Schedule-based Transit Network Research Articles

Schedule-based transit assignment with online bus arrival information

Most public transportation services deviate from their published schedule. To cope with the delay caused by the unreliable service, passengers use online information about the bus arrival time which affects their route choice behavior. Current schedule-based transit assignment models fail to capture the passengers’ adaptive response to unreliable service, resulting in an inaccurate estimation of passenger wait time and passenger loads on various transit routes. The current study proposes schedule-based transit assignment models that incorporate online bus arrival information when modeling the passenger route choice in a stochastic and time-dependent transit network. The authors propose that passengers employ strategies when traveling between different origin–destination pairs not only due to the limited capacity of vehicles but also to cope with the transit delay. The passenger routing problem is modeled as a Markov Decision Process, and efficient algorithms are developed to solve this problem. Depending on the vehicle capacity, two types of assignment models are presented, namely, uncapacitated and capacitated assignments. When penalties for arriving at the destination outside the desired arrival time window are not applied, the uncapacitated assignment problem is formulated as a linear program. On the other hand, the capacitated assignment is formulated as a variational inequality problem for which an efficient Method of Successive Averages-based heuristic solution algorithm is proposed. Computational experiments are presented for a small and a large schedule-based transit network. The results show that denied boarding in an unreliable network leads to higher expected costs to passengers compared to the reliable and uncongested network. Furthermore, the analysis shows that the strategies evaluated with reliable schedule assumption lead to unreliable paths in the network and produces more transferring flow than should happen in practice. The application of our method to a subnetwork of the Twin Cities transit network with artificial demand reveals that passengers traveling from a residential area to the University of Minnesota campus may prefer taking a path with transfer in the event of highly unreliable transit service on the direct routes.

Developing and evaluating transit-based healthcare accessibility in a low- and middle-income country: A case study in Ulaanbaatar, Mongolia

This study examined transit-based accessibility to hospitals in Ulaanbaatar, the capital city of Mongolia, which is one of the low- and middle-income countries (LMICs). Promoting transit-based accessibility to hospitals is an important public health policy goal because limited accessibility can lead to adverse health outcomes. Public transit is especially crucial for people living in LMICs because many of them lack private vehicles. However, transit-based hospital accessibility has not been widely studied in LMICs. With the recent development of open-source transit analysis tools and standardization of schedule-based transit network data protocols, we could build Ulaanbaatar's schedule-based transit network dataset in great detail. We computed transit-based accessibility to hospitals from 128,032 residential parcels in Ulaanbaatar. Overall, transit-based accessibility to hospitals was higher in the central area than in the peripheral areas of Ulaanbaatar. Specifically, transit-based accessibility to hospitals was significantly lower in the ger area (settlements without central infrastructure connection to heat, water, and sewage) than in the non-ger area (apartment area). The results revealed that about 10% of people living in the study area have inadequate transit-based accessibility to hospitals. Our research is one of the first studies attempting to create a detailed schedule-based transit network and measure transit-based accessibility to hospitals in a rapidly growing, under-examined city in LMICs.

A schedule-based timetable model for congested transit networks

This study proposes a model and method for solving the transit timetabling problem with consideration of passenger path choices within a congested and schedule-based transit network. The model has two submodels: transit timetabling and passenger-equilibrium assignment. The transit timetabling submodel generates timetables to improve passengers’ journey experience based on the results of passenger-equilibrium assignment, whereas the passenger-equilibrium assignment loads passengers on transit vehicles based on a fixed vehicle capacity and timetable output from the transit timetabling. An iterative method is developed to connect these two submodels and efficiently determine an optimal solution. The iterative method includes an equilibrium assignment method to simulate passenger loading and suggests a decomposition approach for transit timetabling. The decomposition approach has a significant computational advantage when handling transit systems that involve hundreds of transit vehicles because the algorithm generates a timetable for one transit line in each step rather than for all transit lines. The decomposition approach can therefore handle relatively large problems with more transit lines. The suggested algorithms are analyzed with a hypothetical example and with the practically sized example of South China’s high-speed railway in terms of efficiency, optimality, and applicability.

