Path Choice Behavior Research Articles

Continuum modelling of pedestrian flows: From microscopic principles to self-organised macroscopic phenomena

The dynamics of pedestrian flows can be captured in a continuum modelling framework. However, compared to vehicular flow, this is a much more challenging task. In particular the integration of flow propagation and path choice are known to be problematic. Furthermore, pedestrian flow is characterised by different self-organised phenomena, such as the formation of dynamic lanes and diagonal stripes, which have not yet been captured in a continuum modelling framework.This contribution puts forward a novel multi-class continuum model that captures some of the key features of pedestrian flows. It considers path choice behaviour on both the strategic (pre-trip) and tactical (en-route) level. To achieve this, we present a methodology to derive a continuum model from a microscopic walker model, in this case the social forces model. In doing so, we show that the interaction term present in the social forces model introduces a local path choice component in the equilibrium velocity.Having derived the model, we analyse its properties both by means of mathematical analyses and simulation studies. This reveals the general behaviour of the model, as well as the ability of the model to reproduce self-organised structures, and phase transitions. To the best of our knowledge, this is the first continuum model that is able to reproduce these self-organised structures.

Estimation of mean and covariance of peak hour origin–destination demands from day-to-day traffic counts

This paper proposes a generalized model to estimate the peak hour origin–destination (OD) traffic demand variation from day-to-day hourly traffic counts throughout the whole year. Different from the conventional OD estimation methods, the proposed modeling approach aims to estimate not only the mean but also the variation (in terms of covariance matrix) of the OD demands during the same peak hour periods due to day-to-day fluctuation over the whole year. For this purpose, this paper fully considers the first- and second-order statistical properties of the day-to-day hourly traffic count data so as to capture the stochastic characteristics of the OD demands. The proposed model is formulated as a bi-level optimization problem. In the upper-level problem, a weighted least squares method is used to estimate the mean and covariance matrix of the OD demands. In the lower-level problem, a reliability-based traffic assignment model is adopted to take account of travelers’ risk-taking path choice behaviors under OD demand variation. A heuristic iterative estimation-assignment algorithm is proposed for solving the bi-level optimization problem. Numerical examples are presented to illustrate the applications of the proposed model for assessment of network performance over the whole year.

Within-day traffic assignment and signal setting in road evacuation: a procedure with explicit path enumeration

In the sphere of the SICURO research project, we propose a framework for signal setting design of road intersections with explicit path enumeration. The framework has two main components: an optimization procedure for signal setting design and a within-day simulation procedure to capture effects of signal setting modification on path choice behaviour. This paper describes the elements of the simulation procedure and illustrates some disaggregate results obtained from its application on an experimental test site. Keywords Evacuation, signal setting design, within-day traffic assignment Language: en

Signal Setting In Urban Areas:A Procedure With Day-to-day DynamicAnd Stability Constraints

In this paper a model and a procedure for signal setting design with demand assignment are reported. The model is developed within a day-to-day dynamic framework where demand assignment is dealt with through deterministic (or stochastic) process models. The system of models, based on a what-to approach, generates signal timings taking into account users path choice behaviour as well as stability constraints. The main contribution in this paper is the specification of the heuristic procedure for signal setting optimization, based on genetic algorithm. The procedure is tested on a real scale test site with the objectives to validate the system of models and the optimization procedure. A sensitivity analysis with respect to demand level is also briefly discussed.

