Service Functions for Urban Freeways---An Empirical Study

A service function, defined as a curve relating travel time to flow, is a standard element of many models of transport system operation. In particular, service functions are frequently used within larger models to describe the way in which the travel time on urban freeway segments changes when the flow increases. In this paper, the shape of such curves for urban freeways is studied by examination of two data sets, one from Ontario and one from California. The most striking feature of the plot of travel time versus flow from each of the data sets is that if the data points are divided into two groups according to whether there was or was not a queue within the section when an observation was made, the two groups of points form separate and distinctly different patterns. The differences are so great that it seems impossible to predict travel time by any model which does not consider the difference between the two conditions. Upon reflection, this conclusion turns out to be anything but surprising and a second conclusion is reached: that if service functions are to be used to describe the operating characteristics of freeway segments which are long enough that the flow within the segment is not everywhere the same, then the flow axis must measure the flow through the bottleneck, not the flow into the freeway segment or any sort of average over the segment. The reason for this is that no consistent relationship between flow and travel time that can be expressed by a simple curve exists for any flow other than that through the bottleneck. For the bottleneck flow, an __-shaped service function seems reasonably descriptive, though of only limited use for predicting travel times.