A note on the calculation and calibration of doubly constrained trip distribution models

The use of growth factor models for trip distribution has given way in the past to the use of more complex synthetic models. Nevertheless growth factor models are still used, for example in modelling external trips, in small area studies, in input-output analysis, and in category analysis. In this article a particular growth factor model, the Furness, is examined. Its application and functional form are described together with the method of iteration used in its operation. The expected information statistic is described and interpreted and it is shown that the Furness model predicts a trip distribution which, when compared with observed trips, has the minimum expected information subject to origin and destination constraints. An equivalent entropy maximising derivation is described and the two methods compared to show how the Furness iteration can be used in gravity models with specified deterrence functions. A trip distribution model explicitly incorporating information from observed trips, is then derived.It is suggested that if consistency is to be maintained between iteration, calibration, and the derivation of gravity models, then expected information should be used as the calibration statistic to measure goodness of fit. The importance of consistency in this respect is often overlooked.Lastly, the limitations of the models are discussed and it is suggested that it may be better to use the Furness iteration rather than any other, since it is more fully understood. In particular its ease of calculation makes it suitable for use in small models computed by hand.