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Developments of an Entropy Model for Residential Location with Maximum Zonal Population Constraints

This paper considers recent developments of singly-constrained entropy models which are used for predicting future zonal populations, when the models are required to satisfy given inequality constraints for the maximum zonal populations. Wilson and Batty et al have shown how ad hoc algorithms could be used to modify the usual singly-constrained gravity model, whereas recently Jefferson and Scott have used geometric programming techniques to ensure that the inequality constraints are satisfied. This work develops an approach suggested by Dacey and Norcliffe whereby the inequality constraints are incorporated into the expression for the system entropy. The entropy-maximising method and the more rigorous statistical derivation considered in the paper lead to implicit expressions for the zonal populations which can be evaluated by means of a given algorithm. The asymptotic properties of the model and the inclusion of attractiveness factors are also considered. An interesting feature of this model is that it contains as special cases Wilson's doubly-constrained model and singly-constrained model.