Schedule-based Transit Assignment 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.

Departure Time Choice in Schedule-Based Transit Assignment

This paper investigates existing departure time models for a schedule-based transit assignment and their parametrization. It analyzes the impact of the temporal resolution of travel demand and suggests functions for evaluating the adaptation time as part of the utility of a path. The adaptation time quantifies the time between the preferred and the scheduled departure times. The findings of the analysis suggested that travel demand should be discretized into intervals of 1 min, with interval borders right between the full minute, that is, ±0.5 min. It was shown that longer time intervals led to arbitrary run volumes, even for origin–destination pairs with just one transit line and a fixed headway. Although a linear relationship between adaptation time and adaptation disutility is a common assumption in several publications, it cannot represent certain types of passenger behavior. For some trip purposes, passengers may be insensitive to small adaptation times, but highly sensitive to large adaptations. This requires a nonlinear evaluation function.

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.

Hybrid Random Regret Minimization and Random Utility Maximization in the Context of Schedule-Based Urban Rail Transit Assignment

Route choice is one of the most critical passenger behaviors in public transit research. The utility maximization theory is generally used to model passengers’ route choice behavior in a public transit network in previous research. However, researchers have found that passenger behavior is far more complicated than a single utility maximization assumption. Some passengers tend to maximize their utility while others would minimize their regrets. In this paper, a schedule-based transit assignment model based on the hybrid of utility maximization and regret minimization is proposed to study the passenger route choice behavior in an urban rail transit network. Firstly, based on the smart card data, the space-time expanded network in an urban rail transit was constructed. Then, it adapts the utility maximization (RUM) and the regret minimization theory (RRM) to analyze and model the passenger route choice behavior independently. The utility values and the regret values are calculated with the utility and the regret functions. A transit assignment model is established based on a hybrid of the random utility maximization and the random regret minimization (RURM) with two kinds of hybrid rules, namely, attribute level hybrid and decision level hybrid. The models are solved by the method of successive algorithm. Finally, the hybrid assignment models are applied to Beijing urban rail transit network for validation. The result shows that RRM and RUM make no significant difference for OD pairs with only two alternative routes. For those with more than two alternative routes, the performance of RRM and RUM is different. RRM is slightly better than RUM in some of the OD pairs, while for the other OD pairs, the results are opposite. Moreover, it shows that the crowd would only influence the regret value of OD pair with more commuters. We conclude that compared with RUM and RRM, the hybrid model RURM is more general.

Reducing passengers’ travel time by optimising stopping patterns in a large-scale network: A case-study in the Copenhagen Region

Optimising stopping patterns in railway schedules is a cost-effective way to reduce passengers’ generalised travel costs without increasing train operators’ costs. The challenge consists in striking a balance between an increase in waiting time for passengers at skipped stations and a decrease in travel time for through-going passengers, with possible consequent changes in the passenger demand and route choices. This study presents the formulation of the skip-stop problem as a bi-level optimisation problem where the lower level is a schedule-based transit assignment model that delivers passengers’ route choices to the skip-stop optimisation model at the upper level, and where the upper level in return provides an improved timetable to the lower level. A heuristic method for large-scale urban networks is presented to solve this extremely complex bi-level problem, where the skip-stop optimisation is a mixed-integer problem, whereas the route choice model is a non-linear non-continuous mapping of the timetable. The method was tested on the suburban railway network in the Greater Copenhagen Region (Denmark): the reduction in railway passengers’ in-vehicle travel time was 5.5%, the reduction in passengers’ generalised travel cost was 3.2% and, at the system level, the yearly consumer surplus amounted at 76.7 million DKK (about 10.3 million EUR or 12.7 million USD) when compared to the existing stopping patterns.

Automatic calibration of agent-based public transit assignment path choice to count data

This work describes the calibration of a schedule-based transit assignment inside an iterative microscopic agent-based simulation. The calibration challenge implies that the behavioral rules should be modified in order to move the simulation closer to observed passenger counts. First, route choice set of agents is enriched with travel parameter utilities randomization. Secondly, the calibration interacts directly into the performance evaluation of individual daily plan of activities, so that the plan is also evaluated for its contribution to the count reproduction. In this way, appropriate plans from the calibration perspective can persist along simulation iterations. The Berlin public transport system with day-based counts is used as test scenario. The results show that the calibration approach can work with large scale scenarios, and that it is able to deal with the inter-temporal aspects implied by counts.

