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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...

An Approximate Analytic Model of Many-to-Many Demand Responsive Transportation Systems

Carlos Daganzo
1978

This paper presents an analytic model to predict average waiting and ridingtimes in urban transportation systems (such as dial-a-bus and taxicabs), which provide non-transfer door-to-door transportation with a dynamically dispatched fleet of vehicles. Three different dispatching algorithms are analyzed with a simple deterministic model, which is then generalized to capture the most relevant stochastic phenomena. The formulae obtained have been successfully compared with simulated data and are simple enough for hand calculation. They are, thus, tools which enable analysts to avoid...

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...

Computation of Equilibrium Over Transportation Networks: The Case of Disaggregate Demand Models

Sheffi, Yosef
Carlos Daganzo
1980

The transportation planning forecasting process has been traditionally performed on a sequential, disconnected, heuristic basis, using different methodologies for each one of the stages. In an attempt to improve this situation, a first step toward developing a unified transportation forecasting methodology is described in this paper. This is done by showing how many, seemingly different, problems can be cast as analogous route choice problems on abstract networks and studied with the same methodology. As a consequence of this analogy, it is possible to perform equilibrium analyses and to...

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...

Aggregation with Multinomial Probit and Estimation of Disaggregate Models with Aggregate Data: A New Methodological Approach

Bouthelier, Fernando
Carlos Daganzo
1979

This paper describes an analytic aggregation procedure for disaggregate demand models similar to the one proposed in earlier publications by Westin (1974) and McFadden and Reid (1975). The technique, which uses a multivariate normal approximation for the distribution of the vector of attributes, is based on the multinomial profit algorithm proposed by Daganzo, Bouthelier and Sheffi (1977) and can be applied to an arbitrary number of alternatives. The procedure is computationally so efficient that it enables us to calibrate disaggregate models with aggregate data by maximum likelihood using...

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...