  We describe and validate a novel data-driven approach to the real time
detection and classification of traffic anomalies based on the identification
of atypical fluctuations in the relationship between density and flow. For
aggregated data under stationary conditions, flow and density are related by
the fundamental diagram. However, high resolution data obtained from modern
sensor networks is generally non-stationary and disaggregated. Such data
consequently show significant statistical fluctuations. These fluctuations are
best described using a bivariate probability distribution in the density-flow
plane. By applying kernel density estimation to high-volume data from the UK
National Traffic Information Service (NTIS), we empirically construct these
distributions for London's M25 motorway. Curves in the density-flow plane are
then constructed, analogous to quantiles of univariate distributions. These
curves quantitatively separate atypical fluctuations from typical traffic
states. Although the algorithm identifies anomalies in general rather than
specific events, we find that fluctuations outside the 95\% probability curve
correlate strongly with the spikes in travel time associated with significant
congestion events. Moreover, the size of an excursion from the typical region
provides a simple, real-time measure of the severity of detected anomalies. We
validate the algorithm by benchmarking its ability to identify labelled events
in historical NTIS data against some commonly used methods from the literature.
Detection rate, time-to-detect and false alarm rate are used as metrics and
found to be generally comparable except in situations when the speed
distribution is bi-modal. In such situations, the new algorithm achieves a much
lower false alarm rate without suffering significant degradation on the other
metrics. This method has the additional advantage of being self-calibrating.
