Extreme value methods for estimating road traffic capacity

Common sense suggests that, at any point on a road network, there is an absolute limit to the volume of traffic which can be carried. But previous attempts to measure this "limiting capacity" have met with difficulties. First, there may not be enough vehicles to saturate the section of road under observation. Second, the flow may be constrained by a bottleneck upstream or downstream. Third, even under favourable conditions, the flows actually observed at saturation point tend to vary over a wide range, giving little clear indication as to what the value of the limiting capacity might be. In this paper, consideration is given to the variations in flow which occur over a time during normal traffic conditions, and to the characteristics of the extreme values which occur from time to time under these conditions. Two distinct types of statistical theory can be applied to extreme values. First, one can apply straight- forward probability theory, to predict the largest flows likely to be observed during a given period, assuming an idealised traffic stream with a known flow counting distribution. Second, one can attempt to deduce an upper limit from observed flow data using asymptotic methods of the kind which are frequently used in connection with meteorological and flood defense problems. Both methods are applied to a sample of 9000 flow values recorded at a site in London. Both methods are shown to fit the data reasonably well, but only the asymptotic method reveals a clear upper limit. Possible applications of the method are briefly discussed.