Investigation of Speed-Flow Relationship Under Congested Conditions on a Freeway

The purpose of this work is to investigate the relationship between speed and flow within congestion, that is, the lower portion of the standard curve, and in particular to identify an equation to describe this portion of the relationship. Data were obtained for Toronto, Ontario, from the Gardiner Expressway RESCU System and the Highway 401 COMPASS System. The data were first screened to remove dubious data points and observations that were from transitions between congested and uncongested conditions. They were then analyzed using regression analysis for four types of function: quadratic, cubic, exponential, and power. The principal findings related to the shape of the speed-flow curve within congestion are as follows. It is important to utilize data from a full range of flows in order to fit a curve to represent the congested part of the speed-flow curve. To obtain this range, data from several sites may be needed. Despite the combination of sites, there is often what might be termed a “data gap” between easily available congested data (up to perhaps 1,800 vphpl) and flow rates for queue discharge flow. When data for that gap are available, the speeds under congested conditions seem to increase fairly rapidly at high congested flows. There appears to be a difference in the speed-flow relationship among different freeways and under construction conditions on one of them. If there are different curves for different freeways (or free-flow speeds) for the top half of the speedflow relationship, it seems reasonable that there might also be for the bottom half. However, it also appears to be the case that downstream conditions such as construction can affect the speed-flow curve itself at an upstream location. This makes sense in that operations within the queue are governed by the downstream queue discharge, but it is a change from what one expects for the other two segments of the speedflow curve.