Three-phase classification of an uninterrupted traffic flow: a k-means clustering study

We investigated the speed time series of the vehicles at a section of a highway in the city of Isfahan, Iran. Using k-means clustering algorithm, we find that the natural number of clustering for this set of data is 3. This is in agreement with the three-phase theory of uninterrupted traffic flows. According to this theory, the three traffic phases are categorized as free flow (F), synchronized (S) and wide moving jam (J). We obtain the transition speeds and densities at F-S and also S-J transitions. We also apply the Shannon entropy analysis on the speed time series over finite windows, which equips us to monitor in areal time the instant state of a traffic flow.