Validation of a schedule‐based capacity restraint transit assignment model for a large‐scale network

This paper describes the application of a capacity restraint trip assignment algorithm to a real, large‐scale transit network and the validation of the results. Unlike the conventional frequency‐based approach, the network formulation of the proposed model is dynamic and schedule‐based. Transit vehicles are assumed to operate to a set of pre‐determined schedules. Passengers are assumed to select paths based on a generalized cost function including in‐vehicle and out‐of‐vehicle time and line change penalty. The time‐varying passenger demand is loaded onto the network by a time increment simulation method, which ensures that the capacity restraint of each vehicle during passenger boarding is strictly observed. The optimal‐path and path‐loading algorithms are applied iteratively by the method of successive averages until the network converges to the predictive dynamic user equilibrium. The Hong Kong Mass Transit Railway network is used to validate the model results. The potential applications of the model are also discussed.     

A computer model for finding the time-dependent minimum path in a transit system with fixed schedules

This paper describes the development of a computer model and algorithms for finding the time-dependent minimum path between two stations in a multi-route, multi-mode transit system running to fixed schedules. Selection of the minimum path can be based either on journey time or on weighted time. A worked example using a simple transit network is given to illustrate how the model works. The model has several applications in transport planning: it can be used for generating route schedule information to guide transit users, for assisting in route schedule coordination, and for analyzing transit system accessibility.     

Transit Users’ Route‐Choice Modelling in Transit Assignment: A Review

Abstract

This paper reviews the main studies on transit users’ route choice in the context of transit assignment. The studies are categorized into three groups: static transit assignment, within‐day dynamic transit assignment, and emerging approaches. The motivations and behavioural assumptions of these approaches are re‐examined. The first group includes shortest‐path heuristics in all‐or‐nothing assignment, random utility maximization route‐choice models in stochastic assignment, and user equilibrium based assignment. The second group covers within‐day dynamics in transit users’ route choice, transit network formulations, and dynamic transit assignment. The third group introduces the emerging studies on behavioural complexities, day‐to‐day dynamics, and real‐time dynamics in transit users’ route choice. Future research directions are also discussed.     

A simulation‐based reliability assessment approach for congested transit network

This paper is an attempt to develop a generic simulation‐based approach to assess transit service reliability, taking into account interaction between network performance and passengers' route choice behaviour. Three types of reliability, say, system wide travel time reliability, schedule reliability and direct boarding waiting‐time reliability are defined from perspectives of the community or transit administration, the operator and passengers. A Monte Carlo simulation approach with a stochastic user equilibrium transit assignment model embedded is proposed to quantify these three reliability measures of transit service. A simple transit network with a bus rapid transit (BRT) corridor is analysed as a case study where the impacts of BRT components on transit service reliability are evaluated preliminarily.     

A stochastic transit assignment model using a dynamic schedule-based network

Using the schedule-based approach, in which scheduled time-tables 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 which consists of four components: in-vehicle time; waiting time; walking time; and a time penalty for each line change. With the exception of in-vehicle time, each of the other cost components is weighted by a sensitivity coefficient which varies among travelers and is defined by a density function. This time-dependent and stochastic minimum path is generated by a specially developed branch and bound algorithm. The assignment procedure is conducted over a period in which both passenger demand and train headways are varying. Due to the stochastic nature of the assignment problem, a Monte Carlo approach is employed to solve the problem. A case study using the Mass Transit Railway System in Hong Kong is given to demonstrate the model and its potential applications.     

