Geodesic
Average loss rate in discrete nonhomogeneous $M/G/\infty$ model
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 1 (2018), pp. 31-41 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we investigate asymptotical behavior of average loss rate in discrete version of $M/G/\infty$–model under assumption that distributions of active periods lenghtes belong to the set consisting of finite number distributions with different regularly varying tails. We indicate some conditions under which influence of each distribution on system performance measures is nontrivial.
Keywords: long–range dependence, heavy–tailed distributions, \linebreak $M/G/\infty$ arrival process, ON/ОFF–process, finite buffer, average loss rate. 
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     title = {Average loss rate in discrete nonhomogeneous $M/G/\infty$ model},
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}
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O. I. Sidorova. Average loss rate in discrete nonhomogeneous $M/G/\infty$ model. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 1 (2018), pp. 31-41. http://geodesic.mathdoc.fr/item/VTPMK_2018_1_a2/

[1] D'Apice C., Khokhlov Yu. S., Sidorova O. I., “Bounds to buffer–overflow probability in the case of different distributions of system active periods”, Transactions of the 5th St. Petersburg Workshop on Simulation (Russia, June 26–July 2, 2005), 223–226

[2] Sidorova O. I., “Upper and lower bounds for the probability of packet loss and the probability of buffer overflow in a model with heterogeneous sources”, Herald of Tver State University. Series: Applied Mathematics, 2008, no. 11, 53–61 (in Russian)

[3] 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

[4] Crovella M., Kim G., Park K., “On the relationship between file sizes, transport protocols, and self–similar network traffic”, Proceedings of the Fourth International Conference on Network Protocols, ICNP’96, 1996, 171–180

[5] Jelenkovi$\acute{c}$ P. R., “Subexponential loss rates in a $GI/GI/1$ queue with applications”, Queueing Systems, 33 (1999), 91–123 | DOI | MR

[6] Jelenkovi$\acute{c}$ P. R., Lazar A. A., “Asymptotic results for multiplexing subexponential on–off processes”, Advances in Applied Probability, 31:2 (1999), 394–421 | DOI | MR

[7] 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

[8] Tsybakov B., Georganas N. D., “Selfsimilar traffic and upper bounds to buffer overflow in an ATM queue”, Performance Evaluation, 36:1 (1998), 57–80 | DOI

[9] Tsybakov B., Georganas N. D., “Overflow and loss probabilities in a finite ATM buffer fed by self–similar traffic”, Queueing systems, 32 (1999), 233–256 | DOI | MR

[10] Tsybakov B., Georganas N. D., “Overflow and losses in a network queue with a self–similar input”, Queueing systems, 35 (2000), 201–235 | DOI | MR