An Assessment of the Space-Time Differential Model for Aggregate Trip Behavior to Planned Suburban Shopping Centers

Aggregate trip behavior to planned suburban shopping centers is studied in terms of changes in trip distance and shopping time within a framework of trip frequency, center scale, and consumer mobility. Such changes are expressed by a second-order differential equation. The assumed shopping strategy is that consumers accelerate the shopping trip cycle by minimizing trip distances. This can be solved to provide theoretical norms to assess against an exploratory data set compiled from 2,810 surveys undertaken in 1980/82 and 1988/89 over a range of centers. The analysis shows a significant relationship between the gravity coefficient and trip frequency. The samples are tested for periodicity using Fourier analysis. The results show that “small” centers are more likely to exhibit periodic behavior. “Large” centers do not follow this hypothesis. Both the gravity coefficient and trip frequency are shown to be quadratic functions of center size. The nonlinearity may be introduced by the agglomeration of shopping opportunities at larger centers. A critical value for “small-” and “large-”center behavior is determined from the minimum points of these distributions. A second equation from classical diffusion analysis is tested for “large” center behavior, where consumers accelerate spatial choice through a time minimization strategy. The results suggest that this strategy occurs at the midrange specialty center during the afternoon of the pre-Christmas rush rather than at large regional centers. The empirical characteristics of the three types of trip behavior are summarized.