Modelling public transport on‐board congestion: comparing schedule‐based and agent‐based assignment approaches and their implications

Transit systems are subject to congestion that influences system performance and level of service. The evaluation of measures to relieve congestion requires models that can capture their network effects and passengers' adaptation. In particular, on‐board congestion leads to an increase of crowding discomfort and denied boarding and a decrease in service reliability. This study performs a systematic comparison of alternative approaches to modelling on‐board congestion in transit networks. In particular, the congestion‐related functionalities of a schedule‐based model and an agent‐based transit assignment model are investigated, by comparing VISUM and BusMezzo, respectively. The theoretical background, modelling principles and implementation details of the alternative models are examined and demonstrated by testing various operational scenarios for an example network. The results suggest that differences in modelling passenger arrival process, choice‐set generation and route choice model yield systematically different passenger loads. The schedule‐based model is insensitive to a uniform increase in demand or decrease in capacity when caused by either vehicle capacity or service frequency reduction. In contrast, nominal travel times increase in the agent‐based model as demand increases or capacity decreases. The marginal increase in travel time increases as the network becomes more saturated. Whilst none of the existing models capture the full range of congestion effects and related behavioural responses, existing models can support different planning decisions. Copyright © 2016 John Wiley & Sons, Ltd.     

A bi‐level programming approach — Optimal transit fare under line capacity constraints

The fare of a transit line is one of the important decision variables for transit network design. It has been advocated as an efficient means of coordinating the transit passenger flows and of alleviating congestion in the transit network. This paper shows how transit fare can be optimized so as to balance the passenger flow on the transit network and to reduce the overload delays of passengers at transit stops. A bi‐level programming method is developed to optimize the transit fare under line capacity constraints. The upper‐level problem seeks to minimize the total network travel time, while the lower‐level problem is a stochastic user equilibrium transit assignment model with line capacity constraints. A heuristic solution algorithm based on sensitivity analysis is proposed. Numerical example is used to illustrate the application of the proposed model and solution algorithm.     

Scheduling considerations for a branching transit route

This paper addresses the impacts of different scheduling alternatives for a branching transit route. It examines different schedule alternatives that might be used to optimize the route performance in terms of the passenger traveling time distributed among branch passengers and trunk‐line passengers. The schedule alternatives considered include transit vehicle allocation to different branches, offset shifting across vehicles on different branches, and vehicle holding (slack time) in the transit vehicle schedule. With these variables, several vehicle schedules are devised and examined based on a wide variety of possible passenger boarding scenarios using deterministic service models. Test outcomes provide general conclusions about the performance of the strategies. Vehicle assignment leading to even headways among branches is generally preferred for the case of low passenger demand. However, when passenger demand is high, or the differences between the passenger demands on branches are significant, unequal vehicle assignment will be helpful to improve the overall route performance. Holding, as a proactive strategy in scheduling, has the potential to be embedded into the schedule as a type of slack time, but needs further evidence and study to determine the full set of conditions where it may be beneficial. Offset shifting does not show sufficient evidence to be an efficient strategy to improve route performance in the case of low or high passenger demand.     

Modelling rain effects on risk‐taking behaviours of multi‐user classes in road networks with uncertainty

This paper proposes a new travel time reliability‐based traffic assignment model to investigate the rain effects on risk‐taking behaviours of different road users in networks with day‐to‐day demand fluctuations and variations in travel time. A generalized link travel time function is used to capture the rain effects on vehicle travel times and road conditions. This function is further incorporated into daily demand variations to investigate those travel time variations arising from demand uncertainty and rain condition. In view of these rain effects, road users' perception errors on travel times and risk‐taking behaviours on path choices are incorporated in the proposed model with the use of a logit‐based stochastic user equilibrium framework. This new model is formulated as a variational inequality problem in terms of path flows. A numerical example is used to illustrate the application of the proposed model for assessment of the rain effects on road networks with uncertainty.     

Time control point strategy coupled with transfer coordination in bus schedule design

A schedule consisting of an appropriate arrival time at each time control point can ensure reliable transport services. This paper develops a novel time control point strategy coupled with transfer coordination for solving a multi‐objective schedule design problem to improve schedule adherence and reduce intermodal transfer disutility. The problem is formulated using a robust mixed‐integer nonlinear programming model. The mixed‐integer nonlinear programming model is equivalently transformed into a robust mixed‐integer linear programming model, which is then approximated by a deterministic mixed‐integer linear programming model through Monte Carlo simulation. Thus, the optimal scheduled arrival time at each time control point can be precisely obtained using cplex . Numerical experiments based on three bus lines and the mass rapid transit system in Singapore are presented, and the results show that the schedule determined using the developed model is able to provide not only reliable bus service but also a smooth transfer experience for passengers. Copyright © 2016 John Wiley & Sons, Ltd.     

