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高速公路通过能力一般被认为是车流与流速或车流与车流密度关系曲线上的最高点。在过去的研究与应用中，仅这两个曲线中的一条被用来估计通过能力。隐含于另外一条没有被采用的曲线中的信息会由此而浪费。如果这两条曲线被分开来估计的话，就会有两个不同的通过能力估计值。同时应该注意到，既使是仅用一条曲线时，分别对应于车流堵塞与非堵塞的两个曲线段也是通常分开来估计的。这同样存在信息缺失问题。本研究采用样条回归模型同时估计两个曲线。其中，每一曲线被表达成两个直线方程的组合。为采用此法，本研究提出并编写了计算机最优化算法。该优化算法不仅估计两条曲线和两组直线方程，而且同时给出唯一通过能力值。应用该算法得出的计算结果显示这一高速公路通过能力估计方法是可行的。

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 don't 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 uncongested conditions are usually estimated separately, which is another case where not all the information is utilized 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 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.