Journey time estimator for assessment of road network performance under demand uncertainty

This paper proposes a journey time estimator (JTE) to estimate the stochastic journey time of each path for performance assessment in road network with uncertainty due to day-to-day demand variations. The stochastic network framework is adopted in this paper, in which link flows and path journey times are modeled as random variables so as to fully utilize the first- and the second-order statistical properties of the partial data collected for the journey time estimation. The second-order statistical property is referred to the variance–covariance (var–cov) of the observed path journey times and link flows available for the estimation. In this paper, the proposed JTE is formulated as a bi-level optimization problem. The objective of the upper-level problem is a variant of the Least Squares function, which considers the mean and var–cov of the observed path journey times. In addition, the observed statistical distribution of the link flow is also used to formulate a chance constraint in the upper-level problem. The lower-level problem is the reliability-based stochastic user equilibrium traffic assignment problem in stochastic network, which explicitly considers the reliability-based path choice behaviors of the road users under demand uncertainty. A heuristic iterative estimation-assignment algorithm is employed to solve the proposed bi-level problem. Numerical examples are provided to demonstrate the applications of the JTE and efficiency of the proposed algorithm.

Traffic dynamics in the correlated networks with user equilibrium

With the consideration of network structure and travelers’ path choice behavior in the congested traffic network, we study the effects of network topologies with degree-degree uncorrelation and correlations (assortative and disassortative correlation) on the performance of traffic network. How the effects of rewiring probability and the degree distribution exponent impact on the traffic congestion and the network efficiency are mainly analyzed. It is found that the correlated network is more vulnerable to traffic congestion compared with uncorrelated ones. Therefore, the uncorrelated network can support much more volume of traffic and have a larger carrying capacity when the traveler’s choice behavior is considered.

Signal Setting Optimisation with Route Choice Behaviour and Acyclic Profiles of Vehicular Flows in Road Networks

Traffic signal setting is an important element in traffic control and in the management of urban road networks both in ordinary conditions (ex. recurrent traffic congestion) and/or in emergency conditions (ex. non-recurrent traffic congestion caused by unexpected events). The paper presents models and procedures for signal setting optimisation of signalised junctions in a congested road network. Two interacting procedures are developed to solve the system of models:•an optimisation procedure, based on a genetic algorithm, to obtain an optimal configuration of signal setting parameters and•a simulation procedure, incorporating a path choice model with explicit path enumeration and a flow propagation model, to capture effects of signal setting configuration on user path choice behaviour.The main research contributions of this work are related to: (i) the modelling of path choice behaviour in a dynamic context with vehicular flow propagation of on link and spill-back; (ii) the optimisation procedure of signal setting parameters. The system of models and procedures has been applied and validated on a real experimental test site, where the transport system is in dynamic conditions due to time-varying road network and travel demand.

Dynamic pricing, heterogeneous users and perception error: Probit-based bi-criterion dynamic stochastic user equilibrium assignment

A probit-based bi-criterion dynamic stochastic user equilibrium (BDSUE) model is presented to capture path choice behavior of heterogeneous users with distinct values of time (VOT) and different perception of travel costs in response to pricing and congestion in a transportation network. Across the population of travelers, the VOT is represented by a continuously distributed random variable, and path travel cost perception errors are multivariate normally distributed. The BDSUE problem is formulated as a fixed point problem in the infinite dimensional space, and solved by a column generation framework which embeds (i) a parametric analysis method (PAM) to transform the continuous problem to the finite dimensional space by finding breakpoints that partition the entire range of VOT into subintervals and define a multi-class dynamic stochastic user equilibrium (MDSUE) problem; (ii) a column generation algorithm to augment a feasible path set for each user class; (iii) a probit-based stochastic path flow updating scheme to solve a restricted MDSUE problem defined by the set of feasible paths using an averaging method; and (iv) dynamic network loading using a particle-based traffic simulator to capture traffic dynamics and determine experienced travel times for a given path flow pattern. Numerical experiments on a medium size network are conducted to explore convergence of the solution algorithm and to illustrate heterogeneous user responses to dynamic tolls.

