On the Use of Self-Similar Processes in Network Simulation

ACM Transactions on Modeling and Computer Simulation

Volumn 10, Issue 2, 2000, Pages 125-151

  López Ardao, José C ^a   López García, Cándido ^a   Suárez González, Andrés ^a   Fernández Veiga, Manuel ^a   Rodríguez Rubio, Raúl ^a  

^a UNIVERSITY OF VIGO   (Spain)

Author keywords

Fractional ARIMA; Long range dependence; Self similar processes; Synthetic generation

Indexed keywords

COMPUTER NETWORKS; COMPUTER SIMULATION; MARKOV PROCESSES; MULTIMEDIA SYSTEMS; TELECOMMUNICATION NETWORKS;

LONG-RANGE DEPENDENCE (LRD); SELF-SIMILAR PROCESSES; SYNTHETIC GENERATION;

TELECOMMUNICATION TRAFFIC;

EID: 0008496361     PISSN: 10493301     EISSN: None     Source Type: Journal    
DOI: 10.1145/364996.365004     Document Type: Article

References (53)

1. ADAS, A. AND MUKHERJEE, A. 1996. Delay-jitter bound and statistical loss bound for heterogeneous correlated traffic - architecture and equivalent bandwidth. Technical Report GIT-CC-96-05 (April), Georgia Institute of Technology, Atlanta, GA.
2. BERAN, J. 1992. A goodness-of-fit test for time series with long range dependence. J. Royal Statist. Soc., Series B 54, 3, 749-760.
3. BERAN, J. 1994, Statistics for Long-Memory Processes, Volume 61 of Monographs on Statistics and Applied Probability. Chapman & Hall, London.
4. BERAN, J., SHERMAN, R., TAQQU, M. S., AND WILLINGER, W. 1995. Long-range dependence in variable-bit-rate video traffic. IEEE Trans. Commun. 43, 2/3/4, 1566-79.
5. Box, G. E. P., JENKINS, G. M., AND REINSEL, C. 1994. Time Series Analysis: Forecasting and Control (third ed.). Prentice Hall, Englewood Cliffs, NJ.
6. Cox, D. R. 1984. Long range dependence: A review. In Statistics: An Appraisal, H. A. David and H. T. David, Eds., 55-74. Iowa State University Press, Ames, IA.
7. Cox, D. R. AND ISHAM, V. 1980. Point Processes. Chapman and Hall, London.
8. CROVELLA, M. E. AND BESTAVROS, A. 1997. Self-similarity in World Wide Web traffic: Evidence and possible causes. IEEE/ACM Trans. Netw. 5, 6 (Dec.), 835-846.
9. DAVIES, R. B. AND HARTE, D. S. 1987. Tests for Hurst effect. Biometrika 74, 95-102.
10. ERRAMILLI, A., NARAYAN, O., AND WILLINGER, W. 1996. Experimental queueing analysis with long-range dependent packet traffic. IEEE/ACM Trans. Netw. 4, 209-223.
11. ERRAMILLI, A., SINGH, R. P., AND PRUTHI, P. 1995. An application of deterministic chaotic maps to model packet traffic. Queueing Syst. 20, 171-206.
12. FELDMANN, A., GILBERT, A. C., HUANG, P., AND WILLINGER, W. 1999. Dynamics of IP traffic: A study of the role of variability and the impact of control. In Proceedings of ACM SIGCOMM '99, 301-313.
13. FENDICK, K. W., SAKSENA, V. R., AND WHITT, W. 1989. Dependence in packet queues. IEEE Trans. Commun. 37, 1173-1183.
14. GARRETT, M. W. AND WILLINGER, W. 1994. Analysis, modeling and generation of self-similar VBR video traffic. In Proceedings of ACM SIGCOMM '94 (London), 269-280.
15. GRAF, H. P. 1983. Long-range correlations and estimation of the self-similarity parameter. Ph.D. Thesis, ETH Zürich.
16. GRANGER, C. W. J. 1980. Long memory relationships and the aggregation of dynamic models. J. Econometrics 14, 227-238.
