Sherratt's Model and Commuter Travel

Abstract

It is suggested that approaches based on Sherratt's model may be useful for dealing with lengths of commuter journeys in cities and a number of relevant p.d.f.'s and expectations are presented for the symmetric case.

Simplified methods for transportation policy analysis: A continuous modelling approach

“…These models are based on a circular symmetry assumption (i.e., -23the densities depend only on the distance from the conurbation center and not on the direction). The normal model has also been used with a directionally-dependent variance (Wilkins, 1969;Vaughan, 1971;Blumenfeld and Weiss, 1974). Joint population and employment densities were modelled by the bivariate normal model (Wilkins, 1961) and the quadrivariate normal model (Vaughan, 1974 andBlumenfeld, 1977).…”

“…Continuous models have been also developed for important travel characteristics such as travel flow densities and intensities (i.e., vehicle-miles travelled per unit area), the number of route crossings and average distance travelled for various routing systems and origin-destination distributions (e.g., Smeed, 1961Smeed, , 1963Smeed, , 1971Smeed, and 1977Fairthorne, 1965;Holroyd, 1966 andHolroyd and Miller, 1966;Wilkins, 1969;Vaughan, 1971Vaughan, , 1972Vaughan, , 1974Vaughan, , 1976Vaughan, , 1977Vaughan, and 1979. Schneider (1967) presents a different approach for direct estimation of travel flow density at a point.…”

“…In the published literature only one continuous model of this type was found. This is the normal model with the mean constant and the variance a function of direction (Sherratt, 1960;Wilkins, 1969;Vaughan, 1971;Blumenfeld and Weiss, 1974 (Vaughan, 1974 andBlumenfeld, 1977).…”

“…The above bivariate density is also called in the literature the elliptical city model and has been used by Wilkins (1969) and Vaughan (1971).…”

A Continuous Model of Traffic Flow

“…Wilkins [26] uses this setting to obtain expected values for distance traveled. Vaughan [25] extended this work and developed a rather flexible, continuous model that he uses to compute quantities such as average distance traveled, route densities, and expected crossings.…”