and Frequency-Based Services Subject to the Bounded Stochastic User Equilibrium

In many European metropolitan areas, the urban transit system is a mixture of schedule- and frequency-based services. This study proposes an integrated transit frequency and schedule design problem (ITFSDP), where frequencies and schedules are simultaneously determined, and develops a biobjective model for the ITFSDP to minimize operation costs and total passenger-perceived generalized travel cost. Meanwhile, the passengers’ route choice behavior is described by the bounded stochastic user equilibrium (BSUE). The in-vehicle congestion effect is represented using a set of constraints that differ in terms of the sitting and standing costs as sitting and standing passengers perceive crowding differently. This set of constraints captures the realistic behavioral feature that having occupied a seat, users remain seated at subsequent stops in the same vehicle. The problem is formulated as a mixed integer nonlinear programming problem, which is subsequently linearized to a mixed integer linear programming problem and solved using a branch and bound algorithm. A column generation and reduction phase is embedded in the solution algorithm to obtain the bounded choice set according to the BSUE constraints. Experiments are conducted to illustrate the model’s properties and the performance of the solution method. In particular, we demonstrate a Braess-like paradoxical phenomenon in the context of transit scheduling and highlight that well-synchronized transit services can deteriorate the network performance in terms of the total passengers’ generalized travel cost when considering passenger congestion costs because of crowding.

Adaptive transit scheduling to reduce rider vulnerability during heatwaves

ABSTRACT Extreme heat events induced by climate change present a growing risk to transit passenger comfort and health. To reduce exposure, agencies may consider changes to schedules that reduce headways on heavily trafficked bus routes serving vulnerable populations. This paper develops a schedule optimization model to minimize heat exposure and applies it to local bus services in Phoenix, Arizona, using agent-based simulation to inform travel demand and rider characteristics. Rerouting as little as 10% of a fleet is found to reduce network-wide exposure by as much as 35% when operating at maximum fleet capacity. Outcome improvements are notably characterized by diminishing returns, owing to skewed ridership and the inverse relationship between fleet size and passenger wait time. Access to spare vehicles can also ensure significant reductions in exposure, especially under the most extreme temperatures. Rerouting, therefore, presents a low-cost, adaptable resilience strategy to protect riders from extreme heat exposure.

Novel model for integrated demand-responsive transit service considering rail transit schedule.

This research aims to develop an optimization model for optimizing demand-responsive transit (DRT) services. These services can not only direct passengers to reach their nearest bus stops but also transport them to connecting stops on major transit systems at selected bus stops. The proposed methodology is characterized by service time windows and selected metro schedules when passengers place a personalized travel order. In addition, synchronous transfers between shuttles and feeder buses were fully considered regarding transit problems. Aiming at optimizing the total travel time of passengers, a mixed-integer linear programming model was established, which includes vehicle ride time from pickup locations to drop-off locations and passenger wait time during transfer travels. Since this model is commonly known as an NP-hard problem, a new two-stage heuristic using the ant colony algorithm (ACO) was developed in this study to efficiently achieve the meta-optimal solution of the model within a reasonable time. Furthermore, a case study in Chongqing, China, shows that compared with conventional models, the developed model was more efficient formaking passenger, route and operation plans, and it could reduce the total travel time of passengers.

Digital Directions:

Wayfinding in spatially complex public transit environments poses unique navigational challenges. Transfers, delays, barriers, and user capacity all influence the usability of a system. Because of the smartphone, how we navigate through these systems, and interact with the surrounding environment, is changing. The smartphone provides a spatio-temporal strategy that removes the reliance on our immediate environment and personalizes the wayfinding process -- unlike that of transit schedules, signs, and maps. How does smartphone usage influence performance and the wayfinding experience? This paper looks at smartphone usage of twelve participants through a shadowed commented walk, known as a Destination-Task Investigation, in Munich’s public transit system. The study provides insights into the role and the influence of smartphones during the wayfinding process. Furthermore, it shows that Apps providing integrated spatio-temporal information, such as Google, were used most frequently, especially for confirmation during navigation.

Integrating COVID-19 health risks into crowding costs for transit schedule planning

The public transport sector worldwide experienced the worst impact in recent history, in terms of ridership loss, due to the COVID-19 pandemic. The pandemic negatively affected passengers' perceptions of public transport and is likely to make a lasting impact on ridership, trip patterns, and modal share. Without any supportive changes to transit operations, ridership is likely to decline. This study explores the setting of frequencies in transit lines and proposes a two-part methodology that addresses the changing perceptions of users, especially in a health-related context. The first part develops a mathematical model that expresses the pre-COVID-19 cost of passenger crowding as an integral part of user costs to determine the optimal headway that considers the trade-offs between user and operator costs. A continuum approximation for the demand of the bus line has been used in the derivation. The second part extends the developed model to include both the costs of the health risks associated with the COVID-19 pandemic and crowding. The developed models will help transit planners and operators to plan and adapt operations to changing health risks during the pandemic and post-pandemic. Several numerical examples are provided to describe the uses and applications of the analytical models using information obtained from the literature.

Evaluating rail transit's comparative advantages in travel cost and time over taxi with open data in two U.S. cities

This paper presents a comparative analysis of rail transit and taxi by travel cost and time based on the large-scale taxi trip data and public transit schedule information in two major U.S. cities. To quantify the relative advantage of one mode over the other, we introduce the notion of travel gradient, which is travel cost difference divided by travel time difference. Based on the signs of travel cost and time differences, we classify all trips into four quadrants. Quadrant II trips are selected for further analysis because rail transit is identified to be competitive with taxi for such trips. We also explore the relation between various trip characteristics and travel gradient with and without considering the spatial variation of such a relation. Main research findings include: (1) around 70% of the taxi trips in the considered datasets can be substituted with rail transit trips if the maximum walking distance is 0.5 miles at each trip end; (2) for around 10% of taxi trips with both modes being viable, rail transit dominates taxi in both travel cost and time; for the rest, rail transit is competitive with taxi; (3) the marginal travel cost saving due to mode switching from taxi to rail transit is about $70; and (4) there exist clearly spatial variations of the relation between trip characteristics and travel gradient. The main policy recommendation from this study is that rail transit can be better marketed by highlighting its relative advantage over taxi in travel time and cost, especially for travels in certain directions and time periods.