An online shortest path algorithm for reliable routing in schedule-based transit networks considering transfer failure probability

Most schedule-based transit assignment models assume deterministic vehicle arrival/departure times, in contrast to random vehicle arrival assumption in frequency-based models. This assumption simplifies user route choice behavior and fails to capture users’ response to unreliable service. Moreover, the inherent inconvenience of transfers, primarily due to uncertain waiting time and failure probability, has always been a challenge in modeling transit networks, to the extent that determining an appropriate transfer penalty for heterogeneous user population is still a question when using planning models. This study aims to bridge the gap between frequency-based and schedule-based transit assignment models, and proposes a path algorithm in schedule-based transit networks with stochastic vehicle arrival times to model users’ adaptive behavior in response to unreliable service. Path reliability is modeled by link failure probability, and an online shortest path algorithm is developed to find a routing policy with minimum expected travel time given preferred arrival time to destination. Complexity analyses and computational tests indicate that the model has potential for application in large-scale transit networks. Numerical tests verify that the model assigns passengers to more reliable paths with lower transfer rate without a need for a large transfer penalty.

Corrigendum to “Least Expected Time Paths in Stochastic Schedule-Based Transit Networks”

Corrigendum to “Least Expected Time Paths in Stochastic Schedule-Based Transit Networks”

Simulation-Based Dynamic Passenger Flow Assignment Modelling for a Schedule-Based Transit Network

The online operation management and the offline policy evaluation in complex transit networks require an effective dynamic traffic assignment (DTA) method that can capture the temporal-spatial nature of traffic flows. The objective of this work is to propose a simulation-based dynamic passenger assignment framework and models for such applications in the context of schedule-based rail transit systems. In the simulation framework, travellers are regarded as individual agents who are able to obtain complete information on the current traffic conditions. A combined route selection model integrated with pretrip route selection and entrip route switch is established for achieving the dynamic network flow equilibrium status. The train agent is operated strictly with the timetable and its capacity limitation is considered. A continuous time-driven simulator based on the proposed framework and models is developed, whose performance is illustrated through a large-scale network of Beijing subway. The results indicate that more than 0.8 million individual passengers and thousands of trains can be simulated simultaneously at a speed ten times faster than real time. This study provides an efficient approach to analyze the dynamic demand-supply relationship for large schedule-based transit networks.

Three Extensions of Tong and Richardson’s Algorithm for Finding the Optimal Path in Schedule-Based Railway Networks

High-speed railways have been developing quickly in recent years and have become a main travel mode between cities in many countries, especially China. Studying passengers’ travel choices on high-speed railway networks can aid the design of efficient operations and schedule plans. The Tong and Richardson algorithm that is used in this model offers a promising method for finding the optimal path in a schedule-based transit network. However, three aspects of this algorithm limit its application to high-speed railway networks. First, these networks have more complicated common line problems than other transit networks. Without a proper treatment, the optimal paths cannot be found. Second, nonadditive fares are important factors in considering travel choices. Incorporating these factors increases the searching time; improvement in this area is desirable. Third, as high-speed railways have low-frequency running patterns, their passengers may prefer to wait at home or at the office instead of at the station. Thus, consideration of a waiting penalty is needed. This paper suggests three extensions to improve the treatments of these three aspects, and three examples are presented to illustrate the applications of these extensions. The improved algorithm can also be used for other transit systems.

A dynamic simulation model of passenger flow distribution on schedule-based rail transit networks with train delays

Abstract In a schedule-based rail transit system, passenger route choices are affected by train delays, and, consequently, the relevant passenger flow distribution of the network will differ from the normal state. In this paper, a passenger's alternative choices, such as selecting another route, waiting, and switching to other transportation modes, and the corresponding influence mechanism are analyzed in detail. Given train time–space diagrams and the time-varying travel demands between the origin and destination (O–D), a dynamic simulation model of passenger flow distribution on schedule-based transit networks with train delays is proposed. Animation demonstration and statistical indices, including the passenger flow volume of each train and station, can be generated from simulation results. A numerical example is given to illustrate the application of the proposed model. Numerical results indicate that, compared with conventional methods, the proposed model performs better for a passenger flow distribution with train delays.

