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Sample path moderate deviations for the cumulative fluid produced by an increasing number of exponential on-off sources

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Abstract

We consider the superposition of the cumulative fluid generated by an increasing number of stationary iid on-off sources with exponential iid on- and off-time distributions. We establish a family of sample path large deviation principles when the fluid is centered and then scaled with a factor between the inverse of the number of sources and its square root. The common rate function in this family also appears in a large deviation principle for the tail probabilities of an integrated Ornstein–Uhlenbeck process. When the produced fluid is centered and scaled with the square root of the inverse of the number of sources it converges to this integrated Ornstein–Uhlenbeck process in distribution. We discuss several representations of the rate function. We apply the results to queueing systems loaded with on-off traffic and approaching critical loading.

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  1. Siemens AG, CT SE 6, 81730, Munich, Germany

    Kurt Majewski

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Majewski, K. Sample path moderate deviations for the cumulative fluid produced by an increasing number of exponential on-off sources. Queueing Syst 56, 9–26 (2007). https://doi.org/10.1007/s11134-007-9023-z

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