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Application of $$\varphi$$ -Sub-Gaussian Random Processes in Queueing Theory

In: Modern Stochastics and Applications

Author

Listed:
  • Yuriy V. Kozachenko

    (Taras Shevchenko National University of Kyiv)

  • Rostyslav E. Yamnenko

    (Taras Shevchenko National University of Kyiv)

Abstract

The chapter is devoted to investigation of the class $$V (\varphi,\psi )$$ of $$\varphi$$ -sub-Gaussian random processes with application to queueing theory. This class of stochastic processes is more general than the Gaussian one; therefore, all results obtained in general case are valid for Gaussian processes by selection of certain Orlicz N-functions $$\varphi$$ and ψ. We consider different queues filled by an aggregate of such independent sources and obtain estimates for the tail distribution of some extremal functionals of incoming random processes and their increments which describe behavior of the queue. We obtain the upper bound for the buffer overflow probability for the corresponding storage process and apply obtained result to the aggregate of sub-Gaussian generalized fractional Brownian motion processes.

Suggested Citation

  • Yuriy V. Kozachenko & Rostyslav E. Yamnenko, 2014. "Application of $$\varphi$$ -Sub-Gaussian Random Processes in Queueing Theory," Springer Optimization and Its Applications, in: Volodymyr Korolyuk & Nikolaos Limnios & Yuliya Mishura & Lyudmyla Sakhno & Georgiy Shevchenko (ed.), Modern Stochastics and Applications, edition 127, pages 21-38, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-03512-3_2
    DOI: 10.1007/978-3-319-03512-3_2
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