Statistical Methods for Optimally Locating Automatic Traffic Recorders

Abstract

This report presents new computer-based statistical methods for the optimal placement of automatic traffic recorders (ATR). The goal of each method is to locate a set of ATRs so as to improve the overall efficiency and accuracy of Annual Average Daily Traffic (AADT) estimates. The precise estimation of AADTs is essential because of the important role they play in many highway design, maintenance, and safety decisions. Because of the huge number of potential ATR sites in a typical state highway, optimal selection of ATR sites is a very large combinatorial problem. Accordingly, site selection is currently accomplished through judgmental and/or design-based sampling techniques (e.g., random sampling). By developing fast and efficient computer algorithms to accomplish the purposive selection of an optimal sample, we demonstrate that model-based sampling is a viable alternative to classical design-based sampling techniques. The algorithms developed in this project include an exchange algorithm and a two-stage sampling algorithm. In the rank-1 exchange algorithm, ATR sites are sequentially added to and deleted from the design. It generates highly efficient designs without exhaustively searching through all possible designs. In the two-stage sampling approach, similar sites are statistically clustered, then approximate design techniques are used to calculate the optimal weight for each cluster. Based on these optimal weights, a random sample of sites is selected from within each cluster. The speed of this two-stage sampling algorithm makes it an ideal approach for large-scale problems. Using traffic data provided by the Minnesota Department of Transportation, we demonstrate empirically that both algorithms are substantially better in terms of average variance of prediction than simple random sampling.