Multimodal Transit Network Research Articles

Quantifying multi-modal public transit accessibility for large metropolitan areas: a time-dependent reliability modeling approach

ABSTRACTThe temporal dimensions of public transit accessibility have recently garnered an increasing amount of interest. However, the existing literature on transit accessibility is heavily based on oversimplified assumptions that transit services operate at deterministic speeds using predetermined timetables. These measurements may overestimate transit accessibility, especially for large metropolitan areas where inter- and intra-modal transfers are frequent. To handle travel time uncertainty, a multi-modal transit accessibility modeling approach is proposed to account for realistic variations in travel time and service reliability. The proposed approach is applied to the mapping of transit accessibility in Shenzhen (China), where transit services exhibit significant travel time variations over space and time. Compared to traditional transit accessibility measures, our method has been demonstrated to better capture intrinsic spatial and temporal accessibility variations with complex multi-modal transit networks. Normal distribution of inter-stop travel times and constant travel speed between GPS sampling points are assumed to simply the computation, which we consider to adjust in future studies to better quantify the dynamics of transit accessibility across space and time.

Estimation of population origin–interchange–destination flows on multimodal transit networks

Previous research has combined automated fare-collection (AFC) and automated vehicle-location (AVL) data to infer the times and locations of passenger origins, interchanges (transfers), and destinations on multimodal transit networks. The resultant origin–interchange–destination flows (and the origin–destination (OD) matrices that comprise those flows), however, represent only a sample of total ridership, as they contain only those journeys made using the AFC payment method that have been successfully recorded or inferred. This paper presents a method for scaling passenger-journey flows (i.e., linked-trip flows) using additional information from passenger counts at each station gate and bus farebox, thereby estimating the flows of non-AFC passengers and of AFC passengers whose journeys were not successfully inferred.The proposed method is applied to a hypothetical test network and to AFC and AVL data from London’s multimodal public transit network. Because London requires AFC transactions upon both entry and exit for rail trips, a rail-only OD matrix is extracted from the estimated multimodal linked-trip flows, and is compared to a rail OD matrix generated using the iterative proportional fitting method.

Multimodal transit network design in a hub-and-spoke network framework

ABSTRACTThis study focuses on the reconfiguration of bus services in an urban area with a newly constructed rail system. A hub-and-spoke network framework is introduced for the multimodal transit system. The rail services are taken as the backbone, and the bus services (main bus lines and feeder bus lines) are reconfigured to better integrate with rail services forming the core of a Mobility as a Service (MaaS). A cluster-based approach is used for selecting hubs from rail stations. Bus stops are taken as non-hub nodes. Main bus lines are designed based on a heuristic line generation approach and feeder bus lines are developed by solving a travelling salesman problem. A bi-level programming model is proposed to determine frequencies of each mode and addressed by the artificial bee colony algorithm. The effectiveness of the proposed methods is illustrated by numerical examples and applied to the Mandl's benchmark compared with existing studies.

Measuring Network-Based Public Transit Performance Using Fuzzy Measures and Fuzzy Integrals

This paper proposes an indicator integration model to measure network-based public transit performance. Coverage, directness, and connectivity indicators were used to measure network-based public transit performances individually. The three indicators exist preferential dependence problem in eliciting indicator weights. The value judgments by 40 representatives were collected by using fuzzy measures. Subsequently, fuzzy integrals were applied to integrate the three indicators considering their preferential dependence. The major contributions are twofold: one contribution is providing a comprehensive performance measurement for multimodal transit networks and the other is resolving preferential dependence between the three indicators. A case study of Taipei City was also discussed to demonstrate the application of the integration model. Five major results were derived from the study: (1) according to the decision group preferences, coverage was preferred to directness, and directness was preferred to connectivity; (2) the districts of Taipei City in the central business district (CBD) generally feature high transit coverage compared with the districts in the surrounding areas; (3) the districts in the surrounding areas generally exhibit high transit connectivity compared with the districts in the CBD; (4) the 12 districts of Taipei City do not differ substantially in transit directness performance; and (5) most of the districts of Taipei City in the CBD exhibit relatively better comprehensive transit performance than the districts in the surrounding areas.

