Fluid queues with long-tailed activity period distributions

Computer Communications

Volumn 21, Issue 17, 1998, Pages 1509-1529

  Boxma, Onno J ^a   Dumas, Vincent ^a,b,c  

^a CWI   (Netherlands)

^b INRIA ROCQUENCOURT   (France)

^c ECOLE POLYTECHNIQUE   (France)

Author keywords

Buffer content; Busy period; Fluid queue; GI G 1l queue; Long range dependence; Long tailed; On off sources; Regularly varying; Subexponential

Indexed keywords

BUFFER STORAGE; COMPUTER NETWORKS; MATHEMATICAL MODELS; PROBABILITY DISTRIBUTIONS; QUEUEING NETWORKS; TELECOMMUNICATION TRAFFIC;

ACTIVITY PERIODS; FLUID QUEUEING SYSTEM;

DATA COMMUNICATION SYSTEMS;

EID: 0032205736     PISSN: 01403664     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0140-3664(98)00219-9     Document Type: Article

References (59)

1. J. Abate, G.L. Choudhury, W. Whitt, Waiting-time tail probabilities in queues with long-tail service-time distributions, Queueing Systems 16 (1994) 311-338.
2. D. Anick, D. Mitra, M.M. Sondhi, Stochastic theory of a data-handling system with multiple sources, Bell Syst. Techn. J. 61 (1982) 1871-1894.
3. S. Asmussen, Applied Probability and Queues, John Wiley and Sons Ltd., 1987.
4. S. Asmussen, Aspects of matrix Wiener-Hopffactorization in applied probability, Math. Scientist 14 (1989) 101-116.
5. K.B. Athreya, P.E. Ney, Branching Processes, Springer-Verlag, 1972.
6. J. Beran, R. Sherman, M.S. Taqqu, W. Willinger, Long-range dependence in variable-bit-rate video traffic, IEEE Transactions on Communications 43 (1995) 1566-1579.
7. N.H. Bingham, C.M. Goldie, J.L. Teugels, Regular Variation, Cambridge University Press, Cambridge, 1987.
8. O.J. Boxma, Fluid queues and regular variation, Performance Evaluation 27 (1996) 699-712.
9. O.J. Boxma, Regular variation in a multi-source fluid queue, in: V. Ramaswami, P.E. Wirth (Eds.), Teletraffic Contributions for the Information Age, Proceedings of ITC-15, North-Holland Publ. Co., Amsterdam, 1997, pp. 391-402.
10. O.J. Boxma, J.W. Cohen, Heavy-traffic analysis for the GI/G/1 queue with heavy-tailed distributions, Report BS-R9710, CWI, 1997.
11. O.J. Boxma, J.W. Cohen, The M/G/1 queue with heavy-tailed service time distribution, Report, CWI, 1997.
12. O.J. Boxma, V. Dumas, The busy period in the fluid queue, Report BS-R9718, CWI, 1997.
13. O.J. Boxma, V. Dumas, Fluid queues with heavy-tailed activity period distributions, Report BS-R9705, CWI, 1997.
14. F. Brichet, J. Roberts, A. Simonian, D. Veitch, Heavy traffic analysis of a storage model with long range dependent on/off sources, Queueing Systems 23 (1996) 197-215.
15. V.P. Chistyakov, A theorem on sums of independent, positive random variables and its applications to branching processes, Theory Probability Appl. 9 (1964) 640-648.
16. G.L. Choudhury, W. Whitt, Long-tail buffer-content distributions in broad-band networks, Performance Evaluation 30 (1997) 177-190.
17. D.B.H. Cline, Convolutions of distributions with exponential and subexponential tails, J. Austr. Math. Soc. (Series A) 43 (1987) 347-365.
18. J.W. Cohen, Some results on regular variation for distributions in queueing and fluctuation theory, Journal of Applied Probability 10 (1973) 343-353.
19. J.W. Cohen, Superimposed renewal processes and storage with gradual input, Stochastic Processes and their Applications 2 (1974) 31-58.
20. J.W. Cohen, The Single Server Queue, 2nd ed., North-Holland Publ. Co., Amsterdam, 1982.
21. J.W. Cohen, On the effective bandwidth in buffer design for the multi-server channels, Report BS-R9406, CWI, 1994.
22. J.W. Cohen, On the M/G/1 queue with heavy-tailed service time distributions, Report BS-R9702, CWI, 1997.
23. M.E. Crovella, A. Bestavros, Self-similarity in World Wide Web traffic: evidence and possible causes, Performance Evaluation Review 24 (1996) 160-169.
24. N.G. Duffield, Economies of scale in queues with sources having power-law large deviation scalings, Journal of Applied Probability 33 (1996) 840-857.
25. N.G. Duffield, N. O'Connell, Large deviations and overflow probabilities for the general single-server queue, with applications, Math. Proc. Cam. Phil. Soc. 118 (1995) 363-374.
26. P. Embrechts, C.M. Goldie, N. Veraverbeke, Subexponentiality and infinite divisibility, Z. Wahrscheinlichkeitstheorie verw. Gebiete 49 (1979) 335-347.
27. A. Erramilli, O. Narayan, W. Willinger, Experimental queueing analysis with long-range dependent packet traffic, IEEE/ACM Transactions on Networking 4 (1996) 209-223.
28. A. Erramilli, R.P. Singh, P. Pruthi, Chaotic maps as models of packet traffic, in: J. Labetoulle, J.W. Roberts (Eds.), The Fundamental Role of Teletraffic in the Evolution of Telecommunications Networks, Proceedings of the 14th International Teletraffic Congress, North-Holland Publ. Co., Amsterdam, 1994, pp. 329-338.
