A tutorial on recursive models for analyzing and predicting path choice behavior

The problem at the heart of this tutorial consists in modeling the path choice behavior of network users. This problem has been extensively studied in transportation science, where it is known as the route choice problem. In this literature, individuals' choice of paths are typically predicted using discrete choice models. This article is a tutorial on a specific category of discrete choice models called recursive, and it makes three main contributions: First, for the purpose of assisting future research on route choice, we provide a comprehensive background on the problem, linking it to different fields including inverse optimization and inverse reinforcement learning. Second, we formally introduce the problem and the recursive modeling idea along with an overview of existing models, their properties and applications. Third, we extensively analyze illustrative examples from different angles so that a novice reader can gain intuition on the problem and the advantages provided by recursive models in comparison to path-based ones

Route choice and traffic equilibrium modeling in multi-modal and activity-based networks

Que ce soit pour aller au travail, faire du magasinage ou participer à des activités sociales, la mobilité fait partie intégrante de la vie quotidienne. Nous bénéficions à cet égard d'un nombre grandissant de moyens de transports, ce qui contribue tant à notre qualité de vie qu'au développement économique. Néanmoins, la demande croissante de mobilité, à laquelle s'ajoutent l'expansion urbaine et l'accroissement du parc automobile, a également des répercussions négatives locales et globales, telles que le trafic, les nuisances sonores, et la dégradation de l'environnement. Afin d'atténuer ces effets néfastes, les autorités cherchent à mettre en oeuvre des politiques de gestion de la demande avec le meilleur résultat possible pour la société. Pour ce faire, ces dernières ont besoin d'évaluer l'impact de différentes mesures. Cette perspective est ce qui motive le problème de l'analyse et la prédiction du comportement des usagers du système de transport, et plus précisément quand, comment et par quel itinéraire les individus décident de se déplacer. Cette thèse a pour but de développer et d'appliquer des modèles permettant de prédire les flux de personnes et/ou de véhicules dans des réseaux urbains comportant plusieurs modes de transport. Il importe que de tels modèles soient supportés par des données, génèrent des prédictions exactes, et soient applicables à des réseaux réels. Dans la pratique, le problème de prédiction de flux se résout en deux étapes. La première, l'analyse de choix d'itinéraire, a pour but d'identifier le chemin que prendrait un voyageur dans un réseau pour effectuer un trajet entre un point A et un point B. Pour ce faire, on estime à partir de données les paramètres d'une fonction de coût multi-attribut représentant le comportement des usagers du réseau. La seconde étape est celle de l'affectation de trafic, qui distribue la demande totale dans le réseau de façon à obtenir un équilibre, c.-à-d. un état dans lequel aucun utilisateur ne souhaite changer d'itinéraire. La difficulté de cette étape consiste à modéliser la congestion du réseau, qui dépend du choix de route de tous les voyageurs et affecte simultanément la fonction de coût de chacun. Cette thèse se compose de quatre articles soumis à des journaux internationaux et d'un chapitre additionnel. Dans tous les articles, nous modélisons le choix d'itinéraire d'un individu comme une séquence de choix d'arcs dans le réseau, selon une approche appelée modèle de choix d'itinéraire récursif. Cette méthodologie possède d'avantageuses propriétés, comme un estimateur non biaisé et des procédures d'affectation rapides, en évitant de générer des ensembles de chemins. Néanmoins, l'estimation de tels modèles pose une difficulté additionnelle puisqu'elle nécessite de résoudre un problème de programmation dynamique imbriqué, ce qui explique que cette approche ne soit pas encore largement utilisée dans le domaine de la recherche en transport. Or, l'objectif principal de cette thèse est de répondre des défis liés à l'application de cette méthodologie à des réseaux multi-modaux. La force de cette thèse consiste en des applications à échelle réelle qui soulèvent des défis computationnels, ainsi que des contributions méthodologiques. Le premier article est un tutoriel sur l'analyse de choix d'itinéraire à travers les modèles récursifs susmentionnés. Les contributions principales sont de familiariser les chercheur.e.s avec cette méthodologie, de donner une certaine intuition sur les propriétés du modèle, d'illustrer ses avantages sur de petits réseaux, et finalement de placer ce problème dans un contexte plus large en tissant des liens avec des travaux dans les domaines de l'optimisation inverse et de l'apprentissage automatique. Deux articles et un chapitre additionnel appartiennent à la catégorie de travaux appliquant la méthodologie précédemment décrite sur des réseaux réels, de grande taille et multi-modaux. Ces applications vont au-delà des précédentes études dans ce contexte, qui ont été menées sur des réseaux routiers simples. Premièrement, nous estimons des modèles de choix d'itinéraire récursifs pour les trajets de cyclistes, et nous soulignons certains avantages de cette méthodologie dans le cadre de la prédiction. Nous étendons ensuite ce premier travail afin de traiter le cas d'un réseau de transport public comportant plusieurs modes. Enfin, nous considérons un problème de prédiction de demande plus large, où l'on cherche à prédire simultanément l'enchaînement des trajets quotidiens des voyageurs et leur participation aux activités qui motivent ces déplacements. Finalement, l'article concluant cette thèse concerne la modélisation d'affectation de trafic. Plus précisément, nous nous intéressons au calcul d'un équilibre dans un réseau où chaque arc peut posséder une capacité finie, ce qui est typiquement le cas des réseaux de transport public. Cet article apporte d'importantes contributions méthodologiques. Nous proposons un modèle markovien d'équilibre de trafic dit stratégique, qui