negative exponential tends to be the preferred form. The gravity model has been corroborated many times as a basic underlying aggregate relationship (Scott 1988, Cervero 1989, Levinson and Kumar 1995). The rate of decline of the interaction (called alternatively, the impedance or friction factor, or the utility or propensity function) has to be empirically measured, and varies by context. Limiting the usefulness of the gravity model is its aggregate nature. Though policy also operates at an aggregate level, more accurate analyses will retain the most detailed level of information as long as possible. While the gravity model is very successful in explaining the choice of a large number of individuals, the choice of any given individual varies greatly from the predicted value. As applied in an urban travel demand context, the disutilities are primarily time, distance, and cost, although discrete choice models with the application of more expansive utility expressions are sometimes used, as is stratification by income or vehicle ownership. Mathematically, the gravity model often takes the form: where = Trips between origin i and destination j = Trips originating at i = Trips destined for j = travel cost between i and j = balancing factors solved iteratively. See Iterative proportional fitting. = distance decay factor, as in the accessibility model It is doubly constrained, in the sense that for any i the total number of trips from i predicted by the model always (mechanically, for any parameter values) equals the real total number of trips from i. Similarly, the total number of trips to j predicted by the model equals the real total number of trips to j, for any j. Entropy analysis Wilson (1970) gives another way to think about zonal interchange problem. This section treats Wilson’s methodology to give a grasp of central ideas. To start, consider some trips where there are seven people in origin zones commuting to seven jobs in destination zones. One configuration of such trips will be: where 0! = 1. That configuration can appear in 1,260 ways. We have calculated the number of ways that configuration of trips might have occurred, and to explain the calculation, let’s recall those coin tossing experiments talked about so much in elementary statistics. The number of ways a two-sided coin can come up is , where n is the number of times we toss the coin. If we toss the coin once, it can