Abstract
We consider a single-class queueing network with long-range dependent arrival and service processes and show that the normalized queue length converges to a reflected d-dimensional fractional Brownian motion. We identify the covariance of the limiting process in terms of the arrival rates and asymptotic variances of the driving processes. We discuss the case of multiple Hurst parameters and point out that only the largest survive in the limit.
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© 1996 Springer-Verlag New York, Inc.
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Konstantopoulos, T., Lin, SJ. (1996). Fractional Brownian Approximations of Queueing Networks. In: Glasserman, P., Sigman, K., Yao, D.D. (eds) Stochastic Networks. Lecture Notes in Statistics, vol 117. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4062-4_13
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DOI: https://doi.org/10.1007/978-1-4612-4062-4_13
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-94828-7
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