Modeling schedule recovery processes in transit operations for bus arrival time prediction

Many existing algorithms for bus arrival time prediction assume that buses travel at free‐flow speed in the absence of congestion. As a result, delay incurred at one stop would propagate to downstream stops at the same magnitude. In reality, skilled bus operators often constantly adjust their speeds to keep their bus on schedule. This paper formulates a Markov chain model for bus arrival time prediction that explicitly captures the behavior of bus operators in actively pursuing schedule recovery. The model exhibits some desirable properties in capturing the schedule recovery process. It guarantees provision of the schedule information if the probability of recovering from the current schedule deviation is sufficiently high. The proposed model can be embedded into a transit arrival time estimation model for transit information systems that use both real‐time and schedule information. It also has the potential to be used as a decision support tool to determine when dynamic or static information should be used.     

Large-scale application of MILATRAS: case study of the Toronto transit network

This paper documents the efforts to operationalize the conceptual framework of MIcrosimulation Learning-based Approach to TRansit Assignment (MILATRAS) and its component models of departure time and path choices. It presents a large-scale real-world application, namely the multi-modal transit network of Toronto which is operated by the Toronto Transit Commission (TTC). This large-scale network is represented by over 500 branches with more than 10,000 stops. About 332,000 passenger-agents are modelled to represent the demand for the TTC in the AM peak period. A learning-based departure time and path choice model was adopted using the concept of mental models for the modelling of the transit assignment problem. The choice model parameters were calibrated such that the entropy of the simulated route loads was optimized with reference to the observed route loads, and validated with individual choices. A Parallel Genetic Algorithm engine was used for the parameter calibration process. The modelled route loads, based on the calibrated parameters, greatly approximate the distribution underlying the observed loads. 75% of the exact sequence of transfer point choices were correctly predicted by the off-stop/on-stop choice mechanism. The model predictability of the exact sequence of route transfers was about 60%. In this application, transit passengers were assumed to plan their transit trip based on their experience with the transportation network; with no prior (or perfect) knowledge of service performance.     

Surrogate‐based optimization of cordon toll levels in congested traffic networks

The benefit, in terms of social surplus, from introducing congestion charging schemes in urban networks is depending on the design of the charging scheme. The literature on optimal design of congestion pricing schemes is to a large extent based on static traffic assignment, which is known for its deficiency in correctly predict travel times in networks with severe congestion. Dynamic traffic assignment can better predict travel times in a road network, but are more computational expensive. Thus, previously developed methods for the static case cannot be applied straightforward. Surrogate‐based optimization is commonly used for optimization problems with expensive‐to‐evaluate objective functions. In this paper, we evaluate the performance of a surrogate‐based optimization method, when the number of pricing schemes, which we can afford to evaluate (because of the computational time), are limited to between 20 and 40. A static traffic assignment model of Stockholm is used for evaluating a large number of different configurations of the surrogate‐based optimization method. Final evaluation is performed with the dynamic traffic assignment tool VisumDUE, coupled with the demand model Regent, for a Stockholm network including 1240 demand zones and 17 000 links. Our results show that the surrogate‐based optimization method can indeed be used for designing a congestion charging scheme, which return a high social surplus. Copyright © 2016 John Wiley & Sons, Ltd.     

