Entropy and utility in traffic modelling.

The concept of entropy is now widely used in urban and regional modelling, particularly in analyzing interzonal traffic flows. This paper concentrates on the disaggregate behavioral approach to travel demand and discusses entropy in the context of ranking different levels of satisfaction. It is suggested that the observable entropy may replace the unobservable utility provided a unique relationship between entropy and income (total expenditure) can be found such that the marginal entropy with respect to income (total expenditure) is always positive. The discussion then concentrates on what limitations the suggested relationship imposes on utility maximizing systems. Three major classes of problems are analyzed. Firstly what explicit utility functions are compatible with the suggested relationship. Secondly, how reasonable are the utility models found from an economist's point of view. Thirdly, will the utility functions found to hold be compatible with the suggested relationship regardless of how the various commodities and services (or trips to different destinations for different purposes) are grouped together into variables over which utility is defined and entropy measured. The theoretical reasoning gives little or no support to the suggested relationship and this conclusion is strengthened by the results of an empirical study. Turning more explicitly to travel demand a couple of specific models are studied. Again the suggested relationship gains little support and the final conclusion is reached that entropy cannot replace utility in disaggregate analyses of welfare changes. Attention is then directed to the possible similar role of entropy in aggregate travel models. An analysis is not carried out and no conclusion is reached, except that it is intuitively felt that entropy being an excellent equality measure, it may perhaps serve as a simple observable proxy for a more complex social welfare indicator in planning contexts where transportation projects play a central role. For the covering abstract of the symposium, please see irrd abstract no. 224453.