Urban Environment, Travel Behavior, Health, and Resident Satisfaction by Anzhelika Antipova

Author:Anzhelika Antipova
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

4.3.3.1 Entropy Maximization

Wilson published his seminal work in the field where he developed entropy maximizing techniques in 1970. A geographical system of interest is described by a set of variables and parameters that constitute a state space (Wilson 2010, p. 384). Wilson (1970) used entropy as a measure of the degree of order in a system, so entropy-maximizing techniques can find the most ordered, that is, the most likely state of alternative configurations in a system (Clark 1982). In his work on gravity models, principles from information theory have been introduced to develop a typical trip table to create a series of spatial interaction models. Specifically, Wilson (1970) derived a journey-to-work model where he combined deterministic assumptions (i.e., origin and destination constraints) and the probabilistic entropy-maximizing method (Thomas and Huggett 1980, pp. 153–155). By using the entropy-maximizing approach the most probable state of a system of interest subject to constraints can be modeled; the models are “widely applicable” (Wilson 2010, p. 385). For example, trips are connected to structural variables such as number of workers at a residential location and number of jobs at employment locations. The models contribute to multiregional demographic and input–output models, to transport, and to location modeling such as retail.

Gould (1972) explained the mathematics behind the large equations involving the Lagrangian multipliers and applied Wilson’s techniques to find the most likely journey-to-work trip configuration of the system in towns in Northwest England; additionally, he included several constraints such as fixed residential distribution (that is, a finite number of workers), job distribution (a finite number of employment), and overall cost constraints so that the modeled journey-to-work trip distributions by mode could be compared against the known existing patterns in the study area (Clark 1982). The model predicted the distribution of work movements highly accurately (0.95).

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