Mind the map! The impact of transit maps on path choice in public transit

This paper investigates the impact of schematic transit maps on passengers’ travel decisions. It does two things: First, it proposes an analysis framework that defines four types of information delivered from a transit map: distortion, restoration, codification, and cognition. It then considers the potential impact of this information on three types of travel decisions: location, mode, and path choices. 1 Path refers to a unique sequence of entry, transfer, and exit stations/stops in the public transit network. The author differentiates between path and route choices because the latter could refer to a situation among different service routes that follow the same physical path, which is not the purpose of this analysis. 1 Second, it conducts an empirical analysis to explore the impact of the famous London tube map on passengers’ path choice in the London Underground (LUL). Using data collected by LUL from 1998 to 2005, the paper develops a path choice model and compares the influence between the distorted tube map (map distance) and reality (travel time) on passengers’ path choice behavior. Results show that the elasticity of the map distance is twice that of the travel time, which suggests that passengers often trust the tube map more than their own travel experience on deciding the “best” travel path. This is true even for the most experienced passengers using the system. The codification of transfer connections on the tube map, either as a simple dot or as an extended link, could affect passengers’ transfer decisions. The implications to transit operation and planning, such as trip assignments, overcrowding mitigation, and the deployment of Advanced Transit Information System (ATIS), are also discussed.

Numerical simulation of pedestrian flow past a circular obstruction

In this paper, a revisiting Hughes’ dynamic continuum model is used to investigate and predict the essential macroscopic characteristics of pedestrian flow, such as flow, density and average speed, in a two dimensional continuous walking facility scattered with a circular obstruction. It is assumed that pedestrians prefer to walk a path with the lowest instantaneous travel cost from origin to destination, under the consideration of the current traffic conditions and the tendency to avoid a high-density region and an obstruction. An algorithm for the pedestrian flow model is based on a cellcentered finite volume method for a scalar conservation law equation, a fast sweeping method for an Eikonal-type equation and a second-order TVD Runge-Kutta method for the time integration on unstructured meshes. Numerical results demonstrate the effectiveness of the algorithm. It is verified that density distribution of pedestrian flow is influenced by the position of the obstruction and the path-choice behavior of pedestrians.

Congestion Pricing, Heterogeneous Users, and Travel Time Reliability

With the increasing interest in road pricing strategies to alleviate congestion and improve network performance, this study develops a multi-criterion dynamic user equilibrium (MDUE) traffic assignment model that explicitly considers heterogeneous users who seek to minimize three essential decision attributes: travel time, out-of-pocket cost, and travel time reliability in the underlying path choice framework. The value of time in this study is treated as a continuous random variable distributed across the population of trip makers, and travel time reliability is estimated at a path level. Furthermore, the proposed MDUE model is capable of considering different vehicle classes, namely, low-occupancy vehicles and high-occupancy vehicles; thus, with greater realism in trip makers’ path choice behavior, the MDUE model is applicable for analyzing a variety of road pricing scenarios. To address the practical application aspects for large-scale congested networks, novel implementation techniques are proposed to overcome computational obstacles to real-world application. An application to the New York metropolitan regional network is demonstrated, and a set of numerical experiments is conducted on this network to explore the convergence behavior, solution quality, and required computational time of the MDUE algorithm.

An Activity-Based Land Use and Transportation Optimization Model

This paper investigates the joint optimization problem of land use development and transportation network improvement. A novel bi-level model is proposed to solve this problem. The upper level is to determine residential/employment developments and road link capacity expansions with a budget so that the maximal population (residents/ employees) is accommodated while satisfying user utility (in terms of level of service) requirement. The accommodated population distribution by residential/employment locations and user utility are obtained by the lower level. The lower level is the combined network user equilibrium model. It models user location choice, activity pattern choice and path choice behaviors under the determined land use development and transportation network improvement in the upper level. A heuristic solution algorithm is designed for solving the proposed bi-level programming problem. A numerical example is presented to illustrate the applications and merits of the proposed model and solution algorithm.

