Dynamic Traffic Assignment: Properties and Extensions (original) (raw)

Stochastic and deterministic formulations of dynamic traffic assignment

Dynamic traffic assignment is now widely recognised as an appropriate approach for modelling route choice and congestion in urban areas during peak periods, and for the evaluation of traffic management measures that are intended for them. Various formulations have been developed in the literature: in the present paper we consider the within-day dynamics of departure-time and route choice using costs based upon travel times and arrival times. We show how a general formulation of this joint choice process can accommodate either stochastic or deterministic user equilibrium principles. A model of traffic flow is required to provide travel times which determine the propagation of traffic through the network and also contribute to the cost of travel. By adopting mechanistic models of traffic movement and hence travel time, we show how temporal departure profiles and route assignments can be calculated according to each of the choice principles and develop cost-throughput relationships for them from this. We consider the effects on these profiles and relationships of various mechanistic travel time models, including deterministic queueing and the more detailed wave model. Detailed comparisons are made between the results according to the various choice and travel time models; we show that a good degree of commonality can be identified between them. The results of this are plausible and compare favourably with those in the literature that arise from the use of simple but non-mechanistic travel time models. We conclude that mechanistic travel time models have a fundamental importance for satisfactory dynamic modelling of congestion and of users' response to it, whichever choice model is adopted.

Dynamic Traffic Assignment: A Survey of Mathematical Models and Techniques

Complex Networks and Dynamic Systems, 2013

This paper presents a survey of the mathematical methods used for modeling and solutions for the traffic assignment problem. It covers the static (steady state) traffic assignment techniques as well as dynamic traffic assigment in lumped parameter and distributed parameter settings. Moreover, it also surveys simulation based solutions. The paper shows the models for static assignment, variational inequality method, projection dynamics for dynamic travel routing, discrete time and continuous time dynamic traffic assignment and macroscopic Dynamic Traffic Assignment (DTA). The paper then presents the macroscopic DTA in terms of the Wardrop principle and derives a partial differential equation for experienced travel time function that can be integrated with the macroscopic DTA framework.

Properties of Dynamic Traffic Assignment with Physical Queues

Journal of the Eastern Asia Society for Transportation Studies, 2005

Queue spillback is a common phenomenon in congested transportation networks. Nevertheless, traditionally, dynamic traffic assignment (DTA) problems are developed with the point-queue concept in which queue spillback is not captured. Indeed, one recent focus in DTA research is to capture this phenomenon and develop solution methods for the physical- queue DTA formulations. However, the properties of these problems, which have important implications on the theoretical advances and computational issues on transportation planning and operations, are not well recognized and understood. This paper summarizes the properties of physical-queue DTA, compares those with point-queue DTA, and discusses their implications. In particular, the interrelationship among properties including First-In-First-Out, causality, travel-time-link-flow consistency, and queue spillback are emphasized in this paper.

Analysis of dynamic traffic models and assignments

In Proceedings of the 39th Annual Conference of Universities Transport Study January 3 5 2007 Harrogate Uk Universities Transport Study Group, 2007

This paper develops a comprehensive framework for analysing and solving traffic models and assignments in dynamic setting. Traffic models capture the time-varying travel times and flows on a road network and traffic assignments represent the corresponding responses of travellers. There are two different kinds of traffic assignments: dynamic user equilibrium and dynamic system optimum. Under dynamic user equilibrium, traffic is assigned such that for each origin-destination pair in the network, the individual travel costs experienced by each traveller, no matter which combination of travel route and departure time he/she chooses, are equal and minimal. The system optimum assigns traffic such that the total system cost of the network system is minimized. The system optimal traffic pattern provides a useful benchmark for evaluating various transport policy measures such as implementing dynamic road tolls. This system optimal assignment is formulated as a state-dependent optimal control problem. The analysis developed in this paper is novel and it can work with general travel cost functions. Numerical examples are provided for illustration and discussion. Finally, some concluding remarks are given. previous research (see for example, Friesz et al., 1993;, we have gained substantial knowledge on the formulations, properties, and solution methods of dynamic user equilibrium assignment. Dynamic system optimal assignment is an important yet relatively underdeveloped area. Dynamic system optimal assignment process suggests that there is a central "system manager" to distribute network traffic over time in a fixed study period. Consequently, the total, rather than individual, travel cost of all travellers through the network is minimised. Although system optimal assignment is not a realistic representation of network traffic, it provides a bound on how we can make the best use of the road system, and as such it is a useful benchmark for evaluating various transport policy measures. This paper presents a comprehensive framework of dynamic traffic models and traffic assignments. The paper is organized as follows. In Section 2, we review some fundamental requirements on traffic models for use in dynamic traffic assignments, Section 3 presents the formulation of dynamic user equilibrium assignment and the associated travel cost functions. In Section 4, we present the formulation and optimality conditions of dynamic system optimal assignment. Dynamic system optimal assignment problem is formulated as a state-dependent optimal control problem. To understand and solve the dynamic system optimality conditions, we also provide a detailed interpretation of various cost components appear at system optimality. We further develop a novel sensitivity analysis to derive and compute the dynamic externality. Section 5 presents the solution algorithms for solving the sensitivity analysis and the dynamic traffic assignments. The solution algorithms are developed using a dynamic programming approach. Following this, we show some

