A within-day dynamic traffic assignment model for urban road networks (original) (raw)
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A new continuous formulation of Dynamic Traffic Assignment, where a user equilibrium is expressed as a fixed point problem in terms of arc flow temporal profiles, is proposed. The precise aim of the paper is to integrate spillback modelling into an existing formulation of DTA, based on implicit path enumeration, which is capable of representing explicitly the formation and dispersion of vehicle queues on the road network, but allows the queue length to overcome the arc length. Specifically, we take into account the interaction among network links upstream and downstream road intersections deriving from time varying entering and exiting arc capacities due to vehicle queue spillovers, which is equivalent to introducing constraints on the queue lengths. To achieve this extension we introduce a sequence of models, that is the arc entering capacity model, the arc exiting capacity model, and the arc travel time model for time varying exiting capacity, describing, for given turning flow temporal profiles, the dynamic of the network nodes and arcs, and capable of representing the propagation of congestion among contiguous road links. Some numerical examples are devised to appreciate the relevant effect of spillback modelling in the context of DTA.
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
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.
Transportation Research Record Journal of the Transportation Research Board, 2009
The paper reports on the algorithmic treatment and computer implementation of a macroscopic dynamic traffic assignment model called LADTA. The modelling assumptions and the mathematical analysis founding the model are first stated. Detailed descriptions of the main algorithms are given, together with the principles of the computer implementation. It is shown how the design of the software architecture allows for distributed computation of a traffic assignment. The practical ability of this implementation to tackle with large size networks is illustrated by an application to the Paris road network, which comprises around 1,300 zones and 39,000 links.
Convergent Algorithm for Dynamic Traffic Assignment
Transportation Research Record, 1991
A link flow formulation and a convergent solution algorithm for the dynamic user equilibrium (DUE) traffic assignment problem for road networks with multiple trip origins and destinations are presented. The link flow formulation does not implicitly assume complete enumeration of all origin-destination paths as does the equivalent path flow formulation. DUE is a temporal generalization of the static user equilibrium (SUE) assignment problem with additional constraints to ensure temporally continuous paths of flow. Whereas SUE can be solved by methods of linear combinations, these methods can create temporally discontinuous flows if applied to DUE. This convergent dynamic algorithm (CDA) uses the Frank-Wolfe method of linear combinations to find successive solutions to DUE while holding node time intervals fixed from each origin. In DUE, the full assignment period of several hours is discretized into shorter time intervals of 10 to 15 min each, for which trip departure matrices are as...
Calculation of dynamic traffic equilibrium assignments
The calculation of dynamic equilibrium assignments of traffic is important in the analysis of congested road networks. The calculations involved are substantially more intricate than are the corresponding ones for static equilibria. Few authors have published details of dynamic equilibrium assignments; where details are given, some fail to achieve a good approximation to equilibrium whilst others generate assignments that are discontinuous in time. This paper addresses the issue of formulating dynamic traffic assignment in a way that is readily solvable and which leads to solutions that are of good quality and hence are plausible. Two aspects of the formulation have been found to be crucial in achieving this: these are the way in which time varying costs and flows are associated with each other in the mathematical condition that is solved for equilibrium, and the assumptions that are made implicitly about the continuity of the assigned flows. We consider simple test examples that use small networks and simple demand profiles so that dynamic equilibrium assignments can be calculated directly. We show that use of the best general formulation will lead to good quality solutions that are close approximations to the known one. However, we show that relatively innocuous variations in the formulation, such as inappropriate association of flows with costs or assumption of continuous assignments, can lead to unsatisfactory and noisy solutions that are implausible. This work provides a possible explanation and remedy for the implausible character of many published dynamic assignments.
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