Asymptotic loss probability in a finite buffer fluid queue with heterogeneous heavy-tailed On-Off processes

Annals of Applied Probability

Volumn 13, Issue 2, 2003, Pages 576-603

  Jelenković, Predrag ^a,b   Momčilović, Petar ^a,b  

^a Och Spine at New York Presbyterian Hospitals   (United States)

^b Columbia University ^*  (United States)

Author keywords

Fluid queue; Long range dependence; On Off processes; Statistical multiplexing; Subexponential distributions

Indexed keywords

EID: 3543050679     PISSN: 10505164     EISSN: 10505164     Source Type: Journal    
DOI: 10.1214/aoap/1050689595     Document Type: Article

References (35)

1. AGRAWAL, R., MAKOWSKI, A. and NAIN, PH. (1999). On a reduced load equivalence for fluid queues under subexponentiality. Queueing Systems Theory Appl. 33 5-41.
2. ANICK, D., MITRA, D. and SONDHI, M. (1982). Stochastic theory of a data handling system with multiple sources. Bell Syst. Tech. J. 61 1871-1894.
3. ATHREYA, K. B. and NEY, P. E. (1972). Branching Processes. Springer, Berlin.
4. BOXMA, O. J. (1996). Fluid queues and regular variation. Performance Evaluation 27/28 699-712.
5. CHISTYAKOV, V. P. (1964). A theorem on sums of independent positive random variables and its application to branching random processes. Theory Probab. Appl. 9 640-648.
6. CHOUDHURY, G. L. and WHITT, W. (1997). Long-tail buffer-content distributions in broadband networks. Performance Evaluation 30 177-190.
7. COHEN, J. W. (1974). Superimposed renewal processes and storage with gradual input. Stochastic Process. Appl. 2 31-58.
8. COHEN, J. W. (1982). The Single Server Queue. North-Holland, Amsterdam.
9. CROVELLA, M. and BESTAVROS, A. (1997). Self-similarity in World Wide Web traffic: Evidence and possible causes. IEEE/ACM Trans. Networking 5 835-846.
10. DUFFIELD, N. G. (1998). Queueing at large resources driven by long-tailed M/G/∞-modulated processes. Queueing Systems Theory Appl. 28 245-266.
11. DUMAS, V. and SIMONIAN, A. (2000). Asymptotic bounds for the fluid queue fed by subexponential on/off sources. Adv. in Appl. Probab. 32 224-255.
12. GLYNN, P. V. and WHITT, W. (1994). Logarithmic asymptotics for steady-state tail probabilities in a single-server queue. In Studies in Applied Probability (J. Galambos and J. Gani, eds.) 31A 131-156. Applied Probability Trust, Sheffield, UK. (Special issue of J. Appl. Probab.)
13. GOLDIE, C. M. and KLÜPPELBERG, C. (1998). Subexponential distributions. In A Practical Guide to Heavy Tails: Statistical Techniques for Analysing Heavy Tailed Distributions (R. Adler, R. Feldman and M. S. Taqqu, eds.) 435-459. Birkhäuser, Boston.
14. HEATH, D., RESNICK, S. and SAMORODNITSKY, G. (1998). Heavy tails and long range dependence in on/off processes and associated fluid models. Math. Oper. Res. 23 145-165.
15. HEATH, D., RESNICK, S. and SAMORODNITSKY, G. (1999). How system performance is affected by the interplay of averages in a fluid queue with long range dependence induced by heavy tails. Ann. Appl. Probab. 9 352-375.
16. HEYMAN, D. P. and LAKSHMAN, T. V. (1996). Source models for VBR broadcast-video traffic. IEEE/ACM Trans. Networking 4 40-48.
17. JELENKOVIĆ, P. (1999). Subexponential loss rates in a GI/GI/1 queue with applications. Queueing Systems Theory Appl. 33 91-123.
18. JELENKOVIĆ, P. (2000). On the asymptotic behavior of a fluid queue with a heavy-tailed M/G/∞ arrival process. Oper. Res. Lett. To appear.
19. JELENKOVIĆ, P. and LAZAR, A. (1999). Asymptotic results for multiplexing Subexponential on-off processes. Adv. in Appl. Probab. 31 394-421.
20. JELENKOVIĆ, P., LAZAR, A. and SEMRET, N. (1997). The effect of multiple time scales and subexponentiality of MPEG video streams on queueing behavior. IEEE J. Select. Areas Comm. 15 1052-1071.
21. JELENKOVIĆ, P. and MOMČILOVIĆ, P. (2001). Capacity regions for network multiplexers with heavy-tailed fluid on-off sources. In Proc. IEEE Infocom, Anchorage, Alaska.
22. KRISHNAN, K. R. and MEEMPAT, G. (1997). Long-range dependence in VBR video streams and ATM traffic engineering. Performance Evaluation 30 45-56.
23. LELAND, W. E., TAQQU, M. S., WILLINGER, W. and WILSON, D. V. (1993). On the self-similar nature of Ethernet traffic. In Proc. ACM SIGCOMM 183-193. ACM, New York.
24. LIKHANOV, N. and MAZUMDAR, R. (2000). Cell loss asymptotics in buffers fed by heterogeneous long-tailed sources. In Proc. IEEE Infocom, Tel-Aviv, Israel.
25. LIU, Z., NAIN, PH., TOWSLEY, D. and ZHANG, Z. L. (1999). Asymptotic behavior of a multiplexer fed by a long-range dependent process. J. Appl. Probab. 36 105-118.
26. LOYNES, R. M. (1962). The stability of a queue with non-independent inter-arrival and service times. Proc. Cambridge Philos. Soc. 58 497-520.
27. PAKES, A. G. (1975). On the tails of waiting-time distribution. J. Appl. Probab. 12 555-564.
28. PARULEKAR, M. and MAKOWSKI, A. M. (1997). Tail probabilities for M/G/∞ input processes (I): Preliminary asymptotics. Queueing Systems Theory Appl. 27 271-296.
29. RESNICK, S. and SAMORODNITSKY, G. (1999). Activity periods of an infinite server queue and performance of certain heavy tailed fluid queues. Queueing Systems Theory Appl. 33 43-71.
30. RESNICK, S. and SAMORODNITSKY, G. (2001). Steady state distribution of the buffer content for M/G/∞ input fluid queues. Bernoulli 7 191-210.
31. ROLSKI, T., SCHLEGEL, S. and SCHMIDT, V. (1999). Asymptotics of Palm-stationary buffer content distribution in fluid flow queues. Adv. in Appl. Probab. 31 235-253.
32. RUBINOVITCH, M. (1973). The output of a buffered data communication system. Stochastic Process. Appl. 1 375-380.
33. VAMVAKOS, S. and ANANTHARAM, V. (1998). On the departure process of a leaky bucket system with long-range dependent input traffic. Queueing Systems Theory Appl. 28 191-214.
34. WEISS, A. and SHWARTZ, A. (1995). Large Deviations for Performance Analysis: Queues, Communications, and Computing. Chapman and Hall, London.
35. ZWART, B., BORST, S. and MANDJES, M. (2000). Exact asymptotics for fluid queues fed by multiple heavy-tailed on-off flows. Ann. Appl. Probab. To appear.