Foundations of Dynamic Traffic Assignment: The Past, the Present and the Future

Networks & Spatial Economics, 2001

Dynamic Traffic Assignment (DTA) has evolved substantially since the pioneering work of Merchant and Nemhauser. Numerous formulations and solutions approaches have been introduced ranging from mathematical programming, to variational inequality, optimal control, and simulation-based. The aim of this special issue is to document the main existing DTA approaches for future reference. This opening paper will summarize the current understanding of

Dynamic Traffic Assignment under Equilibrium and Non-equilibrium: Do We Need a Paradigm Shift?

… of the 3rd International Symposium on …, 2010

In this discussion paper we present to the DTA community our view of the future development of what is currently referred to as non-equilibrium DTA approaches. We propose the concept of equilibrium user strategies in congested networks as an extension of the well-known Wardrop equilibrium. Equilibrium user strategies provide a theoretical framework that should bring focus in the development of dynamic process or day-to-day DTA models.

Dynamic traffic assignment: model classifications and recent advances in travel choice principles

2011

Dynamic Traffic Assignment (DTA) has been studied for more than four decades and numerous reviews of this research area have been conducted. This review focuses on the travel choice principle and the classification of DTA models, and is supplementary to the existing reviews. The implications of the travel choice principle for the existence and uniqueness of DTA solutions are discussed, and the interrelation between the travel choice principle and the traffic flow component is explained using the nonlinear complementarity problem, the variational inequality problem, the mathematical programming problem, and the fixed point problem formulations. This paper also points out that all of the reviewed travel choice principles are extended from those used in static traffic assignment. There are also many classifications of DTA models, in which each classification addresses one aspect of DTA modeling. Finally, some future research directions are identified.

Dynamic Traffic Assignment: Theory, Computation and Emerging Paradigms

2015

Dynamic traffic assignment (DTA) is now an established research specialty overlapping several fields of scholarly enquiry: civil engineering, industrial engineering, operations research, statistics, mathematics, computer science, regional science, city planning, complexity science, sustainability science, and economics. Several hundred scientists and engineers around the globe are devoting substantial energy to DTA research. Moreover, the theory and computational methods arising from DTA research continue to move closer to application and decision support in real-world environments. In 2012 we issued a call for a broad spectrum of DTA research manuscripts in order to provide a snapshot in time of the diverse points of view being pursued by scholars around the world. Presenters at the Fourth International Symposium on Dynamic Traffic Assignment at Martha's Vineyard, USA, were invited to submit manuscripts for possible publication in Networks and Spatial Economics. From those invitations, we have assembled a collection of 29 papers, each of which has been comprehensively reviewed. Those 29 papers have been arranged as Parts I and II, which will appear under separate covers. Part I focuses on fundamental methodological advances in dynamic traffic assignment including network loading models, continuous time models, day to day dynamics. Part II focuses on application of dynamic traffic assignment in

A Strategic Model for Dynamic Traffic Assignment

Networks and Spatial Economics, 2000

In this paper, we propose a model of dynamic traffic assignment where strategic choices are an integral part of user behaviour. The model is based on a discrete-time description of flow variation through a road network involving arcs with rigid capacities. In such network, a driver's strategy consists in a rule that assigns to each node of the network a set of arcs in the forward star of that node, sorted according to some preference order. The main element of the model is a 'within-day' submodel where strategic volumes are loaded onto the network in accordance with the first-in first-out discipline and user preferences. An equilibrium assignment is achieved when expected delays of active strategies are minimal, for every origin-destination pair. We prove the existence of such an assignment and provide numerical results on test networks.

Analytical models of the dynamic traffic assignment problem

Networks and Spatial Economics, 2001

A review of analytical formulations of the dynamic traf®c assignment problem is presented, focusing on the authors' experience with variational inequality approaches. Solution algorithms and computational issues requiring additional study are discussed.