An Analysis of Public Transit Connectivity Index in Tehran. The Case Study: Tehran Multi-Modal Transit Network

Public transit is a major priority in modern management of large cities and metropolitan areas in particular. Public transit systems in such cities consist of a large number of nodes and lines which are represented by a complex network. A station for public transit is a bridge between the people and public transit network, based on which, the concept of input and output power for each station can be defined. The objective of this study is the application of the transit connectivity indices to the multimodal transit network in the city of Tehran. The public transit network data employed in this study is taken from Tehran Traffic Control Company, and Tehran Urban and Suburban Railway Operation Company. The methodology for measuring transit connectivity consists of three measures: Node connectivity, Line connectivity and Regional connectivity, where activity density is applied to these measures. The results of node connectivity analysis shows that most of the node connectivity in concentrated in the city center with many nodes in the center along routes going north and south. The line connectivity analysis shows that there is a concentration of highly connected lines that are near Tehran municipality region 12 and 16. Finally, we find that areas with more metro and bus facilities with respect to the other areas, have a better regional connectivity. One of these areas includes Sadeghiyeh Metro Station which is the junction of Tehran Metro Line 2 and Tehran Metro Line 5 which have a high connectivity power. Results of this study can be used to suggest some ideas on how future investments in rail and bus should be prioritized. Particularly in Transit Oriented Development (TOD) and sustainble development projects, urban planners can design transit stations with high performance to access the crucial services in poor areas.

Multimedia application to an extended public transportation network in South Korea: optimal path search in a multimodal transit network

Various traffic network usage formats have arisen along with the popularization of automobiles and the continued service extension of busses, subways, and other forms of public transportation. Due to various characteristics of public transportation networks, unlike general street networks, many issues can affect public transportation, and an optimal course search should be considered. Present research considers plans to improve the overall efficiency of public transportation systems with regard to destination, means, route, and other factors to be selected efficiently in this environment as public transportation usage increases. From this perspective, it suggests the characteristics that a multimodal transit network route search algorithm should have and a corrective algorithm that implements this in an applicable program. Implementation was done in Google android application which provides a simple user interface to find optimal routes in Google Map. The proposed application would enable overall quality-of-service improvement and balanced usage of public transportation, efficient traffic management, and other advantages.

Modelling joint activity-travel pattern scheduling problem in multi-modal transit networks

Over the past decades, many activity-based travel behaviour models have been proposed based on individuals’ independent decision making. The modelling of individuals’ joint activity/travel choices, however, has received less attention. In reality, both independent and joint activities/travels form individual’s normal daily activity-travel patterns. Travel surveys have indicated that joint activity/travel constitutes an important part in individuals’ daily activity-travel patterns. On this basis, explicit modelling of joint activity/travel choices is an essential component for long-term transport planning. In this study, an activity-based network equilibrium model is proposed for scheduling two-individual joint activity-travel patterns (JATPs) in congested multi-modal transit networks. The proposed model can be used to comprehensively investigate individuals’ activity choices (e.g. activity start time and duration, activity sequence) and travel choices (e.g. departure time, route and mode) in multi-modal transit networks, including both independent ones and joint ones. The time-dependent JATP choice problem is converted into an equivalent static user equilibrium model by constructing a joint-activity-time-space (JATS) super-network platform. Joint travel benefit is modelled by incorporating a commonality factor in the JATP utility. A solution algorithm without prior JATP enumeration is proposed to solve the JATP scheduling problem on the JATS super-network. Numerical results show that individuals’ independent and joint activity/travel choices can be simultaneously investigated by the proposed model. The impacts of joint travel benefit on individuals’ independent and joint activity-travel choices are explicitly investigated.

Individual utility‐based path suggestions in transit trip planners

The opportunities offered by telematics development and the features required by travellers moving on more complex multimodal transit networks push to investigate new methods for generating path advice in transit trip planners. First, the study focuses on characteristics and limits of the methods used by current trip planners for path generation and then analyses the new methods applied by a new generation of trip planners (most at the prototypical developing stage). These methods use a group or, better, an individual traveller utility function, which allows personal preferences to be pointed out. As the individual utility functions in the transport modelling literature has been largely neglected, the second part of the study reports the state-of-the-art and some theoretical considerations on individual path utility function modelling, and recalls the approaches developed for including individual utility in new trip planners. Further, the results of individual utility function estimations, using surveys relative to the city of Rome, are presented and some aspects of the utility function calibration, including the info provider learning process of traveller preferences, are explored. The analyses show a significant improvement in using individual functions for path advice and a substantial influence of network complexity on the learning process.

