Characterizing the variability of arrival processes with indexes of dispersion

The author proposes to characterize the burstiness of packet-arrival processes with indexes of dispersion for intervals and counts. These indexes, which are functions of the variance of intervals and counts, are relatively straightforward and can estimate and convey much more information than simpler indexes (such as the coefficient of variation) that are often used to describe burstiness quantitatively. The author defines and evaluates the indexes of dispersion for some of the simple analytical models that are frequently used to represent highly variable processes. The indexes for a number of measured point processes that were generated by workstations communicating to file servers over a local area network are also estimated. It is shown that nonstationary components in the measured packet-arrival data distort the shape of the indexes, and ways to handle nonstationary data are proposed. To show how to incorporate measures of variability into analytical models and to offer an example of how to model the measured packet-arrival processes, the author describes a fitting procedure based on the index of dispersion for counts for the Markov-modulated Poisson process