Constrained Estimation of Direct Demand Functions and Trip Matrices

Estimating the parameters of origin destination (OD) travel demand functions, and hence predicting OD trip volumes, requires data on OD travel demands, but data on travel demands between individual OD pairs are often unavailable or are costly to obtain. However, data on sums (or other linear combinations) of OD travel demands are often more easily or more cheaply available. A recent paper in this journal by M. Carey et al. (Carey, M., C. Hendrickson, K. Siddharthan. 1981. A method for direct estimation of origin/destination trip matrices. Trans. Sci.15 32–49.) presented a constrained least-square estimation model to take advantage of these kinds of data. The statistical properties of the model were not discussed and were not obvious. The present paper extends the model, solves an equality constrained version, and shows that it has desirable statistical properties, and is a special case of a more general model, which is presented and discussed. Also discussed are observational errors in the constraint equations, nonnegativity and inequality constraints and demand functions which are nonlinear in their parameters.