The Influence of Transport Attractors Scattering on the Private Transport Trip Lengths in Cities

The available results of the travel surveys on urban private motorised transport indicate a similarity in the obtained trip length distributions, which is reflected in a noticeable positive skewness of the distribution and a prevalence of shorter distances over the longer ones. This is evident in various urban areas worldwide, but there is no common theoretical background for the observed travel patterns to date. This paper presents the first step towards explaining these patterns, and it is based on the hypothesis of bivariate normality of the scattering of transport attractors on a city territory. This hypothesis made it possible to obtain an analytical formula for the distribution of distances between attractors for the case when one of them is located in the city downtown. The obtained formula corresponds to the classical Rayleigh distribution. Experimental studies on the distribution of the coordinates of transport attractors and distances between them were carried out using the data from transport models of three Ukrainian cities – Sumy, Kharkiv, and Kyiv. These studies operated with samples of sufficient size. To check the normality of the attractors’ coordinates, the Mahalanobis distances were used. To check the conformity of the distances between attractors to the derived theoretical distribution, the Kolmogorov-Smirnov test for goodness of fit was applied. These checks showed positive results – the distribution of attractors’ coordinates appeared close to bivariate normal, and the Rayleigh distribution appeared useful to represent the distances between attractors. This allows us to make a preliminary conclusion that the reason for the similarity of known trip length distribution plots for urban private transport trips is the location of transport attractors on a city territory, which can be considered close to bivariate normal. The results obtained in this paper create opportunities for further research, particularly by theoretical consideration of a more general case of making the trips between attractors located outside the city downtown with further experimental checks.