The Effects of Sense of Progression and Cognitive Distance on Path Choice and Walking Behavior While Aiming To Reach Destination

Problem statement: Studies focused on walking behavior have indicated the relationship of different factors of built environment with walking to reach destination and walking for recreation. Furthermore, according to literature on path choice behavior, there is a relationship between walking behavior and path choice of pedestrians. Empirical studies on path choice behavior have also shown that the effects of different environmental variables on path choice vary with the purpose of the trip; whether recreational purposes or work-related walking trips. However there is a necessity to theoretically understand why consideration of purpose of the trip is important in studies of walking as well as path choice behavior. Furthermore, since reaching the destination is the most important travel purpose in daily activities, the environmental variables related to walking to reach the destination as well as path choice when aiming to reach destination need special consideration, if the goal is to encourage walking in daily basis. Approach: This study, therefore, relied on literature review to find answer to the research questions. Two concepts of instrumental and divertive behavior were used to answer the first research question. Research proceeded with making an effort to extract and introduce the main environmental variables related to walking and path choice of pedestrians when aiming to reach the destination. Results: Based on the definition of instrumental and divertive behavior, the necessity of consideration of purpose of the trip and its effects on environmental variables affecting walking as well as path choice behavior were theoretically verified. Moreover, two factors of cognitive distance and sense of progression were found to be the most important factors affecting walking and path choice behavior while aiming to reach destination. The physical features contributing to creation of sense of progression were also extracted and introduced. It is also suggested that sense of progression affects walking and path choice behavior through affecting cognitive distance and generating positive affective responses. Conclusion: It is suggested that future empirical studies be conducted to support the hypothesized relationships extracted and introduced in this study. Such studies would contribute to planning and design of urban spaces which would encourage walking in a daily basis.

Evaluation and Design of Transport Network Capacity under Demand Uncertainty

A flexible evaluation and design model for transport network capacity under demand variability is proposed. The future stochastic demand is assumed to follow a normal distribution. Traveler path choice behavior is assumed to follow the probit stochastic user equilibrium. The network reserve capacity is used to evaluate the performance of the network. Since the future demand is stochastic, the reserve capacity is measured by possible increases in both mean and standard deviation (SD) of the base demand distribution. The proposed model therefore represents the flexibility of the network in its robustness to origin-destination demand variation (i.e., high SD). The proposed model can also determine an optimal network design to maximize the reserve capacity of the network for both the mean and the SD of the increased demand distribution. The implicit programming approach is applied to solve the optimization problem. Sensitivity analysis is adopted to provide all necessary derivatives. The model and algorithm are tested with a hypothetical network to illustrate the merits of the proposed model.

Bi-level programming model and hybrid genetic algorithm for flow interception problem with customer choice

This paper investigates how to optimize the facility location strategy such as to maximize the intercepted customer flow, while accounting for “flow-by” customers’ path choice behaviors and their travel cost limitation. A bi-level programming static model is constructed for this problem. An heuristic based on a greedy search is designed to solve it. Consequently, we proposed a chance constrained bi-level model with stochastic flow and fuzzy trip cost threshold level. For solving this uncertain model more efficiently, we integrate the simplex method, genetic algorithm, stochastic simulation and fuzzy simulation to design a hybrid intelligent algorithm. Some examples are generated randomly to illustrate the performance and the effectiveness of the proposed algorithms.

MAXIMIZING CAR OWNERSHIP UNDER CONSTRAINTS OF ENVIRONMENT SUSTAINABILITY IN A CITY

This study aims to optimize road traffic flow and forecast the maximum car ownership accommodated in a city to satisfy environmental requirement and quantify road traffic capacity. A bi-level optimization model is established, where upper level is a maximum car ownership model, whose objective function is the total zonal car ownerships and the constraint is that traffic environment load on a link should not exceed the transportation environmental capacity, while lower level is a fixed demand user equilibrium assignment model, which simulates travelers' path choice behavior. To realize the feedback between the two levels and solve the optimization problems simultaneously, an optimal algorithm based on sensitivity analysis was developed, namely acquire derivative function of link volume and traffic demand with respect to zonal car ownership, and feedback the function into upper level program. Finally, we verify the bi-level model and the algorithm with a case study.

