Estimation of speed–flow and flow–density relations on the motorway network in the greater Copenhagen region

Abstract

The speed-flow and flow-density relations at the motorway network of the greater Copenhagen region are explored based on a large data sample consisting of a total of 5.3 million observations at 398 locations. It is concluded that the US Bureau of Public Road (BPR) speed-flow formula from 1964 is an adequate average description of the non-queuing conditions in static assignment models, while the variation of travel speed should be taken into account in meso- and micro-simulation models. The variance of the variation of the non-queuing conditions appears to be fairly independent of the flow. The flow-density curve for the non-queuing conditions should according to theory have a convex shape to be consistent with the speed-flow curve. This was confirmed by the data. It was also shown that the variance hereby is linearly increasing with density. A linearly decreasing relationship between density and flow may be assumed for the queuing situation. Data confirmed this, although less clearly than for the non-queuing situation. This equals a derived curved formulation of the speed-flow relationship. Data for the queuing situation revealed more variance in driving speed. The variance of the variation may be assumed constant in the flow-density curves, meaning an increasing variance of speed. Finally, it was concluded, that the speeds at the capacity limit is highly unstable, within a range from 30 to 90 km/h. The transition point between the non-queuing and queuing conditions was more clearly defined in the flow-density curves than in the speed- flow curves.