permet d'affecter la demande sur les arcs du réseau sans en excéder la capacité, tout en modélisant comment la probabilité qu'un arc atteigne sa capacité modifie le choix de route des usagers.Traveling is an essential part of daily life, whether to attend work, perform social activities, or go shopping among others. We benefit from an increasing range of available transportation services to choose from, which supports economic growth and contributes to our quality of life. Yet the growing demand for travel, combined with urban sprawl and increasing vehicle ownership rates, is also responsible for major local and global externalities, such as degradation of the environment, congestion and noise. In order to mitigate the negative impacts of traveling while weighting benefits to users, transportation planners seek to design policies and improve infrastructure with the best possible outcome for society as a whole. Taking effective actions requires to evaluate the impact of various measures, which necessitates first to understand and predict travel behavior, i.e., how, when and by which route individuals decide to travel. With this background in mind, this thesis has the objective of developing and applying models to predict flows of persons and/or vehicles in multi-modal transportation networks. It is desirable that such models be data-driven, produce accurate predictions, and be applicable to real networks. In practice, the problem of flow prediction is addressed in two separate steps, and this thesis is concerned with both. The first, route choice analysis, is the problem of identifying the path a traveler would take in a network. This is achieved by estimating from data a parametrized cost function representing travelers' behavior. The second step, namely traffic assignment, aims at distributing all travelers on the network's paths in order to find an equilibrium state, such that no traveler has an interest in changing itinerary. The challenge lies in taking into account the effect of generated congestion, which depends on travelers' route choices while simultaneously impacting their cost of traveling. This thesis is composed of four articles submitted to international journals and an additional chapter. In all the articles of the thesis, we model an individual's choice of path as a sequence of link choices, using so-called recursive route choice models. This methodology is a state-of-the-art framework which is known to possess the advantage of unbiased parameter estimates and fast assignment procedures, by avoiding to generate choice sets of paths. However, it poses the additional challenge of requiring one to solve embedded dynamic programming problems, and is hence not widely used in the transportation community. This thesis addresses practical and theoretical challenges related to applying this methodological framework to real multi-modal networks. The strength of this thesis consists in large-scale applications which bear computational challenges, as well as some methodological contributions to this modeling framework. The first article in this thesis is a tutorial on predicting and analyzing path choice behavior using recursive route choice models. The contribution of this article is to familiarize researchers with this methodology, to give intuition on the model properties, to illustrate its advantages through examples, and finally to position this modeling framework within a broader context, by establishing links with recently published work in the inverse optimization and machine learning fields. Two articles and an additional chapter can be categorized as applications of the methodology to estimate parameters of travel demand models in several large, real, and/or multi-dimensional networks. These applications go beyond previous studies on small physical road networks. First, we estimate recursive models for the route choice of cyclists and we demonstrate some advantages of the recursive models in the context of prediction. We also provide an application to a time-expanded public transportation networks with several modes. Then, we consider a broader travel demand problem, in which decisions regarding daily trips and participation in activities are made jointly. The latter is also modeled with recursive route choice models by considering sequences of activity, destination and mode choices as paths in a so-called supernetwork. Finally, the subject of the last article in this thesis is traffic assignment. More precisely, we address the problem of computing a traffic equilibrium in networks with strictly limited link capacities, such as public transport networks. This article provides important methodological contributions. We propose a strategic Markovian traffic equilibrium model which assigns flows to networks without exceeding link capacities while realistically modeling how the risk of not being able to access an arc affects route choice behavior

K shortest paths in stochastic time-dependent networks

A substantial amount of research has been devoted to the shortest path problem in networks where travel times are stochastic or (deterministic and) time-dependent. More recently, a growing interest has been attracted by networks that are both stochastic and time-dependent. In these networks, the best route choice is not necessarily a path, but rather a time-adaptive strategy that assigns successors to nodes as a function of time. In some particular cases, the shortest origin-destination path must nevertheless be chosen a priori, since time-adaptive choices are not allowed. Unfortunately, finding the a priori shortest path is NP-hard, while the best time-adaptive strategy can be found in polynomial time. In this paper, we propose a solution method for the a priori shortest path problem, and we show that it can be easily adapted to the ranking of the first K shortest paths. Moreover, we present a computational comparison of time-adaptive and a priori route choices, pointing out the effect of travel time and cost distributions. The reported results show that, under realistic distributions, our solution methods are effectiveShortest paths; K shortest paths; stochastic time-dependent networks; routing; directed hypergraphs