Modeling park-and-ride location choice of heterogeneous commuters

There is extensive literature on drive-to-transit trips, yet very few studies focus on commuters’ park-and-ride location choice decisions. This study investigates park-and-ride location choice behavior of heterogeneous commuters in the Austin Metropolitan Statistical Area. Data from a transit on-board survey conducted by Capital Metro in 2010 were used. Besides, schedule-based transit networks and a detailed regional highway network were used to calculate path attributes. A thorough analysis on the choice set generation was conducted, and two criteria were used to determine the most appropriate park-and-ride choice set for each observed trip. Finally, user heterogeneity was accounted by adding interaction terms in the utility functions and by using mixed logit models. Empirical models reveal that designation of a park-and-ride facility by transit agency and the frequency of transit paths to destination have the highest positive effect, while transit transfers, auto travel time, and walking time have the most significant negative impact on the utility of a park-and-ride location. More specifically, correlation analysis reveals that travelers who are more likely to be motivated by short auto travel time are also more likely to be motivated by few transfers and short walking time. In addition, this study implies that non-Caucasians prefer higher fraction of their auto path on freeways; and commuters with higher income are less motivated by high transit service frequency. The estimated models in this study can have immediate application in travel forecasting, specifically for drive-to-transit trip assignment, as well as in setting policy for park-and-rides service design.

Least Expected Time Paths in Stochastic Schedule-Based Transit Networks

We consider the problem of determining a least expected time (LET) path that minimizes the number of transfers and the expected total travel time in a stochastic schedule-based transit network. A time-dependent model is proposed to represent the stochastic transit network where vehicle arrival times are fully stochastically correlated. An exact label-correcting algorithm is developed, based on a proposed dominance condition by which Bellman’s principle of optimality is valid. Experimental results, which are conducted on the Ho Chi Minh City bus network, show that the running time of the proposed algorithm is suitable for real-time operation, and the resulting LET paths are robust against uncertainty, such as unknown traffic scenarios.

Trip-Based Path Algorithms Using the Transit Network Hierarchy

In this paper, we propose a new network representation for modeling schedule-based transit systems. The proposed network representation, called trip-based, uses transit vehicle trips as network edges and takes into account the transfer stop hierarchy in transit networks. Based on the trip-based network, we propose a set of path algorithms for schedule-based transit networks, including algorithms for the shortest path, a logit-based hyperpath, and a transit A*. The algorithms are applied to a large-scale transit network and shown to have better computational performance compared to the existing labeling algorithms.

Cost Functions for Strategies in Schedule-Based Transit Networks with Limited Vehicle Capacities

Passengers in congested transit networks need to understand capacity constraints of vehicles when network congestion prevents boarding a vehicle. A strategy concept was developed for schedule-based networks. The passenger is assumed to know the schedule, to be aware of the capacity constraints, and to realize the possibility of being unable to board a vehicle. Therefore, the passenger must plan for several what-if scenarios at each decision point of the trip. The concept of strategies in networks with capacity constraints was extended in a study. The strategy costs were defined in terms of a random variable. Properties of this random variable, mean value and variance, for example, were used to define new types of cost functions. This approach accounts for passengers' aversion to travel time variability and risk. In the literature, these ideas were originally developed for path choice models in private traffic but had not yet been applied to public transport. In the current study, the developed mean excess approach was adjusted so that it could be applied to public transport.

Congestion Pricing for Schedule-Based Transit Networks

In this paper, we develop models for adjusting or setting fares on a transit system to encourage passengers to choose travel strategies that lead to the least travel delay for the entire system. In our problem setting, these fares vary with time of day. Similar to the one used to reduce congestion on vehicular traffic networks, our goal is to adjust or set fares so that a user equilibrium solution under the new fares yields the least delay or is system optimal. On the other hand, pricing frameworks for traffic networks such as marginal cost pricing do not readily apply because the travel delay in transit systems involves factors different from those in vehicular traffic and cannot be expressed in closed functional forms. The models herein are schedule based and account for loading priorities and individual vehicle capacities explicitly. Differences among the proposed models are illustrated with a small network.

