SOME EXPERIENCE WITH A MULTIPLE LINEAR REGRESSION METHOD OF ESTIMATING PARAMETERS OF THE TRAFFIC SIGNAL DEPARTURE PROCESS

Abstract Before any method of data collection becomes accepted as a practical tool, it should first be widely tested. This paper analyses in detail a regression method of estimating saturation flow, effective green time and pcu values on traffic signal approaches which has previously been suggested by one of the authors. The method is applied by dividing the green time given to an approach into consecutive “first”, “middle” and “last” counting periods, covering the build up to saturation flow at the start of green, the period of constant saturation flow and the fall-off of saturation flow during the amber period. To estimate parameters, the number of straight-on cars in each counting period is regressed against its length and the number of vehicles of other types departing. It is shown that the method as previously described should be modified in two ways; first, counts from amber periods should not be included in the regression when pcu values are being estimated, and second, a weighted rather than unweighted regression should be used to ensure constant variance of the error term. An optimal sampling policy which produces parameter estimates with minimum variance is described. Applications of the method to data from several sites are described. It is shown that standard errors of parameter estimates are simply related to measurable variables. This allows simple formulae for the minimum number of observations required to achieve specified accuracies to be determined. Formulae for minimum sample sizes required to detect specified differences in saturation flow are also derived. In particular, it is shown that it is most economical, in term of sample size, to use data from single lane sites when testing differences in saturation flow between different times of day. When data from more than one site are available for testing differences, a composite test can be used which reduces sample sizes at individual sites over those required when testing a single difference.