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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, South Korea, South Korea, South Korea |
2. | Department of Statistics, Changwon National University, Changwon 641-773, South Korea |
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. |
show all references
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. |
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