17. GRANGER, C. W. J. AND JOYEUX, R. 1980. An introduction to long-range time series models and fractional differencing. J. Time Series Anal. 1, 15-30.
18. GRASSE, M., FRATER, M. R., AND ARNOLD, J. F. 1997. Origins of long-range dependence in variable bit rate video traffic. In Proceedings of the Fifteenth International Teletraffic Congress ITC-15, V. Ramaswami and P. E. Wirth, Eds., Elsevier Science B. V., 1379-1388.
19. GROSSGLAUSER, M. AND BOLOT, J.-C. 1996. On the relevance of long-range dependence in network traffic. In Proceedings of ACM SIGCOMM '96 (Stanford University, CA, August), 15-24.
20. HASLETT, J. AND RAFTERY, A. E. 1989. Space-time modeling with long-memory dependence: Assessing Ireland's wind power resource (with discussion). App. Stat. 38, 1-50.
21. HEYMAN, D. P. AND LAKSHMAN, T. V. 1996. What are the implications of long-range dependence for VBR-video traffic engineering? IEEE/ACM Trans. Netw. 4, 3 (June), 301-317.
22. HEYMAN, D. P., TABATABAI, A., AND LAKSHMAN, T. V. 1991. Statistical analysis and simulation study of video teleconferencing traffic in ATM networks. In Proceedings IEEE GLOBECOM '91, 21-27. Also in IEEE Trans. Circuits Syst. Video Technol., 2, 1, (March).
23. HOSKING, J. R. M. 1981. Fractional differencing. Biometrika 68, 1, 165-176.
24. HOSKING, J. R. M. 1984. Modeling persistence in hydrological time series using fractional differencing. Water Resources Res. 20, 12, 1898-1908.
25. HUANG, C., DEVETSIKIOTIS, M., LAMBADARIS, I., AND KAYE, A. R. 1995a. Fast simulation for self-similar traffic in ATM networks. In Proceedings of IEEE ICC '95 (Seattle, Sept.), 438-444.
26. HUANG, C., DEVETSIKIOTIS, M., LAMBADARIS, I., AND KAYE, A. R. 1995b. Modeling and simulation of self-similar variable bit rate compressed video: A unified approach. In Proceedings of ACM SIGCOMM '95 (Cambridge, MA), 114-125.
27. HURST, H. E. 1951. Long-term storage capacity of reservoirs. Trans. Am. Soc. Civil Eng. 116, 770-799.
28. KAPLAN, L. M. AND KUO, C.-C. J. 1994. Extending self-similarity for fractional Brownian motion. IEEE Trans. Signal Proc. 42, 12 (Dec.), 3526-3530.
29. KLEINROCK, L. 1975. Queueing Systems. Wiley, New York.
30. KRUNZ, M. AND MAKOWSKI, A. 1996. Modeling video traffic using M/G/ ∞ input processes: A compromise between Markovian and LRD models. IEEE J. Selected Areas Commun. 16, 5, 733-748.
31. KRUNZ, M., SASS, R., AND HUGHES, H. 1995. Statistical characteristics and multiplexing of MPEG streams. In Proceedings of IEEE INFOCOM '95 (Boston, April), 455-462.
32. LAU, W.-C., ERRAMILLI, A., WANG, J. L., AND WILLINGER, W. 1995. Self-similar traffic generation: The random midpoint displacement algorithm and its properties. In Proceedings of IEEE ICC '95 (Seattle, Sept.), 466-472.
33. LELAND, W. E., TAQQU, M. S., WILLINGER, W., AND WILSON, D. V. 1993. On the self-similar nature of Ethernet traffic. Comput. Commun. Rev. 23, 183-193.
34. LELAND, W. E., TAQQU, M. S., WILLINGER, W., AND WILSON, D. V. 1994. On the self-similar nature of Ethernet traffic (extended version). IEEE/ACM Trans. Netw. 2, 1 (Feb.), 1-15.
35. LI, S. Q. AND HWANG, C. L. 1993. Queue response to input correlation functions: Continuous spectral analysis. IEEE/ACM Trans. Netw. 1, 6 (Dec.), 678-692.