The multi-class schedule-based transit assignment model under network uncertainties

Demand and supply uncertainties at schedule-based transit network levels strongly impact different passengers’ travel behavior. In this paper, a new multi-class user reliability-based dynamic transit assignment model is presented. Passengers differ in their heterogeneous risk-taking attitudes towards the random travel cost. The stochastic characteristics of the main travel cost components (in-vehicle travel time, waiting time, and early or late penalty) are demonstrated by specifying the demand and supply uncertainties and their interactions. Passenger route and departure time choice is determined by each passenger’s respective reliability requirements. Vehicle capacity constraint for random passenger demand is handled by an in-vehicle congestion parameter. The proposed model is formulated as a fixed-point problem, and solved by a heuristic MSA-type algorithm. The numerical result shows that the risk-taking attitude will impact greatly on passengers’ travel mode and departure time choices, as well as their money and time costs. This model is also capable of generating transit service attributes such as the stochastic vehicle dwelling time and the deviated timetable.

Finding the K shortest paths in a schedule-based transit network

Finding the shortest paths in a schedule-based public transit network is similar to finding the shortest paths in a network with multi-costs constrained and time-window constraints. We consider a schedule-based transit network, where each node in the network has a list of scheduled departure times for transit vehicles. The objective of this paper is to find out the first K shortest paths in a schedule-based transit network. An algorithm with a time complexity of O ( S ¯ 2 L ¯ 3 ) + O ( L ¯ 4 S ¯ R l max ) + O ( S ¯ L ¯ R l max K ( L ¯ 3 log ( L ¯ 3 ) + L ¯ 3 ) ) is proposed to enumerate these paths. We compare the time complexity of our algorithm with that of two existing path finding algorithms. We show that our algorithm has a better performance in computational time complexity than the two existing path finding algorithms, though it is only applicable if the number of transfers does not exceed 2. Also, for large sized real transit network, our algorithm determines the K shortest paths in a much shorter time frame than the existing two algorithms.

A dynamic schedule-based model for congested transit networks

In this paper we propose a model and algorithm for solving the equilibrium assignment problem in a congested, dynamic and schedule-based transit network. We assume that the time varying origin–destination trip demand is given. All travelers have full predictive information (that have been gained through past experience) about present and future network conditions and select paths that minimize a generalized cost function that encompasses four components: (a) in-vehicle time; (b) waiting time; (c) walking time; and (d) a line change penalty. All transit vehicles have a fixed capacity and operate precisely as specified in pre-set timetables. Passengers queue at platforms according to the single channel first-in-first-out discipline. By using time-increment simulation, the passenger demand is loaded onto the network and the available capacity of each vehicle is updated dynamically. After each simulation run, the passenger arrival and departure profiles at all stations are recorded and these are used to predict dynamic queuing delays. From such delays, minimum paths are updated and used for the next simulation run. The user equilibrium assignment problem is solved iteratively by the method of successive averages.

A schedule‐based dynamic transit network model — Recent advances and prospective future research

AbstractUsing the schedule‐based approach, in which scheduled timetables are used to describe the movement of vehicles, a dynamic transit assignment model is formulated. Passengers are assumed to travel on a path with minimum generalized cost that consists of four components: in‐vehicle time; waiting time; walking time; and a time penalty for each line change. A specially developed branch and bound algorithm is used to generate the time‐dependent minimum path. The assignment procedure is conducted over a period in which both passenger demand and train headway are varying. This paper presents an overview of the research that has been carried out by the authors to develop the schedule‐based transit assignment model, and offers perspectives for future research.

Estimation of time-dependent origin–destination matrices for transit networks

In this paper, the estimation of time-dependent origin–destination (O–D) matrices for transit network based on observed passenger counts is given. The dynamic assignment framework is based on a schedule-based transit network model, which can help determine the time-dependent least cost paths between all O–D pairs, and for each of them the clock arrival times at the end nodes of all observed links (if any) in the transit network. An entropy-based approach is then employed to estimate the time-dependent O–D matrices based on the observed passenger counts at those observed links in the network. An efficient sparse algorithm is also proposed to solve the resulting mathematical programming problem. The estimation methodology is tested in a transit network from the Mass Transit Railway (MTR) system in Hong Kong which is one of the busiest railway systems in the world. Both cases with and without prior information of the O–D matrices are considered for this network. The predicted matrices are then compared with the true matrices obtained from a sophisticated electronic fare collection system of MTR. Good agreement between predicted and observed matrices are found.