Sven Erlander

A mathematical model for traffic on a two-lane road with some empirical results—II. Empirical results

DATA OBTAINED BY THE SWEDISH ROAD INSTITUTE WERE USED TO EVALUATE THE MODEL. SOME SUPPORT FOR THE APPLICABILITY OF THE MODEL WAS OBTAINED, E.G. FROM THE FACT THAT THE ESTIMATED DISTRIBUTIONS OF DESIRED SPEEDS ARE CONSISTENT WITH THE VARIOUS SPEED LIMITS. WHEN APPLICABLE, THE MODEL CAN BE USED IN TRAFFIC AND SAFETY STUDIES TO CALCULATE THE EFFECT UPON VARIOUS TRAFFIC CHARACTERISTICS OF MEASURES SUCH AS INCREASED VISIBILITY OR SPEED LIMITS. /TRRL/

Efficient population behavior and the simultaneous choices of origins, destinations and routes

In this paper we derive a new model for the simultaneous choices of origins, destinations and routes, i.e. the combined distribution and assignment problem. The new model - the continuous Dispersed Equilibrium model or the CDE model - is obtained as the optimal solution of a certain optimization problem. The objective function of the optimization problem contains two terms: an entropy term and a cost function. Furthermore, it is shown how this optimization problem can be obtained as the continuous formulation of the corresponding discrete problem of deriving the most probable flow pattern under efficient population behavior. Hence, the CDE model represents the most probable flows under efficient behavior. We also discuss the relationship of the CDE model to the classical Combined Distribution and Assignment model - the CDA model.

A MATHEMATICAL MODEL FOR TRAFFIC ON A TWO-LANE ROAD WITH SOME EMPIRICAL RESULTS: I THEORETICAL MODEL AND ESTIMATION PROBLEMS

THE AUTHOR USES THE MODEL TO DERIVE TRAFFIC CHARACTERISTICS SUCH AS AVERAGE SPEEDS, DESIRED SPEEDS, OVERTAKING MANOEVRES, SPEED DISTRIBUTION OF VEHICLES IN THE SAME LANE TRAFFIC DENSITY, SPEED OF ONCOMING VEHICLES, AND MINIMUM SIGHT DISTANCES FOR OVERTAKING. /TRRL/

Cost-Minimizing Choice Behavior in Transportation Planning

This book stems from a desire to understand the underlying assumptions and structureof the choice probability models most often used in transportation planning. The bookinvestigates how far a new w ...

Welfare, freedom of choice and composite utility in the logit model

Discrete choice models characterize the alternatives in the choice set by utilities/attributes. The decision making is described by a probability distribution over the choice set. In this paper we introduce a welfare measure based on expected payoff and expected freedom of choice for the simple one parameter logit model. In this case the welfare measure turns out to be the so called composite utility. This means that the composite utility can be interpreted as the combined benefit of expected payoff and expected freedom of choice. The proposed welfare measure can be extended to the linear-in-parameters logit model and nested logit models and others. The proposed welfare measure is formulated in terms of the choice probability distribution. It depends on the form of the probabilities, but not on any particular derivation of the distribution.

ON THE ESTIMATION OF TRIP MATRICES IN THE CASE OF MISSING AND UNCERTAIN DATA

The problem of missing data in the base (calibration) year is of major importance when applying the gravity model in transportation planning, because base year data are used for calibration of the model. In this report this problem is tackled by solving an optimization problem for the prediction year for values of the entropy level and the proportions of trips in a given stratification of the cells of the trip matrix estimated in the base year. The problem of uncertain data in the prediction year is handled by replacing equality constraints for the marginal totals in the prediction year by interval constraints. Computational methods are pointed out. (TRRL)

ON THE RELATIONSHIP BETWEEN THE DISCRETE AND CONTINUOUS MODELS FOR COMBINED DISTRIBUTION AND ASSIGNMENT

The relationship between the discrete and continuous models for the combined distribution and assignment problem is presented. In particular, it is shown that, under certain conditions, the classic continuous flow formulation of the combined distribution and assignment problems can be viewed as the continuous approximation of the discrete model formulated in terms of the Efficiency Principle.

SUGGESTIONS FOR AN IMPROVED SYSTEM FOR STATISTICAL DATA ABOUT ROAD ACCIDENTS AND ROAD TRAFFIC

Data information systems for road accidents and road traffic must satisfy high standards of relevance and quality. The general outline of an improved system for collecting road accident data is given. The system is characterized by the use of statistical sampling methods. The police, the insurance companies and the hospitals are recommended as sources of information about the total accident population. A statistical sample of all identified accidents is then investigated in more detail by special local investigation groups. A hypothetical numerical example is given to show how the suggested system would work in practise. Road accident data should not be isolated from road traffic data. An improved system for collecting information on road traffic is also discussed. This consists of a basic system (founded on statistical sampling methods) for estimation of the total volume of traffic and a few other essential variables such as the volume divided into speed and vehicle types.

Behavioral Foundations of Spatial Interaction Models

This chapter gives an overviewof the content of the book. The book deals with a new approach to logit type discrete choice probability models – for transportation networks in particular. The models are derived from a new definition of cost-minimizing behavior – the likelihood of a sample is decreasing as a function of average cost. The formal definitions are given in Chap. 4: Definition 1 (multinomial logit model) and Definition 4 (general logit model). The results for the multinomial logit model and the general logit model are obtained in Propositions 1 and 3 respectively. All logit type choice probability functions satisfy the new definition. The new definition is in Part I applied to networks with constant link costs. It is shown that the simple (multinomial) logit model exhibits cost-minimizing behavior. Furthermore cost-minimizing behavior implies the logit model. A number of standard logit models are derived – stochastic route choice model, multi-attribute discrete choice model, gravity model and the general logit model. New structured logit models, different from the standard nested logit model, are obtained. A welfare measure based on cost and a measure of freedom of choice is given. The new welfare measure is shown to be identical with composite cost. The presence of cost-minimizing behavior in an observed data set can be investigated by using the property that the likelihood is decreasing as a function of average cost. This is used in constructing a graphical test for cost-minimizing behavior. In Part II of the book the new definition of cost-minimizing behavior is extended to the case of volume dependent separable link costs. Here equilibrium is studied. Cost-minimizing behavior implies that the most probable trip patterns are user equilibria. The most probable flow patterns are approximately obtained by solving the optimization problem obtained by relaxing the integer constraints and replacing the cumulative cost function with the Beckmann integral.Models are derived for route choice, combined choice of origin, destination and route as well as combined choice of origin, destination, mode and route.

Cost minimizing behavior in random discrete choice modeling

This chapter on cost minimizing behavior in random discrete choice modeling is one in a book of essays published in honor of David Boyce for his contributions to the fields of transportation modeling and regional science. In this chapter, the authors describe and define the new notion of cost minimization behavior applied to the most simple case of a discrete choice situation. The authors then show how the multi-attribute multinomial logit model and the gravity model for trip distribution can be derived from this new definition. Instead of considering the rational behavior for an individual decision maker, by making an assumption regarding the probability distribution for the random cost component, the authors define rational behavior for a group of decision makers. The authors also discuss cost minimizing behavior in the general case of discrete choice modeling.