Integrated Mode Choice and Dynamic Traveler Assignment in Multimodal Transit Networks: Mathematical Formulation, Solution Procedure, and Large-Scale Application

This paper introduces an integrated mode choice–multimodal transit assignment model and solution procedure intended for large-scale urban applications. The cross-nested logit mode choice model assigns travelers to car, transit, or park-and-ride. The dynamic multimodal transit assignment–simulation model determines minimum hyperpaths and assigns and simulates transit and park-and-ride travelers iteratively until the network approaches a state of equilibrium. After a given number of iterations, the updated transit network travel times are fed into the mode choice model and the model reassigns travelers to transit, car, or park-and-ride. The outer feedback loop between the mode choice model and the transit assignment model continues until the mode probabilities for each traveler do not change between iterations. A unique contribution of the method presented in this paper is that it reaches mode choice convergence with the use of disaggregate agents (travelers) instead of aggregate modal flows at the origin–destination level. The integrated model is successfully implemented on the Chicago Transit Agency’s bus and train network in Illinois. Different procedures for reaching convergence are tested; the results suggest that a gap-based formulation is more efficient than the method of successive averages.

Integrated Frequency Allocation and User Assignment in Multimodal Transit Networks

This paper presents an integrated solution method to the frequency-setting problem using optimization and assignment simulation. With a bilevel solution framework, an optimization problem is run at the upper level under the assumption that the total transit demand is fixed. The objective is to maximize wait time savings under the budget, fleet size, vehicle load, and policy headway constraints. At the lower level, an assignment and simulation algorithm is run; the algorithm models the demand response to the new frequency setting and transmits updated ridership and flow values to the upper level. The procedure is repeated until the improvement in the wait time savings converges. The platform is tested on the Chicago Transit Authority network in Illinois for the morning peak. The wait time savings in this experiment are converging and are found to be comparable with the results of a stand-alone frequency-setting algorithm that finds optimal solutions. Results are comparable with the optimal results of a stand-alone platform introduced in another study that modeled the demand response locally by using elasticities as opposed to networkwide modeling using assignment. The integrated platform can be used for medium-term strategic and long-term planning decisions.

Finding Least Cost Hyperpaths in Multimodal Transit Networks

This paper presents a least cost hyperpath algorithm that captures the complexities that arise in a transit network because of the number of transfers, the standing and overcrowding penalties, the availability of walking and biking in addition to the transit modes, and the mode-specific limitations such as availability of bike parking. The problem was formulated as a mathematical program, and then a hybrid label setting–correcting algorithm was proposed as a solution. The multi-modal time- and approach-dependent algorithm does not require spatial or temporal expansion of the network; this feature results in good computational performance for large-scale applications. Scenario runs performed on the large-scale Chicago Transit Authority network, in Illinois, validate the accuracy and performance of the algorithm.

Cascading Failures in Weighted Complex Networks of Transit Systems Based on Coupled Map Lattices

Study on the vulnerability and robustness of urban public transit networks (PTNs) has great implications for PTNs planning and emergency management, particularly considering passengers’ dynamic behaviors. We made a complex weighted network analysis based on passenger flow for Beijing’s bus stop network and multimodal transit network coupled with bus and urban rail systems. The analysis shows that there are small-world or scale-free properties in these two networks, which make them display different robustness under link or node failures. With consideration of the dynamic flow redistribution, we propose a model based on coupled map lattices to analyze the cascading failures of these two weighted networks. We find that the dynamic flow redistribution can significantly improve the tolerance of small-world or scale-free PTN against random faults. Because of the coupling of bus and rail systems, the multimodal network with scale-free topology and flow distribution structures displays an increasing tolerance even against intentional attack; however, its cascade is also much more intense once the failure is triggered. We find some thresholds of topological and flow coupling strength in the spreading process, which can be exploited to develop strategies to control cascade failures.

