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This paper deals with a car-following model relating driver reaction time, temporal headway and deceleration response to accident frequency. The central goal is to assess the sensitivity of collision probability to a shift in expected reaction time. This problem reduces to determining the sensitivity of the probability of ruin to changes in the drift of the process of cumulative differences between reaction times and temporal headways. A diffusion-type approximation is used and it is shown that additive changes in mean reaction time correspond to multiplicative changes in collision probability. A numerical example is given to illustrate the potential effects of a mere 0.1 sec decrease in mean reaction time. [ABSTRACT FROM AUTHOR]

The traffic assignment and distribution problems are customarily treated as though they were independant rather than related and interacting. In this paper a combined traffic distribution-assignment model is formulated as a mathematical program, based on the equilibrium traffic distribution model and a linear programming assignment model. The behavior of this model using the DANZIG- WOLFE decomposition principle is investigated and illustrated by means of an example. A number of areas for extension are indicated and an alternative formulation that has certain advantages is also [ABSTRACT FROM AUTHOR]

Before we can construct models for multilane traffic flow, we must be able to describe single-lane traffic. This paper considers some of these methods of description including the use of headway and counting distributions. Another method of describing point processes is by means of product densities. These are essentially joint probabilities of two or more vehicles passing a point at different specified times. Product densities have been used in many fields including particle physics, ecology, and road traffic. The idea of using product densities is simple and attractive, but they do have two major disadvantages: (i) except in simple cases, headway distributions are very difficult to derive from product densities, and (ii) product density estimates for different time lags are cor- related, so that tests of hypotheses are not easy to perform. An alternative to product densities is proposed. For want of a better name these are called termination rates. The termination rate after lag τ is the probability of a vehicle passing a point in a small interval of time, divided by the length of the small interval and conditional upon the last vehicle having passed a time τ previously. These are very similar to mortality rates for humans or scrap page rates for commodities with limited life-times. The interrelations between these statistics are quoted but not derived. Various sets of data are used to illustrate the less common statistics. Some analysis is given of a sample of data from the Congress (now Eisenhower) Expressway in Chicago. Variance to mean ratios are used to show that there is a strong correlation between lanes even though the autocorrelations of headways within lanes are very small. Bivariate termination rates have been estimated for each lane. Given a vehicle in one lane, it was found that the expected number of vehicles in a neighboring lane within 2 or 3 sec was enhanced by about 10-15 percent. [ABSTRACT FROM AUTHOR]