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On Convergence Rate to Stationarity of Queues with General Gaussian Input

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Analytical and Stochastic Modelling Techniques and Applications (ASMTA 2015)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9081))

Abstract

The paper studies the rate of convergence to stationarity of the fluid queueing system with a constant service rate which is fed by a Gaussian process with stationary increments. It is assumed that variance of the input process is regularly varying with index \(2H\in (1,\,2)\). It is proved that the convergence rate is exactly the same that has been obtained for the fluid system fed by the corresponding fractional Brownian motion.

E. Morozov—This work is supported by Russian Foundation for Basic research, projects 15–07–02341 A, 15–07–02354 A,15–07–02360 A, and also by the Program of strategic development of Petrozavodsk State University.

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Correspondence to Oleg Lukashenko .

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Lukashenko, O., Morozov, E. (2015). On Convergence Rate to Stationarity of Queues with General Gaussian Input. In: Gribaudo, M., Manini, D., Remke, A. (eds) Analytical and Stochastic Modelling Techniques and Applications. ASMTA 2015. Lecture Notes in Computer Science(), vol 9081. Springer, Cham. https://doi.org/10.1007/978-3-319-18579-8_10

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  • DOI: https://doi.org/10.1007/978-3-319-18579-8_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-18578-1

  • Online ISBN: 978-3-319-18579-8

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