A tool for measuring and visualizing connectivity of transit stop, route and transfer center in a multimodal transportation network

Agencies at the federal, state and local level are aiming to enhance the public transportation system (PTS) as one alternative to alleviate congestion and to cater to the needs of captive riders. To effectively act as a viable alternative transportation mode, the system must be highly efficient. One way to measure efficiency of the PTS is connectivity. In a multimodal transportation system, transit is a key component. Transit connectivity is relatively complex to calculate, as one has to consider fares, schedule, capacity, frequency and other features of the system at large. Thus, assessing transit connectivity requires a systematic approach using many diverse parameters involved in real-world service provision. In this paper, we use a graph theoretic approach to evaluate transit connectivity at various levels of service and for various components of transit, such as nodes, lines, and transfer centers in a multimodal transportation system. Further, we provide a platform for computing connectivity over large-scale applications, using visualization to communicate results in the context of their geography and to facilitate public transit decision-making. The proposed framework is then applied to a comprehensive transit network in the Washington-Baltimore region. Underpinning the visualization, we introduce a novel spatial data architecture and Web-based interface designed with free and open source libraries and crowd-sourced contextual data, accessible on various platforms such as mobile phones, tablets and personal computers. The proposed methodology is a useful tool for both riders and decision-makers in assessing transit connectivity in a multimodal transit network in a number of ways such as the identification of under-served transit areas, prioritization and allocation of funds to locations for improving transit service.

Modelling impacts of adverse weather conditions on activity–travel pattern scheduling in multi-modal transit networks

In general, adverse weather has significant influence on individuals’ activity/travel choice behaviour and such influence is obviously greater in cities which suffer frequent rainy periods. Thus, the impacts of weather conditions should be taken into account in long-term transit service planning. In this paper, an activity-based network equilibrium model for scheduling daily activity–travel patterns (DATPs) in multi-modal transit networks under adverse weather conditions (with different rainfall intensities) is developed. The interdependency of individuals’ activity/travel choices and weather conditions are comprehensively investigated. In the proposed model, the DATP choice problem under adverse weather conditions is transformed into an equivalent static transit assignment problem by constructing a novel super-network platform. A rule-based algorithm is proposed to automatically generate the super-network taking into account the rain effects implicitly. The effects of adverse weather on different transit modes and different activities are explicitly modelled. An efficient solution algorithm without prior enumeration of DATPs is proposed for solving the DATP scheduling problem in multi-modal transit networks. Numerical examples are presented to illustrate application of the proposed model and the solution algorithm.

Estimation of Origin-Destination Demand Matrix for the Urban Multimodal Traffic Network

In this paper we consider a procedure for the estimation of origin-destination (O-D) matrices for a multimodal transit network. The structure of urban multimodal transport system is fully analyzed and then a bi-level programming model is established for O-D demand matrices estimation, where the upper-level problem seeks to minimize the sum of error measurements in traffic counts and O-D matrices, while the lower-level problem is to assign a target O-D matrix onto the network according to the user equilibrium principle. And a heuristic algorithm is proposed, finally a numeral example is given which indicates that the solution approach can be applied in practice.

A measure of equity for public transit connectivity

An equitable transit system can cater to the needs of captive riders and maximize transit service coverage. Historically transit equity has not considered in planning or has been an afterthought in the process; leading to the underutilization of transit and encouraging travelers to be auto dependent. In this paper, the authors propose a methodology to estimate transit equity using a number of attributes such as frequency, speed, capacity, and built environment in a multi-modal transit network. We propose a methodology to measure transit equity from a graph theoretical approach for all levels of transit service coverage integrating routes, schedules, socio-economic, demographic and spatial activity patterns.The objective of using equity is to quantify and evaluate transit service in terms of prioritizing transit locations for funding; conforming with federal regulations; providing service delivery strategies, especially for areas with large multi-jurisdictional, multi-modal transit networks; providing an indicator of multi-level transit capacity for planning purposes and assessing the effectiveness and efficiency for node/stop prioritization while choosing transit as a mode of travel. The methodology uses a stylized connectivity measure with a Gini index for equity estimation at different levels such as stop, line, zone and area. An example problem is presented to demonstrate the proposed methodology. The approach is then applied to the Washington–Baltimore region in the United States. The results show the existing transit service coverage at different locations. The proposed approach can be utilized as a tool for transit service planning.

