Regularities and a descriptive algorithm of the trip to work distribution

This paper presents the results of a study whose aim was to identify the actual regularities of the trip-to-work distribution and to apply them in an algorithm of trip prediction, using descriptive parameters instead of unknown control factors. It was shown that the observed trip length distributions (TLD), which reflect the probability of a trip to a t-radius ring of an urban area, may be approximated by multiplication of a basic probability of a trip to an infinitesimal area G(t) and attraction points masses M(t) in the ring. Using this relation, on the basis of actual TLD of 24 cities, a real shape of G(t) was obtained and it was established that it corresponds to the seminormal Gauss Law. It was found that in the base formula of trip demand beside the Gauss Law and the masses of interactive zones three important factors must be also taken into consideration for correct trip prediction: (a) the differences between zones' quality, (b) work zones' professional acceptability, and (c) the change of the part of walk in the intrazonal trip because of demand pressure. The influence of the differences in the quality of the origin-destination zones is quantitative estimated by a factor, which expresses an overlap of quality distributions of these two zones. It was shown that household income, which was taken to represent the zonal quality factor, can be simply described by the Rayleigh distribution, which gives an easy way for this overlap calculation. A technique for treatment by the two other factors is also proposed. Regarding the use of the account regularities, a basic descriptive model of iterative trip prediction was created and tested, with mathematical and numerical demonstration of its convergence. An important factor in the full algorithm of trip-to-work prediction is the starting value of the average distance T of the trips for entire urban area. Based on a study of T-response functions, a solution for calculation of the starting value of T for each transport mode was given. The descriptive algorithm of trip prediction complies with the following principles: (a) it is the same for all urban areas and all transport modes; (b) it is based on a unitary seminormal Gauss Law of trip density distribution; (c) it operates in each range of the distances for a discontinuous, nonhomogeneous, local unbalanced urban area and does not require data on trips in the past; (b) it is based on a minimal number of zonal descriptive macro-characteristics of the population, work places, and distances. The test of the established algorithm, carried out in the case of two cities at different periods with completely different social and transport systems, revealed good agreement between predicted and observed trips and showed that the diversity of the TLD pattern can be explained by the variety of the quality, of the professional acceptability, mode split and of the zonal mass scattering, without requiring different G(t) functions. Consequently, a real TLD cannot be described as a general algebraic function of distances, but can be predicted correctly.