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November 2010 Reduced long-range dependence combining Poisson bursts with on–off sources
David A. Rolls
Braz. J. Probab. Stat. 24(3): 479-501 (November 2010). DOI: 10.1214/09-BJPS105


A workload model using the infinite source Poisson model for bursts is combined with the on–off model for within burst activity. Burst durations and on–off durations are assumed to have heavy-tailed distributions with infinite variance and finite mean. Since the number of bursts is random, one can consider limiting results based on “random centering” of a random sum for the total workload from all sources. Convergence results are shown to depend on the tail indices of both the on–off durations and the lifetimes distributions. Moreover, the results can be separated into cases depending on those tail indices. In one case where all distributions are heavy tailed it is shown that the limiting result is Brownian motion. In another case, convergence to fractional Brownian motion is shown, where the Hurst parameter depends on the heavy-tail indices of the distribution of the on, off and burst durations.


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David A. Rolls. "Reduced long-range dependence combining Poisson bursts with on–off sources." Braz. J. Probab. Stat. 24 (3) 479 - 501, November 2010.


Published: November 2010
First available in Project Euclid: 2 August 2010

zbMATH: 1298.60093
MathSciNet: MR2719698
Digital Object Identifier: 10.1214/09-BJPS105

Rights: Copyright © 2010 Brazilian Statistical Association


Vol.24 • No. 3 • November 2010
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