Multi-commodity flow estimation with partial counts on selected links
The purpose of this research is to formulate a multi-commodity network flow model for vehicular traffic in a geographic area and develop a procedure for estimating traffic counts based on available partial traffic data for a selected subset of highway links. Due to the restriction of time and cost, traffic counts are not always observed for every highway link. Typically, about 50% of the links have traffic counts in urban highway networks. Also, it should be noted that the observed traffic counts are not free from random errors during the data collection process. As a result, an incoming flow into a highway node and an outgoing flow from the node do not usually match. They need to be adjusted to satisfy a flow conservation condition, which is one of the fundamental concepts in network flow analysis. In this dissertation, the multi-commodity link flows are estimated in a two-stage process. First, traffic flows of "empty" links, which have no observation data, are filled with deterministic user equilibrium traffic assignments. This user equilibrium assignment scheme assumes that travelers select their routes by their own interests without considering total cost of the system. The assignment also considers congestion effects by taking a link travel cost as a function of traffic volume on the link. As a result, the assignment problem has a nonlinear objective function and linear network constraints. The modified Frank-Wolfe algorithm, which is a type of conditional gradient method, is used to solve the assignment problem. The next step is to consider both of the observed traffic counts on selected links and the deterministic user equilibrium assignments on the group of remaining links to produce the final traffic count estimates by the generalized least squares optimization procedure. The generalized least squares optimization is conducted under a set of relevant constraints, including the flow conservation condition for all highway intersections.