An optimal transportation routing approach using GIS-based dynamic traffic flows

This paper examines the value of real-time traffic information gathered through Geographic Information Systems for achieving an optimal vehicle routing within a dynamically stochastic transportation network. We present a systematic approach in determining the dynamically varying parameters and implementation attributes that were used for the development of a Web-based transportation routing application integrated with real-time GIS services. We propose and implement an optimal routing algorithm by modifying Dijkstra’s algorithm in order to incorporate stochastically changing traffic flows. We describe the significant features of our Web application in making use of the real-time dynamic traffic flow information from GIS services towards achieving total costs savings and vehicle usage reduction. These features help users and vehicle drivers in improving their service levels and productivity as the Web application enables them to interactively find the optimal path and in identifying destinations effectively

Dynamic routing on stochastic time-dependent networks using real-time information

In just-in-time (JIT) manufacturing environments, on-time delivery is one of the key performance measures for dispatching and routing of freight vehicles. Both the travel time delay and its variability impact the efficiency of JIT logistics operations, that are becoming more and more common in many industries, and in particular, the automotive industry. In this dissertation, we first propose a framework for dynamic routing of a single vehicle on a stochastic time dependent transportation network using real-time information from Intelligent Transportation Systems (ITS). Then, we consider milk-run deliveries with several pickup and delivery destinations subject to time windows under same network settings. Finally, we extend our dynamic routing models to account for arc traffic condition dependencies on the network. Recurrent and non-recurrent congestion are the two primary reasons for travel time delay and variability, and their impact on urban transportation networks is growing in recent decades. Hence, our routing methods explicitly account for both recurrent and non-recurrent congestion in the network. In our modeling framework, we develop alternative delay models for both congestion types based on historical data (e.g., velocity, volume, and parameters for incident events) and then integrate these models with the forward-looking routing models. The dynamic nature of our routing decisions exploits the real-time information available from various ITS sources, such as loop sensors. The forward-looking traffic dynamic models for individual arcs are based on congestion states and state transitions driven by time-dependent Markov chains. We propose effective methods for estimation of the parameters of these Markov chains. Based on vehicle location, time of day, and current and projected network congestion states, we generate dynamic routing policies using stochastic dynamic programming formulations. All algorithms are tested in simulated networks of Southeast-Michigan and Los Angeles, CA freeways and highways using historical traffic data from the Michigan ITS Center, Traffic.com, and Caltrans PEMS

On modal availability, travel strategies and traffic equilibrium on a multimodal network

27 pagesTransportation modes, including Walking and other private modes as well as transit services, provide travel options to the individual trip-maker along a transportation network. On a single basis, any modal option is featured here in terms of travel time to destination conditionally to immediate availability, expected wait time in the adverse case and the probability of availability. The paper is focused on availability in order to state its roles in travel strategy for route choice and traffic assignment onto a multimodal network. It deals with, successively, mode characterization, local travel strategy, network hyperpaths and traffic equilibrium. Assumedly, a private mode is available on a full, continuous basis, while a transit service is available on a partial, discrete basis due to station dwell time and service frequency. However, a capacitated transit service under saturation amounts to a fully available travel option which includes an initial wait time. A local travel strategy at a choice node is made up of either an ordered sequence of discrete options, or a continuous option, or a combination of both so that the discrete options are used opportunistically if available or the continuous one otherwise. This leads us to revisit the common line problem of transit assignment. A framework and an algorithm are provided to search for optimal travel strategies. The sequential treatment along a multimodal network is based on hyperpaths under availability conditions. Traffic equilibrium is addressed in the static setting; the system state includes the vector of trip flows by destination and network link together with vectors of strategy proportions by node and destination

Value of Traveler Information for Adaptive Routing in Stochastic Time-Dependent Networks

Real-time information plays an important role in travelers’ routing choices in an uncertain network by enabling online adaptation to revealed traffic conditions. The quality of the information affects its effectiveness. Usually there are some limitations in the information provided to the travelers, spatially, temporally or both. In this thesis, three variants of an optimal adaptive routing problem with partial online information problem are introduced: global information with time lag, global pre-trip information and radio information on a subset of links without time lag. A generic description of online information is provided. An algorithm is designed for the optimal routing problem in stochastic time-dependent networks with partial online information and specializations required for each of the three variants are given. A test example is conducted and computationally verifies the non-negative value of information. The work in this thesis is potentially of interest to traveler information systems evaluation and design