Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Fluid Queueing Model with Fractional Brownian Input

  • Lee, Jiyeon (Department of Statistics, Yeungnam University)
  • Published : 2002.12.01
Download PDF
⟨ Previous Next ⟩

Abstract

We consider an unlimited fluid queueing model which has Fractional Brownian motion(FBM) as an input and a single server of constant service rate. By using the result of Duffield and O'Connell(6), we investigate the asymptotic tail-distribution of the stationary work-load. When there are multiple homogeneous FBM inputs, the workload distribution is similar to that of the queue with one FBM input; whereas for the heterogeneous sources the asymptotic work-load distributions is dominated by the source with the largest Hurst parameter.

Keywords

References

  1. 「정보통신연구」 v.14 no.1 인터넷 트래픽의 측정동향 및 분석기법 연구 김현숙;이명용;정종명
  2. A Practical Guide to Heavy Tails Statistical Techniques and Applications Robert J. Adler;Raisa E. Feldman;Murad S. Taqqu
  3. Statistics for Lon-Memory Processes J. Beran
  4. IEEE Transactions on Communications v.43 Lon-Range Dependence in Variable-Bit-Rate Video Traffic J. Beran;R. Sherman;M. S. Taqqu;W. Willinger https://doi.org/10.1109/26.380206
  5. Queueing Systems v.33 Heavy-traffic Analysis for the GI/G/1 Queue with Heavy-Tailed Distributions O. J. Boxma;J. W. Cohen https://doi.org/10.1023/A:1019124112386
  6. Mathematical Proceedings of the Cambeidge Philosphical Society v.118 Large Deviations and Overflow Probabilities for the General Single-Server Queue, with Applications N. G. Duffield;N. O.'Connell https://doi.org/10.1017/S0305004100073709
  7. IEEE/ACM Transactions on Networking v.4 Experimental queueing analysis with lond-range dependent packet traffic A. Erramilli;O. Narayan;W. Willinger https://doi.org/10.1109/90.491008
  8. Mathematics of Operations Research v.23 Heavy Tails and Long Range Dependence in On/Off Processes and Associated Fluid Models D. Heath;S. Resnick;G. Samorodnitsky https://doi.org/10.1287/moor.23.1.145
  9. ACM/IEEE Transactions on Networking v.2 On the Self-Similar Nature of Ethernet Traffic W. E. Leland;M. S. Taqqu;W. Willinger;D. V. Wilson https://doi.org/10.1109/90.282603
  10. SIAM Review v.1 Fractional Broenian Motions, Fractional Noises and Applications B. B. Mandelbrot;J. W. Van Ness https://doi.org/10.1137/1010093
  11. Journal of Applied Probability v.36 Large Buffer Asymptotics for the Queue with FBM Input L. Massoulie;A. Simonian https://doi.org/10.1239/jap/1032374642
  12. Proceedings of the Sixth Berkeley Symposium Sample Behaviour of Gaussian Process M. B. Marcus;L. A. Shepp
  13. Performance Evaluation v.42 Nonparametric Estimation of Long-Tailed Density Functions and Its Application to the Analysis of World Wide Web traffic N. M. Markovitch;U. R. Krieger https://doi.org/10.1016/S0166-5316(00)00031-6
  14. Queueing System v.16 A Storage Model with Self-Similar Input I. Norros https://doi.org/10.1007/BF01158964
  15. IEEE Journal on Selected Areas in Communications v.13 On the use of fractional Brownian motion in the theory of connectionless networks I. Norros https://doi.org/10.1109/49.400651
  16. Self-Similar Network Traffic and Performance Evaluation K. Park;W. Willinger
  17. The Annals of Statistics v.25 Heavy Tail Modeling and Teletraffic Data Sindey I. Resnick https://doi.org/10.1214/aos/1069362376
  18. Proceedings of ACM SIGCOMM '95 Self-similarity through hight-variability; statical analysis of Ethernet LAN traffic at the source level W. Willinger;M. S. Taqqu;R. Sherman;D. Wilson