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Generalized sub-Gaussian fractional Brownian motion queueing model

Abstract

It is well known that often the one-dimensional distribution of a queue content is not Gaussian but its tails behave like a Gaussian. We propose to consider a general class of processes, namely the class of \(\varphi \)-sub-Gaussian random processes, which is more general than the Gaussian one and includes non-Gaussian processes. The class of sub-Gaussian random processes contains Gaussian processes also and therefore is of special interest. In this paper we provide an estimate for the queue content distribution of a fluid queue fed by \(N\) independent strictly \(\varphi \)-sub-Gaussian generalized fractional Brownian motion input processes. We obtain an upper estimate of buffer overflow probability in a finite buffer system defined on any finite time interval \([a,b]\) or infinite interval \([0,\infty )\). The derived estimate captures more accurately the performance of the queueing system for a wider-range of input processes.

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Correspondence to R. Yamnenko.

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Yamnenko, R., Kozachenko, Y. & Bushmitch, D. Generalized sub-Gaussian fractional Brownian motion queueing model. Queueing Syst 77, 75–96 (2014). https://doi.org/10.1007/s11134-013-9375-5

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  • DOI: https://doi.org/10.1007/s11134-013-9375-5

Keywords

  • Fractional Brownian motion
  • Buffer overflow probability
  • Sub-Gaussian processes

Mathematics Subject Classification

  • 60K25
  • 60G20