Tail asymptotics of fluid queues in a distributed server system fed by a heavy-tailed ON-OFF flow

Byeongchan  Lee; Jonghun  Yoon; Yang Woo  Shin; Ganguk  Hwang

doi:10.3934/jimo.2016.12.637

Article Contents

2016, Volume 12, Issue 2: 637-652. Doi: 10.3934/jimo.2016.12.637

This issue Previous Article Optimal investment strategy on advertisement in duopoly Next Article Analysis of an M/M/1 queue with vacations and impatience timers which depend on the server's states

Tail asymptotics of fluid queues in a distributed server system fed by a heavy-tailed ON-OFF flow

1.
Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Daejeon 305-701
2.
Department of Statistics, Changwon National University, Changwon 641-773

Received: September 2014

Revised: March 2015

Published: April 2016

Abstract Related Papers Cited by

Abstract

The appearance of heavy-tailedness in users' traffic significantly degrades the performance of communication systems, and a distributed server system is considered as a good solution to this problem because of its distributed service characteristic by multiple servers. So we tackle the question in this paper that a distributed server system can alleviate heavy-tailedness, so that users experience good QoS as if there were no heavy-tailedness. To this end, we first mathematically model a distributed server system and obtain a heavy-tailed random sum with the help of the theory of perturbed random walk. We then analyze the tail asymptotic of the heavy-tailed random sum to find a condition with which the distributed server system can alleviate heavy-tailedness.

Keywords:

Mathematics Subject Classification: Primary: 68M20, 68M14; Secondary: 60G50.

Citation:

Related Papers

Cited by

References

[1]	A. Aleškevičien.e, R. Leipus and J. Šiaulys, Tail behavior of random sums under consistent variation with applications to the compound renewal risk model, Extremes, 11 (2008), 261-279.doi: 10.1007/s10687-008-0057-3.
[2]	S. Asmussen, H. Schmidli and V. Schmidt, Tail probabilities for non-standard risk and queueing processes with subexponential jumps, Advances in Applied Probability, (1999), 442-447.doi: 10.1239/aap/1029955142.
[3]	P. Embrechts, C. Klüppelberg and T. Mikosch, Modelling Extremal Events: For Insurance and Finance, Springer-Verlag, Berlin, 1997.doi: 10.1007/978-3-642-33483-2.
[4]	G. Faÿ, B. González-Arévalo, T. Mikosch and G. Samorodnitsky, Modeling teletraffic arrivals by a Poisson cluster process, Queueing Systems, 54 (2006), 121-140.doi: 10.1007/s11134-006-9348-z.
[5]	S. Foss, D. Korshunov, and S. Zachary, An Introduction to Heavy-tailed and Subexponential Distributions, $2^{nd}$ edition, Springer, New York, 2013.doi: 10.1007/978-1-4614-7101-1.
[6]	W. E. Leland, M. S. Taqqu, W. Willinger and D. V. Wilson, On the self-similar nature of Ethernet traffic, ACM SIGCOMM Computer Communication Review, 23 (1993), 183-193.
[7]	K. W. Ng, Q. H. Tang and H. Yang, Maxima of sums of heavy-tailed random variables, Astin Bulletin, 32 (2002), 43-56.doi: 10.2143/AST.32.1.1013.
[8]	V. Paxson and S. Floyd, Wide area traffic: the failure of Poisson modeling, IEEE/ACM Transactions on Networking (ToN), 3 (1995), 226-244.doi: 10.1145/190314.190338.
[9]	Z. Palmowski and B. Zwart, Tail asymptotics of the supremum of a regenerative process, Journal of applied probability, (2007), 349-365.doi: 10.1239/jap/1183667406.
[10]	C. Y. Robert and J. Segers, Tails of random sums of a heavy-tailed number of light-tailed terms, Insurance: Mathematics and Economics, 43 (2008), 85-92.doi: 10.1016/j.insmatheco.2007.10.001.
[11]	F. Semchedine, L. Bouallouche-Medjkoune, and D. Aïssani, Task assignment policies in distributed server systems: A survey, Journal of Network and Computer Applications, 34 (2011), 1123-1130.doi: 10.1016/j.jnca.2011.01.011.
[12]	K. Sigman, Appendix: A primer on heavy-tailed distributions, Queueing Systems, 33 (1999), 261-275.doi: 10.1023/A:1019180230133.
[13]	G. E. Willmot and H. Yang, Martingales and ruin probability, Actuarial Research Clearing House, 1 (1996), 521-527.