Generalized sub-Gaussian fractional Brownian motion queueing model
| Autor: | Dennis Bushmitch, Yurij Kozachenko, Rostyslav E. Yamnenko |
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| Rok vydání: | 2013 |
| Předmět: |
Discrete mathematics
Queueing theory Fractional Brownian motion Stochastic process Gaussian Management Science and Operations Research Computer Science Applications symbols.namesake Distribution (mathematics) Computational Theory and Mathematics symbols Fluid queue Applied mathematics Queue Gaussian process Mathematics |
| Zdroj: | Queueing Systems. 77:75-96 |
| ISSN: | 1572-9443 0257-0130 |
| DOI: | 10.1007/s11134-013-9375-5 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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