An integrated multi‐objective model to determine the optimal rescue path and traffic controlled arcs for disaster relief operations under uncertainty environments

This study proposes an integrated multi‐objective model to determine the optimal rescue path and traffic controlled arcs for disaster relief operations under uncertainty environments. The model consists of three sub‐models: rescue shortest path model, post‐disaster traffic assignment model, and traffic controlled arcs selection model to minimize four objectives: travel time of rescue path, total detour travel time, number of unconnected trips of non‐victims, and number of police officers required. Since these sub‐models are inter‐related with each other, they are solved simultaneously. This study employs genetic algorithms incorporated with traffic assignment and K‐shortest path methods to determine optimal rescue path and controlled arcs. To cope with uncertain information associated with the damaged network, fuzzy system reliability theory (weakest t‐norm method) is used to measure the access reliability of rescue path. To investigate the validity and applicability of the proposed model, studies on an exemplified case and a field case of Chi‐Chi earthquake in Taiwan are conducted. The performances of three rescue strategies: without traffic control, selective traffic control (i.e. the proposed model) and absolute traffic control are compared. The results show that the proposed model can maintain the efficiency of rescue activity with minimal impact to ordinary trips and number of police officers required.     

Calibrating a transit assignment model using smart card data in a large-scale multi-modal transit network

This paper describes a practical automated procedure to calibrate and validate a transit assignment model. An optimization method based on particle swarm algorithm is adopted to minimize a defined error term. This error term which is based on the percentage of root mean square error and the mean absolute percent error encompasses deviation of model outputs from observations considering both segment level as well as the mode level and can be applied to a large scale network. This study is based on the frequency-based assignment model using the concept of optimal strategy while any transit assignment model can be used in the proposed methodological framework. Lastly, the model is validated using another weekday data. The proposed methodology uses automatic fare collection (AFC) data to estimate the origin–destination matrix. This study combines data from three sources: the general transit feed specification, AFC, and a strategic transport model from a large-scale multimodal public transport network. The South-East Queensland (SEQ) network in Australia is used as a case study. The AFC system in SEQ has voluminous and high quality data on passenger boardings and alightings across bus, rail and ferry modes. The results indicate that the proposed procedure can successfully develop a multi-modal transit assignment model at a large scale. Higher dispersions are seen for the bus mode, in contrast to rail and ferry modes. Furthermore, a comparison is made between the strategies used by passengers and the generated strategies by the model between each origin and destination to get more insights about the detailed behaviour of the model. Overall, the analysis indicates that the AFC data is a valuable and rich source in calibrating and validating a transit assignment model.

     

Design of public transit network in urban area with elastic demand

This research focuses on an efficient design of transit network in urban areas. The system developed is used to create, analyze and optimize routes and frequencies of transit system in the network level. The analysis is based on elastic demand, so the shift of demand between modes in network due to different service level is of prime consideration. The developed system creates all feasible routes connecting all pairs of terminals in the network. Out of this vast pool of routes, a set of optimal routes is generated for a certain predetermined number that maintains connectivity of significant demand. Based on these generated routes, the system fulfils transportation demand by assigning demand that considers path and route choices for non-transit users and transit users. Together with the assignment of demand, transit frequencies are optimized and the related fleet-size is calculated. Having an optimal setting of solution, the system is continued by reconnecting the routes to find some other better solutions in the periphery of the optimal setting. A set of mathematical programming modules is developed. Real data from Sioux Falls city network is used to evaluate the performance of the model and compare with other heuristic methods.     

Learning-based framework for transit assignment modeling under information provision

The modeling of service dynamics has been the focus of recent developments in the field of transit assignment modeling. The emerging focus on dynamic service modeling requires a corresponding shift in transit demand modeling to represent appropriately the dynamic behaviour of passengers and their responses to Intelligent Transportation Systems technologies. This paper presents the theoretical development of a departure time and transit path choice model based on the Markovian Decision Process. This model is the core of the MIcrosimulation Learning-based Approach to TRansit Assignment. Passengers, while traveling, move to different locations in the transit network at different points in time (e.g. at stop, on board), representing a stochastic process. This stochastic process is partly dependent on the transit service performance and partly controlled by the transit rider’s trip choices. This can be analyzed as a Markovian Decision Process, in which actions are rewarded and hence passengers’ optimal policies for maximizing the trip utility can be estimated. The proposed model is classified as a bounded rational model, with a constant utility term and a stochastic choice rule. The model is appropriate for modeling information provision since it distinguishes between individual’s experience with the service performance and information provided about system dynamics.     

