The highway speed-volume relationship revisited

Abstract

The highway speed-volume relationship has been studied by a number of authors, and is an important issue in urban transportation. Estimates of the relationship may be used to examine congestion externalities, calculate optimal tolls, and calibrate traffic simulation models. A recent paper in this journal by Fare, Grosskopf, and Yoon [2; hereafter referred to as FGYI views highways as a production process, with flow of cars and highway scale representing inputs, and speed representing the output. FGY then present a functional speed-flow relationship grounded in production theory. In addition to the basis in production theory, FGY observe that their function is consistent with the law of variable proportions. FGY state that, unlike most other specifications that have been employed, their function is able to describe the characteristic speed-volume relationship where speed increases with volume over a range of low volume, attains a maximum, then decreases with volume. Unfortunately, as shown below, the parameter estimates presented by the authors are incorrect, due to the authors’ use of faulty software. In addition, FGY incur some minor problems in their application, which are also addressed below. Nonetheless, with some minor adjustments, the production theory approach to the speed-volume relationship remains appealing and useful. FGY begin with a general, short-run production function of the form G = g(x, N), where G represents common speed of vehicles, x > 0 represents fixed highway scale, and N E R, is defined as the flow of cars in a lane past a fixed point. This short-run production function is required to satisfy several properties of production functions listed by FGY. In Eq. (2.3) of their paper, FGY present the function