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

Part of the Springer Optimization and Its Applications book series (SOIA,volume 90)

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.

Keywords

  • Gaussian Random Variable
  • Storage Process
  • Tail Distribution
  • Hurst Parameter
  • Buffer Overflow

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Correspondence to Rostyslav E. Yamnenko .

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Kozachenko, Y.V., Yamnenko, R.E. (2014). Application of \(\varphi\)-Sub-Gaussian Random Processes in Queueing Theory. In: Korolyuk, V., Limnios, N., Mishura, Y., Sakhno, L., Shevchenko, G. (eds) Modern Stochastics and Applications. Springer Optimization and Its Applications, vol 90. Springer, Cham. https://doi.org/10.1007/978-3-319-03512-3_2

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