Design and development of interactive trip planning for web-based transit information systems

This article presents a Web-based transit information system design that uses Internet Geographic Information Systems (GIS) technologies to integrate Web serving, GIS processing, network analysis and database management. A path finding algorithm for transit network is proposed to handle the special characteristics of transit networks, e.g., time-dependent services, common bus lines on the same street, and non-symmetric routing with respect to an origin/destination pair. The algorithm takes into account the overall level of services and service schedule on a route to determine the shortest path and transfer points. A framework is created to categorize the development of transit information systems on the basis of content and functionality, from simple static schedule display to more sophisticated real time transit information systems. A unique feature of the reported Web-based transit information system is the Internet-GIS based system with an interactive map interface. This enables the user to interact with information on transit routes, schedules, and trip itinerary planning. Some map rendering, querying, and network analysis functions are also provided.     

A computational model for the probit‐based dynamic stochastic user optimal traffic assignment problem

This paper focuses on computational model development for the probit‐based dynamic stochastic user optimal (P‐DSUO) traffic assignment problem. We first examine a general fixed‐point formulation for the P‐DSUO traffic assignment problem, and subsequently propose a computational model that can find an approximated solution of the interest problem. The computational model includes four components: a strategy to determine a set of the prevailing routes between each origin–destination pair, a method to estimate the covariance of perceived travel time for any two prevailing routes, a cell transmission model‐based traffic performance model to calculate the actual route travel time used by the probit‐based dynamic stochastic network loading procedure, and an iterative solution algorithm solving the customized fixed‐point model. The Ishikawa algorithm is proposed to solve the computational model. A comparison study is carried out to investigate the efficiency and accuracy of the proposed algorithm with the method of successive averages. Two numerical examples are used to assess the computational model and the algorithm proposed. Results show that Ishikawa algorithm has better accuracy for smaller network despite requiring longer computational time. Nevertheless, it could not converge for larger network. Copyright © 2010 John Wiley & Sons, Ltd.     

Multi‐objective airport gate assignment problem in planning and operations

We consider the assignment of gates to arriving and departing flights at a large hub airport. This problem is highly complex even in planning stage when all flight arrivals and departures are assumed to be known precisely in advance. There are various considerations that are involved while assigning gates to incoming and outgoing flights (such a flight pair for the same aircraft is called a turn) at an airport. Different gates have restrictions, such as adjacency, last‐in first‐out gates and towing requirements, which are known from the structure and layout of the airport. Some of the cost components in the objective function of the basic assignment model include notional penalty for not being able to assign a gate to an aircraft, penalty for the cost of towing an aircraft with a long layover, and penalty for not assigning preferred gates to certain turns. One of the major contributions of this paper is to provide mathematical model for all these complex constraints that are observed at a real airport. Further, we study the problem in both planning and operations modes simultaneously, and such an attempt is, perhaps, unique and unprecedented. For planning mode, we sequentially introduce new additional objectives to our gate assignment problem that have not been studied in the literature so far—(i) maximization of passenger connection revenues, (ii) minimization of zone usage costs, and (iii) maximization of gate plan robustness—and include them to the model along with the relevant constraints. For operations mode, the main objectives studied in this paper are recovery of schedule by minimizing schedule variations and maintaining feasibility by minimal retiming in the event of major disruptions. Additionally, the operations mode models must have very, very short run times of the order of a few seconds. These models are then applied to a functional airline at one of its most congested hubs. Implementation is carried out using Optimization Programming Language, and computational results for actual data sets are reported. For the planning mode, analyst perception of weights for the different objectives in the multi‐objective model is used wherever actual dollar value of the objective coefficient is not available. The results are also reported for large, reasonable changes in objective function coefficients. For the operations mode, flight delays are simulated, and the performance of the model is studied. The final results indicate that it is possible to apply this model to even large real‐life problems instances to optimality within short run times with clever formulation of conventional continuous time assignment model. Copyright © 2013 John Wiley & Sons, Ltd.