Probit-Based Time-Dependent Stochastic User Equilibrium Traffic Assignment Model

This study presents a time-dependent stochastic user equilibrium (TDSUE) traffic assignment model within a probit-based path choice decision framework that explicitly takes into account temporal and spatial correlation (traveler interactions) in travel disutilities across a set of paths. The TDSUE problem, which aims to find time-dependent SUE path flows, is formulated as a fixed-point problem and solved by a simulation-based method of successive averages algorithm. A mesoscopic traffic simulator is employed to determine (experienced) time-dependent travel disutilities. A time-dependent shortest-path algorithm is applied to generate new paths and augment a grand path set. Two vehicle-based implementation techniques are proposed and compared in order to show their impact on solution quality and computational efficiency. One uses the classical Monte Carlo simulation approach to explicitly compute path choice probabilities, and the other determines probabilities by sampling vehicles’ path travel costs from an assumed perception error distribution (also using a Monte Carlo simulation process). Moreover, two types of variance-covariance error structures are discussed: one considers temporal and spatial path choice correlation (due to path overlapping) in terms of aggregated path travel times, and the other uses experienced (or empirical) path travel times from a sample of individual vehicle trajectories. A set of numerical experiments are conducted to investigate the convergence pattern of the solution algorithms and to examine the impact of temporal and spatial correlation on path choice behavior.

Modeling of path-choice behavior based on the regret minimization criteria givena full travel information

This article formulates the drivers' behaviors of path-choice when travel information for a set of paths is given to each driver after finishing his or her trip.While an underpinning theory of the behavioral model stems from a regret matching theory, the basic framework is adjusted to capture the characteristic of congested networks. The notable feature of the model is that each driver is treatedas an individual decision maker as in game theory. In addition, uncertainty thata driver faces is endogenously generated as the results of mutually dependent path-choice behavior. Drivers are modeled to achieve no-regret criteria and to learn uncertain environment with stochastic approximation.Dynamic of updating the propensity of path-choice is characterized by the ODE approach, and is shownto converge to an internally chain recurrent set. However, this is not the case for the congested network with monotone cost functions. If we admit monotone cost function, then the regret matching approach with stochastic approximation has very nice feature that allows a generic travel cost function such as asymmetric Jacobian, piece-wise linear and so on.

Dynamic Network Simulation–Assignment Platform for Multiproduct Intermodal Freight Transportation Analysis

This paper develops a dynamic freight network simulation–assignment platform for the analysis of multiproduct intermodal freight transportation systems. At the core of the platform is a model framework for the mode–path assignment problem in multimodal freight transportation networks. The framework consists of three main components: a multimodal freight network simulation component, a multimodal freight assignment component, and a multiple product intermodal shortest path procedure. The freight network simulation component incorporates a bulk queuing model to evaluate transfer delay experienced by shipments at intermodal transfer terminals, classification yards, and ports. The multimodal freight assignment component determines the network flow pattern from a mode–path alternative set calculated by the multiple product intermodal shortest path procedure, based on the link travel costs and node transfer delays from the multimodal freight network simulation component. This model can represent individual shipment mode–path choice behavior, consolidation policy, conveyance link moving, and individual shipment terminal transfer in an iterative solution framework.

Demand-Driven Traffic Assignment Problem Based on Travel Time Reliability

A novel user equilibrium traffic assignment model based on travel time reliability is presented in view of day-to-day demand fluctuation. Because of daily demand variations, path travel times are not constants, and so they can be viewed as random variables. Assuming that travelers are able to learn the variation of path travel time from experience, a demand-driven user equilibrium principle based on travel time reliability is proposed to characterize travelers’ path choice behavior under uncertainty in travel times caused by demand variation. This principle can be formulated as a variational inequality (VI) problem in terms of path flows. The existence of at least one solution for the VI problem, for which a heuristic solution algorithm is adopted, is rigorously proved. Numerical examples are used to illustrate the applications of the proposed model and the solution algorithm.