Burstiness

Burstiness is the tendency of events to occur in clusters rather than at a constant, even rate over time. It describes temporal inhomogeneity where brief periods of high activity are followed by longer intervals of relative quiet. Burstiness is observed in many systems, including human communication, network traffic, neuronal firing, and linguistic usage, and it contrasts with a homogeneous Poisson process where inter-event times are exponentially distributed and events arrive at a constant average rate.

Quantifying burstiness typically involves examining inter-event times and their variability. A common approach uses the coefficient of variation (CV) of the inter-event intervals. A widely cited burstiness measure is B = (CV − 1)/(CV + 1). This yields B = 0 for a Poisson process, B > 0 for bursty dynamics, and B < 0 for more regular or periodic patterns. Alternative models include heavy-tailed inter-event time distributions and self-exciting processes, such as Hawkes processes, which explicitly generate clustering of events.

Applications span several fields. In network traffic, burstiness affects queueing, latency, and resource provisioning. In text analysis, burstiness describes how certain words or topics appear in bursts within a document or across a corpus. In neuroscience, burst firing can carry different information than steady firing rates. In human dynamics, bursty activity shapes the spread of information and social contagion.

Measurement challenges include sensitivity to observation window, data aggregation, and sampling, as well as distinguishing intrinsic burstiness from external drivers.