Traffic Theory

On the Traffic Assignment Problem with Flow Dependent Costs—I

Carlos Daganzo
1977

In a recent paper LeBlanc et al. presented an efficient mathematical algorithm to solve the multicommodity user-equilibrated network flow distribution problem with flow dependent costs. This paper shows how to generalize the algorithm to networks with link capacities and illustrates the modification with a simple numerical example.

On Stochastic Models of Traffic Assignment

Carlos Daganzo
Sheffi, Yosef
1977

This paper contains a quantitative evaluation of probabilistic traffic assignment models and proposes an alternate formulation. First, the concept of stochastic-user-equilibration (S-U-E) is formalized as an extension of Wardrop's user-equilibration criterion. Then, the stochastic-network-loading (S-N-L) problem (a special case of S-U-E for networks with constant link costs) is analyzed in detail and an expression for the probability of route choice which is based on two general postulates of user behavior is derived. The paper also discusses the weaknesses of existing S-N-L techniques...

Probabilistic Structure of Two-Lane Road Traffic

Carlos Daganzo
1975

In most predictive models for two-lane road traffic, it is assumed that platoons have no physical dimensions, thus restricting their applicability to light traffic where a platoon cannot be long enough to block the progression of the next one. In this paper a model that can be used for heavy traffic is presented. A queueing theory approach in which vehicles are allowed to have physical dimensions yields the platoon length distribution, the delays to fast vehicles, the headway process and the flow density diagram for both the space and time processes. Unlike in other models, the passing...

Some Statistical Problems in Connection with Traffic Assignment

Carlos Daganzo
1977

This paper gives the approximation joint probability distribution function of the link traffic flows on a network. The knowledge of such distribution enables us to derive the log-likehood function for the estimation (with link data) of the traffic diversion parameter, Ф, that appears in most stochastic assignment models. It also enables us to perform goodness to fit statistical tests for the validation of traffic assignment methods. Both of these procedures are illustrated with a small numerical example. It is also pointed out that it is possible to calibrate and/or validate a traffic...

On the Traffic Assignment Problem with Flow Dependent Costs—II

Carlos Daganzo
1977

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.

Another "Paradox” of Traffic Flow

Sheffi, Yosef
Carlos Daganzo
1978

This note presents a counter-intuitive result that arises when stochastic traffic assignment methods are used. The phenomenon is explained and compared to Braess' paradox (Braess, 1968). The relationship to travel demand analysis is pointed out.

An Equilibrium Algorithm for the Spatial Aggregation Poblem of Traffic Assignment

Carlos Daganzo
1980

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...

Network Representation, Continuum Approximations and a Solution to the Spatial Aggregation Problem of Traffic Assignment

Carlos Daganzo
1980

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...

Estimation of Gap Acceptance Parameters: Sequential vs. Simultaneous Method in Light Poisson Traffic

Han, A.F.
Carlos Daganzo
1982

Derivation of Delays Based on Input-Output Analysis

Carlos Daganzo
1983

In a recent paper Michalpoulos and Pisharody (1981) contend that traditional input-output analysis results in substantial overestimation of delays, and they develop an alternate, more laborious, calculation method. This premise is incorrect since input-output analysis is nothing more than a simple accounting method, which by definition gives exact results. It should give results consistent with the more laborious method proposed by those authors.