We examine the problem of characterizing the variability of measured packet-arrival processes produced by individual workstations in a local-area network. Commonly referred to as burstiness, variability can be informally described as producing sequences of abrupt transitions from low to high arrival rates and vice versa. Since variability can be related to the relationship among successive arrivals, we adopt a quantitative definition, based on indices of dispersion, from the theory of point processes.

We illustrate the measurement methodology and discuss the error analysis. We then analyze the first- and second-order statistical properties of interarrival-time and packet-count series, which reveal the structure of the underlying point processes. We estimate indices of dispersion for intervals and counts, which express the autocorrelation structure of a point process, and warn about the effect of nonstationary data. Using an artificial example based on the Markov-modulated Poisson process, we show how to incorporate into a mathematical model the second-order stochastic parameters that represent dispersion. Fitting is done so that the index of dispersion for counts of the MMPP model matches closely that of the data, a procedure that produces what we call a "model of variability".

Finally, we derive a model of variability whose structure follows the structure of the data: the interarrival times of short and long packets are disjoint; the lengths of sequences of short and long packets form a discrete-time Markov-chain; and a generalized two-state semi-Markov process, in which interarrival times in each of the states are autocorrelated, is shown to reproduce with good approximation the correlation structure of the data for time scales up to 500 ms. The approximation requires only estimates of the first- and second-order moments of the interarrival times. To complete the model, which is two-dimensional, we also provide simple characterizations for the lengths of short and long packets. Because of the recursive nature of the model's equations, the model is suited for simulation studies.




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