Simulated estimation of davidson's travel time function

Travel time functions are an important input to traffic assignment procedures and of the functional forms available an asymptotic function proposed by Davidson is regarded as having the strongest theoretical foundation. This paper reports research which provides a first step towards developing data collection guidelines for estimating Davidson’s travel time function. It examines the effects of sample size and representativeness of the sample on the estimation results. To provided controlled conditions for the estimation experiments, the study employs synthetically generated data with known properties. The results indicate that reliable estimates of each of the parameters of the Davidson function can be obtained with 30 to 50 observations so long as the estimation data contains observations at high volume to capacity ratios. Data sets which only contain observations over a limited range of low volumes cannot be expected to produce reliable parameter estimates, particularly for the curvature parameter (J) and the capacity.