36. LIKHANOV, N., TSYBAKOV, B., AND GEORGANAS, N. 1995. Analysis of an ATM buffer with self-similar ("fractal") input traffic. In Proceedings of IEEE INFOCOM '95 (Boston, April), 985-992.
37. LÓPEZ-ARDAO, J., SUÁREZ, A., AND LÓPEZ-GARCÍA, C. 1998. On the effects of long-range dependence on the performance of FDDI. In Proceedings of the Seventh IEEE Workshop on Computer-Aided Modeling, Analysis and Design of Communication Links and Networks (CAMAD'98) (Sao Paulo, Brazil, August 13).
38. LÓPEZ-ARDAO, J. C. 1999. Contribución al análisis del impacto de la correlación en las prestaciones de las redes de alta velocidad. Ph.D. Thesis, Universidad de Vigo (Spain).
39. MANDELBROT, B. 1967. Some noises with 1/f spectrum, a bridge between direct current and white noise. IEEE Trans. Inf. Theory 13, 2 (April), 289-298.
40. MANDELBROT, B. B. AND NESS, J. W. V. 1968. Fractional Brownian motions, fractional noises and applications. SIAM Rev. 10, 4 (Oct.), 422-437.
41. NORROS, I. 1994. A storage model with self-similar input. Queueing Syst. 16, 387-396.
42. PARULEKAR, M. 1997. Buffer engineering for self-similar traffic. Ph.D. Thesis, College Park, University of Maryland.
43. PARULEKAR, M. AND MAKOWSKI, A. M. 1996. Tail probabilities for a multiplexer with self-similar traffic. In Proceedings of IEEE INFOCOM '96 (San Francisco, March), 1452-1459.
44. PAXSON, V. 1997. Fast, approximate synthesis of fractional Gaussian noise for generating self-similar network traffic. Compu. Commun. Rev. 27, 5 (Oct.), 5-18.
45. PAXSON, V. AND FLOYD, S. 1995. Wide-area traffic: The failure of Poisson modeling. IEEE/ACM Trans. Netw. 3, 226-244.
46. RYU, B. K. AND ELWALID, A. 1996. The importance of long-range dependence of VBR video traffic in ATM traffic engineering: Myths and realities. In Proceedings of ACM SIGCOMM '96 (Stanford University, CA, August), 3-14.
47. SAMORODNITSKY, G. AND TAQQU, M. S. 1994. Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance. Chapman & Hall, London.
48. STATISTICAL SCIENCES, INC. 1991. The S+ package, Version 3.0.
49. SUÁREZ, A., LÓPEZ-ARDAO, J., LÓPEZ-GARCÍA, C., RODRÍGUEZ-RUBIO, R., AND SOUSA, M. E. 1999. Concurrent methodology on LRD simulation studies. In proceedings of the Thirteenth European Simulation Multiconference (ESM '99) (Warsaw, Poland, May), 121-128.
50. TSYBAKOV, B. AND GEORGANAS, N. D. 1997. On self-similar traffic in ATM queues: Definitions, overflow probability bound, and cell delay distribution. IEEE/ACM Trans. Netw. 5, 3 (June), 397-409.
51. WILLINGER, W. 1995. Traffic modeling for high-speed networks: Theory versus practice. In Stochastic Networks, Vol. 71 of IMA Volumes in Mathematics and its Applications, P. Kelly and R. Williams, Eds., 395-409, Springer-Verlag, New York.
52. WILLINGER, W., TAQQU, M. S., AND ERRAMILLI, A. 1996. A bibliographical guide to self-similar traffic and performance modeling for modern high-speed networks. In Stochastic Networks: Theory and Applications, F. P. Kelly, S. Zachary, and I. Ziedins, Eds., Oxford University Press, New York.
53. WILLINGER, W., TAQQU, M. S., LELAND, W. E., AND WILSON, D. V. 1995. Self-similarity in high speed packet traffic: Analysis and modeling of Ethernet traffic measurements. Statis. Sci. 10, 67-85.