29. W. Feller, An Introduction to Probability Theory and its Applications, vol. II, 2nd ed., John Wiley and Sons Ltd., 1971.
30. F. Guillemin, G. Rubino, B. Sericola, A. Simonian, Transient characteristics of an M/M/∞ system applied to statistical multiplexing on an ATM link, Rapport de recherche 2386, INRIA, November 1994.
31. D. Heath, S. Resnick, G. Samorodnitsky, Heavy tails and long range dependence in on/off processes and associated fluid models, Technical Report 1144, School of Operations Research and Industrial Engineering, Cornell University, January 1996. Mathematics of Operations Research, in press.
32. P.R. Jelenković, A.A. Lazar, Subexponential asymptotics of a Markov-modulated G/G/1 queue, Journal of Applied Probability, submitted for publication.
33. P.R. Jelenković, A.A. Lazar, Multiplexing on/off sources with subexponential on-periods, CTR Technical Report 457-96-23, Columbia University, New York, NY 10027-6699, USA, July 1996.
34. H. Kaspi, M. Rubinovitch, The stochastic behavior of a buffer with non-identical input lines, Stochastic Processes and their Applications 3 (1975) 73-88.
35. O. Kella, W. Whitt, A storage model with a two-state random environment, Operations Research 40 (S2) (1992) S257-S262.
36. C. Klüppelberg, Subexponential distributions and integrated tails, Journal of Applied Probability 25 (1988) 132-141.
37. L. Kosten, Stochastic theory of a multi-entry buffer (I), Delft Progress Report 1 (1974) 10-18.
38. L. Kosten, Stochastic theory of a multi-entry buffer (II), Delft Progress Report 1 (1974) 44-50.
39. L. Kosten, Stochastic theory of data handling systems with groups of multiple sources, in: W. Bux, H. Rudin (Eds.), Performance of Computer-Communication Systems, North-Holland Publ. Co., Amsterdam, 1984, pp. 321-331.
40. L. Kosten, O.J. Vrieze, Stochastic theory of a multi-entry buffer (III), Delft Progress Report 1 (1975) 103-115.
41. W.E. Leland, M.S. Taqqu, W. Willinger, D.V. Wilson, On the self-similar nature of Ethernet traffic (extended version), IEEE/ACM Transactions on Networking 2 (1994) 1-15.
42. Z. Liu, Ph. Nain, D. Towsley, Z.-L. Zhang, Asymptotic behavior of a multiplexer fed by a long-range dependent process, Technical Report CMPSCI 97-16, University of Massachusetts at Amherst, 1997.
43. A. De Meyer, J.L. Teugels, On the asymptotic behaviour of the distributions of the busy period and service time in M/G/1, Journal of Applied Probability 17 (1980) 802-813.
44. D. Mitra, Stochastic theory of a fluid model of producers and consumers coupled by a buffer, Advances in Applied Probability 20 (1988) 646-676.
45. I. Norros, A storage model with self-similar input, Queueing Systems 16 (1994) 387-396.
46. I. Norros, On the use of fractional Brownian motion in the theory of connectionless networks, IEEE Journal on Selected Areas in Communications 13 (1995) 953-962.
47. A.G. Pakes, On the tails of waiting-time distributions, Journal of Applied Probability 12 (1975) 555-564.
48. M. Parulekar, A.M. Makowski, Tail probabilities for M/G/∞ input processes (I): Preliminary asymptotics, Report, Institute for Systems Research, University of Maryland, 1996.
49. V. Paxson, S. Floyd, Wide area traffic: the failure of Poisson modeling, IEEE/ACM Transactions on Networking 3 (1995) 226-244.
50. N.U. Prabhu, Stochastic Storage Processes, Springer-Verlag, 1980.
51. P. Pruthi, An Application of Chaotic Maps to Packet Traffic Modeling, Ph.D thesis, Department of Teleinformatics, Royal Institute of Technology, Kista, Sweden, 1995.
52. J.W. Roberts, U. Mocci, J. Virtamo, Broadband Network Traffic - Final Report of Action COST 242, Springer-Verlag, 1996.
53. T. Rolski, S. Schlegel, V. Schmidt, Asymptotics of Palm-stationary buffer content distributions in fluid flow queues, Preprint, November 1996.
54. M. Rubinovitch, The output of a buffered data communication system, Stochastic Processes and their Applications 1 (1973) 375-382.
55. A. Simonian, D. Veitch, A storage model with high rate and long range dependent on/off sources, Technical Report, FT-CNET, 1996.
56. W.L. Smith, On the tails of queue time distributions, Mimeo Series 830, Department of Statistics, University of North Carolina, Chapel Hill, 1972.
57. T.E. Stern, A.I. Elwalid, Analysis of separable Markov-modulated rate models for information-handling systems, Advances in Applied Probability 23 (1991) 105-139.
58. W. Willinger, M.S. Taqqu, W.E. Leland, D.V. Wilson, Self-similarity in high-speed packet traffic: analysis and modeling of Ethernet traffic measurements, Statistical Science 10 (1995) 67-85.
59. W. Willinger, M.S. Taqqu, R. Sherman, D.V. Wilson, Self-similarity through high-variability: statistical analysis of Ethernet LAN traffic at the source level, IEEE/ACM Transactions on Networking 5 (1997) 71-86.