Modeling intermodal networks with public transport and vehicle sharing systems

This paper extends a schedule-based transit assignment model to integrate vehicle sharing systems (VSS) with or without fixed stations permitting one-way rentals. It is assumed that travelers receive information through mobile internet on vehicle location and availability and that they can use a real-time booking service. The proposed model extends the functionality of a scheduled-based transit assignment in two ways: (1) It generates intermodal route choice sets combining transit and non-transit trip legs. This functionality enables an accessibility analysis to identify od-pairs benefiting from VSS. (2) It distributes a given travel demand on the route choice set considering capacity constraints of VSS. This functionality can be applied for an impact analysis of a proposed VSS.

A new schedule-based transit assignment model with travel strategies and supply uncertainties

This paper proposes a new scheduled-based transit assignment model. Unlike other schedule-based models in the literature, we consider supply uncertainties and assume that users adopt strategies to travel from their origins to their destinations. We present an analytical formulation to ensure that on-board passengers continuing to the next stop have priority and waiting passengers are loaded on a first-come-first-serve basis. We propose an analytical model that captures the stochastic nature of the transit schedules and in-vehicle travel times due to road conditions, incidents, or adverse weather. We adopt a mean variance approach that can consider the covariance of travel time between links in a space–time graph but still lead to a robust transit network loading procedure when optimal strategies are adopted. The proposed model is formulated as a user equilibrium problem and solved by an MSA-type algorithm. Numerical results are reported to show the effects of supply uncertainties on the travel strategies and departure times of passengers.

Modeling Transit and Intermodal Tours in a Dynamic Multimodal Network

A fixed-point formulation and a simulation-based solution method were developed for modeling intermodal passenger tours in a dynamic transportation network. The model proposed in this paper is a combined model of a dynamic traffic assignment, a schedule-based transit assignment, and a park-and-ride choice model, which assigns intermodal demand (i.e., passengers with drive-to-transit mode) to the optimal park-and-ride station. The proposed model accounts for all segments of passenger tours in the passengers’ daily travel, incorporates the constraint on returning to the same park-and-ride location in a tour, and models individual passengers at a disaggregate level. The model has been applied in an integrated travel demand model in Sacramento, California, and feedback to the activity-based demand model is provided through separate time-dependent skim tables for auto, transit, and intermodal trips.

A Review on Transit Assignment Modelling Approaches to Congested Networks: A New Perspective

This paper reviews a number of studies on both frequency-and schedule-based transit assignment models that have been proposed by far, wherein various behavioural assumptions on a wide range of aspects are embedded. With a reinvestigation on the relationships and homogeneity between different modelling approaches, it explores the representative veins of the models, and thereby extends a new perspective to the existing reviews under a historical context. Meanwhile, both advantages and disadvantages of these methods are presented. On the strength of the analyses and discussions of the state-of-the-art transit assignment models, further research directions are suggested.

Schedule-based transit assignment model with vehicle capacity and seat availability

In this paper, we propose a new schedule-based equilibrium transit assignment model that differentiates the discomfort level experienced by sitting and standing passengers. The notion of seat allocation has not been considered explicitly and analytically in previous schedule-based frameworks. The model assumes that passengers use strategies when traveling from their origin to their destination. When loading a vehicle, standing on-board passengers continuing to the next station have priority to get available seats and waiting passengers are loaded on a First-Come-First-Serve (FCFS) principle. The stimulus of a standing passenger to sit increases with his/her remaining journey length and time already spent on-board. When a vehicle is full, passengers unable to board must wait for the next vehicle to arrive. The equilibrium conditions can be stated as a variational inequality involving a vector-valued function of expected strategy costs. To find a solution, we adopt the method of successive averages (MSA) that generates strategies during each iteration by solving a dynamic program. Numerical results are also reported to show the effects of our model on the travel strategies and departure time choices of passengers.

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.

Schedule-based transit assignment model with travel strategies and capacity constraints

In this paper, we propose a user equilibrium transit assignment model that takes into account transit schedules and individual vehicle capacities explicitly. The model assumes that passengers use travel strategies that can be adaptive over time and graphically represented as subgraphs. When loading a vehicle, on-board passengers continuing to the next stop have priority and waiting passengers can be loaded on a first-come-first-serve basis or in a random manner. The latter is appropriate when passengers mingle on waiting platforms. When a vehicle is full, passengers unable to board must wait for the next vehicle to arrive. The equilibrium conditions can be stated as a variational inequality involving a vector-valued function of expected strategy costs. Although the function is not necessarily continuous or monotonic, a solution to the variational inequality exists. To find a solution, we propose a method that takes successive averages as its iterates and generates strategies during each iteration by solving a dynamic program. Numerical examples empirically demonstrate that the algorithm converges to an equilibrium solution.

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.