Traffic Assignment Algorithm Research Articles

Network representation, continuum approximations and a solution to the spatial aggregation problem of traffic assignment

This paper complements the preceding one, which showed how one could modify equilibrium traffic assignment algorithms for networks with many centroids. In this one it is shown how one can substitute centroids by zones with continuous population densities. The technique, which is mathematically guaranteed to approximate a flow pattern in accordance with Wardrop's user equilibrium criterion, requires some geometrical calculations which can be handled off-line. With the suggested approach, it is possible to represent the spatial distribution of trip ends more realistically and this allows traffic assignment models to capture the effects of short and intrazonal trips in a way previously impossible. The method is shown to be computationally feasible.

An equilibrium algorithm for the spatial aggregation problem of traffic assignment

Present traffic assignment methods require that all possible origins and destinations of trips taking place within a study area be represented as if they were taking place to and from a small set of points or centroids. Each centroid is supposed to represent the location of all trip-ends within a given zone, and this necessarily misrepresents points located at the edges of the zone. In order to alleviate this problem (which we refer to as the spatial aggregation problem) one could use smaller zones and more centroids, but existing traffic assignment algorithms cannot efficiently handle many centroids. This paper introduces an algorithm procedure which is designed to handle a substantially larger number of centroids. In the paper that follows, the technique is further developed to take into account a continuous distribution of population.

User Losses in Earthquake-Damaged Roadway Networks

Network analysis of an earthquake-damaged arterial system is performed using a highly efficient traffic assignment algorithm. The reduced trip volume and increased average trip time can be obtained for any simulated earthquake; the (hourly) loss in total net user benefit is obtained, and is labelled the user loss. The analysis is repeated for a set of discrete earthquakes which model the hazard. The end result is the annual expected user loss; this is a direct measure of seismic risk. In one example the user loss increases more rapidly with intensity than does the repair-replacement costs.

Formulating and solving the network design problem by decomposition

The optimal transportation network design problem is formulated as a convex nonlinear programming problem and a solution method based on standard traffic assignment algorithms is presented. The technique can deal with network improvements which introduce new links, which increase the capacity of existing links, or which decrease the free-flow (uncongested) travel time on existing links (with or without simultaneously increasing link capacity). Preliminary computational experience with the method demonstrates that it is capable of solving very large problems with reasonable amounts of computer time.

On the traffic assignment problem with flow dependent costs—II

This note generalizes the results obtained by Daganzo (1977) in a previous paper by showing how to incorporate link capacities into any equilibrium traffic assignment algorithm. This is done by defining an equivalent uncapacitated traffic equilibrium problem (EP). As an example it is shown how Nguyen's algorithm (Nguyen, 1974) can be easily modified to deal with capacitated networks.

An extension of Dial's algorithm utilizing a model of tripmakers' perceptions

Dial has developed a probabilistic multipath traffic assignment algorithm which is very efficient. However, the assignment of trips to paths is based on a logit model which has some undesirable properties. The purpose of this paper is to extend Dial's algorithm by utilizing a simple model of tripmakers' perceptions and behavior. An important advantage these models have is that they can be calibrated through the study of tripmakers' behavior on a limited set of trips rather than through the study of origin and destination patterns and link flows on a large network. Three traffic assignment models are presented which are computationally equivalent to Dial's model and which can be implemented by making minor changes in his algorithm. One of the new models, based on path likelihoods, contains Dial's model as a special case. The assumptions required about tripmakers' perceptions to obtain this special case seem unreasonable and this explains some of the undesirable properties of Dial's model. In its general form, the new model eliminates some of these undesirable properties. However, like Dial's model, it generally allocates a disproportionate number of trips to portions of a road network in which there is a large number of choices of minor variations in route. The other two models, based on arrival likelihoods and turn likelihoods, both overcome this shortcoming. These two models have different interpretations in terms of tripmaker behavior. The model based on turn likelihoods is the most intuitive and contains Gunnarsson's multipath traffic assignment model as a special case.

A Primal-Dual Traffic Assignment Algorithm

A new algorithm for solving the traffic assignment problem is presented. This is a primal-dual algorithm which utilizes a flow augmentation primal and a shortest path dual procedure. At each iteration a feasible solution is known together with a measure of “goodness” of the solution. It is shown that the algorithm converges to an optimal solution. Experience with the algorithm suggests that this convergence is very rapid.

A Column Generation Algorithm for Optimal Traffic Assignment

A column generation algorithm for solving a class of nonlinear traffic assignment problems is presented. The fundamental advantage of the algorithm is that it does not require the a priori generation of all paths joining each origin-destination pair. The algorithm is capable of handling rather large networks. Computational experience that contrasts column generation with the a priori generation of all paths and compares two different quadratic programming algorithms is reported.

Traffic Assignment In A GIS Environment

This article presents some experiences in running a parallel traffic assignment algorithm in a Geographic Information System (GIS) setting. The GIS software and the need for parallelization are briefly discussed. Two examples of signal setting in real time and the estimation of origin-destination matrices using traffic counts reported by sensors in real time are described.