Understanding Transit Ridership Demand for the Multidestination, Multimodal Transit Network in Atlanta, Georgia: Lessons for Increasing Rail Transit Choice Ridership while Maintaining Transit Dependent Bus Ridership

This study analyses the structure of transit demand in Atlanta’s transit system to understand why different elements of the network appeal to bus and rail riders. By estimating direct demand models of work trip use between pairs of traffic analysis zones, the authors find that self-identified bus riders come from poorer areas having fewer autos per household and seek to reach jobs scattered throughout the metropolitan area. Their demand is highly elastic with respect to travel time. They care not about the presence of transit-oriented development (TOD) attributes at either origins or destinations. Self-identified rail riders primarily access transit by automobile and value fast service to within convenient walking distance of employment, such as in the central business district (CBD) and some but not all TODs. The results suggest that an agency could increase ridership by both groups using a core network of higher speed lines that provide access to decentralised employment centres.

A network equilibrium approach for modelling activity-travel pattern scheduling problems in multi-modal transit networks with uncertainty

An understanding of the interaction between individuals’ activities and travel choice behaviour plays an important role in long-term transit service planning. In this paper, an activity-based network equilibrium model for scheduling daily activity-travel patterns (DATPs) in multi-modal transit networks under uncertainty is presented. In the proposed model, the DATP choice problem is transformed into a static traffic assignment problem by constructing a new super-network platform. With the use of the new super-network platform, individuals’ activity and travel choices such as time and space coordination, activity location, activity sequence and duration, and route/mode choices, can be simultaneously considered. In order to capture the stochastic characteristics of different activities, activity utilities are assumed in this study to be time-dependent and stochastic in relation to the activity types. A concept of DATP budget utility is proposed for modelling the uncertainty of activity utility. An efficient solution algorithm without prior enumeration of DATPs is developed for solving the DATP scheduling problem in multi-modal transit networks. Numerical examples are used to illustrate the application of the proposed model and the solution algorithm.

Dynamic System Optimal Routing in Multimodal Transit Network

The system optimal routing problem has been widely studied for road networks, though less considered for public transit systems. Traditional shortest path–based multimodal itinerary guidance systems may deteriorate the system performance when the assigned lines become congested. The dynamic system optimal routing model for multimodal transit system is formulated for that issue. The transit system is represented by a multilevel graph to explicitly simulate passenger flow and transit system operations. A solution algorithm based on the cross entropy method is proposed, and its performance is compared with the method of successive averages in static and dynamic cases. A numerical study of a simple multimodal transit network provides the basis for comparing system optimal routing and user optimal routing under different congestion levels.

Performance indicators for public transit connectivity in multi-modal transportation networks

Connectivity plays a crucial role as agencies at the federal and state level focus on expanding the public transit system to meet the demands of a multimodal transportation system. Transit agencies have a need to explore mechanisms to improve connectivity by improving transit service. This requires a systemic approach to develop measures that can prioritize the allocation of funding to locations that provide greater connectivity, or in some cases direct funding towards underperforming areas. The concept of connectivity is well documented in social network literature and to some extent, transportation engineering literature. However, connectivity measures have limited capability to analyze multi-modal public transportation systems which are much more complex in nature than highway networks.In this paper, we propose measures to determine connectivity from a graph theoretical approach for all levels of transit service coverage integrating routes, schedules, socio-economic, demographic and spatial activity patterns. The objective of using connectivity as an indicator is to quantify and evaluate transit service in terms of prioritizing transit locations for funding; providing service delivery strategies, especially for areas with large multi-jurisdictional, multi-modal transit networks; providing an indicator of multi-level transit capacity for planning purposes; assessing the effectiveness and efficiency for node/stop prioritization; and making a user friendly tool to determine locations with highest connectivity while choosing transit as a mode of travel. An example problem shows how the graph theoretical approach can be used as a tool to incorporate transit specific variables in the indicator formulations and compares the advantage of the proposed approach compared to its previous counterparts. Then the proposed framework is applied to the comprehensive transit network in the Washington–Baltimore region. The proposed analysis offers reliable indicators that can be used as tools for determining the transit connectivity of a multimodal transportation network.