increasing use is being made of models which express how the number of trips between a pair of places by a given mode depends on the time or cost of travel by the various available modes. these models have run into various difficulties, often associated with the evaluation of benefits resulting from changes. the object of this paper is to set out a general theory from which a variety of models can be derived by making different assumptions about the statistical distributions of parameters which vary from one person to another and which give rise to observable differences in trip making behaviour. this throws light on many of the difficulties encountered with existing models. the basic model assumes that there are observable variables representing times, money costs etc. which are common to all people. each potential trip has a personal generalised cost which is a linear function of the observable variables; the coefficients of this function, which represent terminal costs, values of time etc., have a distribution over the population of potential trips. by integrating over regions of this distribution one obtains trip demand functions which are functions of the observable variables only. in an important particular case, the generalised cost is the sum of a personal parameter specific to the person and the mode eg terminal cost, and a modal variable, normally the generalised cost of travel on the mode, which is assumed to be the same for all persons. it is shown that this case implies, and is implied by, the conventional analysis in which numbers of trips are functions of generalised costs and in which a consumer surplus function is obtained by integrating a demand function. therefore the conventional analysis cannot apply to any more general case. (a) this paper was presented at the 6th international symposium on transportation and traffic theory, sydney, australia, 1974, and is published in the symposium proceedings.

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