Required service rate for mixed traffic

O. I. Sidorova   ; Yu. S. Khokhlov

Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 2 (2021), pp. 56-67

Résumé

In this paper we analyse the nonhomogenous traffic model based on sum of independent Fractional Brownian motion and symmetric $\alpha$-stable Levy process with different Hurst exponents $H_1$ and $H_2=1/\alpha$ and present bounds for the required service rate under QoS constraints. It is well known that for the processes with long-tailed increments effective bandwidths are not expressed by means of the moment generating function of the input flow. However we can derive simple relations between the flow parameters, service rate $C$ and overflow probabilities $\varepsilon (b)$ for finite and infinite buffer. In this way it is possible to find required service rate $C$ under a constraint on maximum overflow probability.

Détail

Keywords: fractional brownian motion, $\alpha$-stable Levy process, mixed taffic models, quality of service estimation, overflow probability, rate of service.

Bibliographie

[1] Goncharov B. A., Sidorova O. I., Khokhlov Yu. S., “Performance estimation in nonhomogeneous traffic models”, Herald of Tver State University. Series: Applied Mathematics, 2018, no. 4, 50–63 (in Russian) | DOI

[2] Rizk A., Fidler M., “Non–asymptotic end–to–end performance bounds for networks with long range dependent FBM cross traffic”, Computer Networks, 56:1 (2012), 127–141 | DOI

[3] Breiman L., “On some limit theorems similar to the arc-sin law”, Theory of Probability and its Applications, 10:2 (1965), 323–331 | DOI | MR | Zbl

[4] Crovella M., Bestavros A., “Self-similarity in world wide web traffic: evidence and possible cases”, Proceedings of the 1996 ACM SIGMETRICS International Conference on Measurement and Modelling of Computer Systems, v. 4, 1996, 160–169 | DOI

[5] Embrechts P., Maejima M., Selfsimilar Process, Prinston University Press, 2002 | MR

[6] Karasaridis A., Broadband network traffic modeling, management and fast simulation based on [alpha]-stable self-similar processes, PhD Thesis, University of Toronto, 1999 | MR

[7] Kelly F. P., “Notes on effective bandwidths”, Stochastic Networks: Theory and Applications, Royal Statistical Society Lecture Notes, eds. Kelly F.P., Zachary S., Ziedins I., Oxford University Press, Oxford, 1996, 141–168 | MR | Zbl

[8] Leland W. E., Taqqu M. S., Willinger W., Willson D. V., “On the self-similar nature of Ethernet traffic (Extended version)”, IEEE/ACM Transactions on Networking, 2 (1994), 1–15 | DOI

[9] Lopez Guerrero.M., On network resource allocation using alpha-stable long-range dependent traffic models, PhD Thesis, University of Ottawa, Ottawa, Ontario, 2004

[10] Mikosch Th., Resnick S., Rootzen H., Stegeman A., “Is network traffic approximated by stable Levy motion or fractional Brownian motion?”, Annals of Applied Probability, 12:1 (2002), 23–68 | DOI | MR | Zbl

[11] Norros I., “A storage model with self–similar input”, Queueing Systems, 16 (1994), 387–396 | DOI | MR | Zbl

[12] Samorodnitsky G., Taqqu M. S., Stable Non–Gaussian Random Processes, Chapman and Hall, 1994 | MR | Zbl

[13] Taqqu M., Willinger W., Sherman R., “Proof of a fundamental result in self-similar traffic modeling”, Computer Communications Review, 27:2 (1997), 5–23 | DOI

[14] Zolotarev V. M., One-dimensional stable distributions, Translations of Mathematical Monographs, American Mathematical Society, Providence, Rhode Island, 1986, 284 pp. | MR | Zbl