On Travel Behaviour Relative to a General Place Utility Field

The character of a trip from an origin to a destination is defined by the quasi-utility functions of place utility, trip assessment, and destination expectation. A specific place utility field is determined by a distance minimisation strategy and is generalised for a trip to a destination in any direction with a constant utility. This field is formed by assessing the direction of all trip possibilities and is shown to form rotations with discrete indexes in the psychological domain. The problem is that these trajectories imply that the individual has no memory of past trips, as for stability they tend to zero over time. A solution is to develop an analogy to a conservation principle (such as in physics) and rewrite the spatial preference results as quantum postulates. The rotations are interpreted as a Hermitian matrix and sets of commutation relations are developed for the transfer of information between psychological and physical space. The major results from this formulation are, first, that the velocity of the trip is critical in determining the uncertainty of the transformation of utility from the psychological domain. Second, the individual's speed is related to the probability of route selection. An equation is defined for the trip in a general place utility field and the result is applied to illustrate the initial spatial preference formation and the axis of indifference. It is shown that an individual with no place utility will resort to maximising choice at a point with the most destination alternatives.