Estimating Roadway Capacity Using the Simultaneous Spline Regression Model

Capacity can be derived as the maximum flow of the functions expressing the relationships between flow and speed or between flow and occupancy. Usually, only one of the relationships is used in the estimation. This results in loss of information in estimation of the capacity. When more than two relationships are used, the derived maximum flows from these two relationships do not coincide, which results in different estimates of capacity. Even when only one relationship of the traffic variables is used, the functions describing the congested and the uncongested conditions are usually estimated separately, which is another case where not all the information is used at the same time. In this study, a simultaneous spline regression model was adopted in estimating capacity using two relationships of traffic variables. Basically, a spline function is a piecewise function, each segment of which defines a traffic condition (e.g., congested or uncongested). An optimal procedure was developed in this study to estimate the two piecewise functions and the breakpoints dividing the two piecewise functions simultaneously with the consideration of a common breakpoint as capacity. With this procedure, a unique estimate of capacity can be derived. Results of this study demonstrated the potential of using this procedure in obtaining a consistent estimate of roadway capacity.