Toward Dynamic Models of Traveller Behavior and Point Patterns of Traveller Origins

Abstract

This paper is concerned with the mathematical modelling of individual travel behavior over both space and time. The goal is to show that it is possible to define quantitatively changing spatial forms and to link these with generating processes. To illustrate, models and data are developed in the paper to describe a selected spatial form and the kind of process which could create it. First, the study uses the circular normal probability density function as a model to define the distribution of traveller origin points about a sample destination point (a bank) for each of five years. The function successfully fits the data, although its parameters vary with time. A learning process is invoked to explain this latter variation and the variation in form it implies: information declines with distance from a node, but gradually learning occurs and the form given by the pattern of destinations at each distance from the node alters. A linear learning model is specified to define this process rigorously, and the model fits data for selected nodes (stores) in Uppsala, Sweden. There seems to be little reason why the results are not generalizable. Clearly, dynamic, mathematical models of travel behavior are required, rather than the static or equilibrium ones which are still widespread in geography and planning.