We consider the problem of optimally partitioning an n-dimensional lattice, L = L, X ... X LN, where Lj is a one-dimensional lattice with kj elements, by means of a binary tree into specified (labeled) subsets of L. Such lattices arise from problems in pattern classification, in nonlinear regression, in defining logical equations, and a number of related areas. When viewed as the partitioning of a vector space, each point in the lattice corresponds to a subregion of the space which is relatively homogeneous with respect to classification or range of a dependent variable. Optimality is defined in terms of a general cost function which includes the following: 1) min-max path length (i. e., minimize the maximum number of nodes traversed in making a decision); 2) minimum number of nodes in the tree; and 3) expected path length. It is shown that an optimal tree can be recursively constructed through the application of invariant imbedding (dynamic programming). An algorithm is detailed which embodies this recursive approach. The algorithm allows the assignment of a "don't care" label to elements of L.

The methodology of discrete time, extended Kalman filtering is applied to the problem of identifying parameters of a macroscopic freeway traffic model. Macroscopic models provide a representation of traffic flow in terms of its gross properties, i.e., volume, density, and speed. The local identifiability of a parameterization of macroscopic model at nominal values of the unknown parameters is checked before any identification is attempted. It is shown that the parameterization is locally identifiable. Two parameters of the model (reaction time and sensitivity to changing density) were identified through the use of this methodology. The data base for studies to date was generated from a microscopic simulation of freeway traffic, which involves following all individual vehicle movements. Techniques for extending the methodology to employ real freeway traffic data, especially as can be obtained from automated surveillance systems, are discussed.

Systems have been installed in several cities in the United States, including Los Angeles, Calif., which allow real-time surveillance and control of freeway traffic. The surveillance function is effected by a system of presence detectors located on the freeways, telemetry, and digital computer processing. Traffic control is effected by using traffic signals to meter traffic entering the freeway through on-ramps. Current research on modeling freeway traffic flow, estimation of traffic conditions from presence-detector data, and control of freeway traffic is utilized to provide a design of a surveillance and control system for a segment of the Hollywood Freeway in Los Angeles. In some aspects of the design, particularly the design of traffic-responsive on-ramp metering algorithms, a sound theoretical foundation which adequately accounts for practical constraints has been established. In other areas, preliminary ideas are presented and approaches to optimal schemes outlined.