Modeling

Probabilistic Structure of Two-Lane Road Traffic

Daganzo, Carlos F.
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...

On Stochastic Models of Traffic Assignment

Daganzo, Carlos F.
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...

Multinomial Probit and Qualitative Choice: A Computationally Efficient Algorithm

Daganzo, Carlos F.
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...

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

Daganzo, Carlos F.
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...

The Statistical Interpretation of Predictions with Disaggregate Demand Models

Daganzo, Carlos F.
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...

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

Bouthelier, Fernando
Daganzo, Carlos F.
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...

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

Sheffi, Yosef
Daganzo, Carlos F.
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...

Optimal Sampling Strategies for Statistical Models with Discrete Dependent Variables

Daganzo, Carlos F.
1980

The object of this paper is to improve the cost-effectiveness of data gathering procedures for models with discrete dependent variables. It is assumed throughout the paper that the true value of the parameter vector is approximately known and that, with that information, one must select a statistically optimal number of observations from different population subgroups to refine the accuracy of the estimate. It is shown that the problem can be reduced to a small mathematical program whose objective function can be written after a few preliminary algebraic manipulations. For binary choice...

Estimation of Gap Acceptance Parameters within and Across the Population from Direct Roadside Observation

Daganzo, Carlos F.
1981

This paper explores the feasibility of maximum likelihood as an approach to determine the parameters of gap acceptance functions when these functions vary from individual to individual. Specifically, it is shown that it is theoretically possible to estimate the average critical gap of a population of drivers (or pedestrians) and its variance, within and across individuals, from direct roadside observations. Although the Multinomial Probit Model provides a natural theoretical framework for the estimation of these parameters, the model seems not to be statistically estimable for this...

Goodness-of-Fit Measures and the Predictive Power of Discrete Models

Daganzo, Carlos F.
1982

Although a number of goodness-of-fit measures for discrete choice models have been proposed and are widely in use, there have been few attempts at interpreting their physical meaning at a practical level. This paper presents a family of goodness-of-fit measures, which contains currently used measures such as the pseudo-correlation coefficient and the percent right, and shows how its members are related. More important, it is shown that one of these measures has an interpretation identical to the correlation coefficient of multiple regression in that it can be used to calculate the...