The burstiness of point processes

Discussion of an approach to the definition and measurement of the qualitative property of ‘burstiness’ of a some stationary point processes. By use of an independent, concurrent labeling process, the occurrence of bursts of arrivals is highlighted. For the case of a Poisson labeling process, multiple labels can be used to generate a decomposition of the point process in subprocesses of differing ‘burstiness.’ Matrix-analytic expressions for correlations and run lengths distributions are obtained for point processes generated by the transiton epochs of a Markov renewal process. Such processes can be used as benchmarks in data-analytic procedures that are proposed.