ITS Berkeley

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...

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.

Traffic Delay at Unsignalized Intersections: Clarification of Some Issues

Carlos Daganzo
1977

Investigations in this area have been directed at finding the delay to a motorist who arrives at an intersection and wishes to cross a high-priority traffic stream. In this paper two conceptual errors that have appeared in some past publications are identified and corrected.

Multinomial Probit and Qualitative Choice: A Computationally Efficient Algorithm

Carlos Daganzo
Bouthelier, Fernando
Sheffi, Yosef
1977

Even though multinomial probit models have many attractive theoretical features and have been proposed for diverse choice problems (such as modal split and route choice in the transportation field), they have never been used in practice due to the lack of an adequate numerical technique for their application. The purpose of this paper is to introduce such a technique and to demonstrate the feasibility of forecasting with multinominal probit models. Our limited computational experience with the proposed numerical technique indicates that it is accurate, and can be efficiently applied to...

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...

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.

The Statistical Interpretation of Predictions with Disaggregate Demand Models

Carlos Daganzo
1979

This paper discusses an element of forecasting with disaggregate demand models that has received little attention so far; namely, the extent to which the accuracy of the final prediction depends on the accuracy of the calibration process. The paper introduces a numerical technique to evaluate approximate confidence intervals for the expected number of people using a transportation facility and approximate prediction intervals for the actual usage. It is shown that, unless the magnitude of the variance of the estimated parameters is considerably small, the predictions that result may be...

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.

Hypernetworks and Supply-Demand Equilibrium Obtained with Disaggregate Demand Models

Sheffi, Yosef
Carlos Daganzo
1978

This paper presents a framework for discussing many transportation demand and supply-demand equilibrium problems. It regards the sequence of choices an individual faces when he or she is about to make a travel (or not-to-travel) decision as a case choice of a route on an abstract network (hypernetwork). Hypernetworks are intimately related to the multinomial probit (MNP) model of travel choice. For instance, the multivariate normal distribution underlying this model enables one to represent processes of travel choice as route choices on networks and to use the networks as visual aids...