Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

POWER TAIL ASYMPTOTIC RESULTS OF A DISCRETE TIME QUEUE WITH LONG RANGE DEPENDENT INPUT

  • Hwang, Gang-Uk (Division of Applied Mathematics Korea Advanced Institute of Science and Technology) ;
  • Sohraby, Khosrow (Telecommunications Networking University of Missouri-Kansas City)
  • Published : 2003.01.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we consider a discrete time queueing system fed by a superposition of an ON and OFF source with heavy tail ON periods and geometric OFF periods and a D-BMAP (Discrete Batch Markovian Arrival Process). We study the tail behavior of the queue length distribution and both infinite and finite buffer systems are considered. In the infinite buffer case, we show that the asymptotic tail behavior of the queue length of the system is equivalent to that of the same queueing system with the D-BMAP being replaced by a batch renewal process. In the finite buffer case (of buffer size K), we derive upper and lower bounds of the asymptotic behavior of the loss probability as $K\;\longrightarrow\;\infty$.

Keywords

References

  1. Applied Probability and Queues S. Asmussen
  2. QUESTA v.33 On a Reduced Load Equivalence for Fluid Queues Under Subexponentiality R. Agrawal;A. M. Makowski;P. Nain
  3. Computer Communications v.21 Fluid Queues with Long-Tail Activity Period Distributions O. J. Boxma;V. Dumas https://doi.org/10.1016/S0140-3664(98)00219-9
  4. IEEE INFOCOM '99 Asymptotic Behavior of a Discrete-Time Queue with Long Range Dependent Input T. Daniels;C. Blondia
  5. Proceedings of IFIP TC6 Networking 2000 Tail Transitions in Queues with Long Range Dependent Input T. Daniels;C. Blondia
  6. Proceedings of the 34th Annual Allertion Conference on Communications On the Relevance of Long-tail Durations for the Statistical Multiplexing of Large Aggregations N. G. Duffield
  7. An Introduction to Probabilty and Its Applications v.Ⅱ W. Feller
  8. Bell System Tech. Journal v.62 Batch delays versus Customer Delays S. Halfin https://doi.org/10.1002/j.1538-7305.1983.tb03527.x
  9. IEEE Transaction on Communications v.46 no.12 Closed-Form Expressions on the Geometric Tail Behavior of Statistical Multiplexers with Heterogeneous Traffic G. U. Hwang;B. D. Choi https://doi.org/10.1109/26.737393
  10. QUESTA v.31 no.3-4 Loss probability in a finite discrete-time queue in terms of the steady state distribution of an infinite queue F. Ishizaki;T. Takine
  11. INFOCOM '97 Bounds for the Tail Distribution in a Queue with the Superposition of General Periodic Markov Sources F. Ishizaki;T. Takine
  12. Advances in Applied Probability v.31 no.2 Asymptotic results for multiplexing on-off sources with subexponential on period P.R. Jelenkovic;A. A. Laza
  13. QUESTA v.33 Subexponential Loss Rates in a GI/GI/1 Queue with Applications P. R. Jelenkovic
  14. INFOCOM 2001 Asymptotic Loss Probability in a Finite Buffer Fluid Queue with Heterogeneous Heavy-Tail On-Off Processes P. R. Jelenkovic;P. Momcilovic
  15. INFOCOM '95 Analysis of an ATM Buffer with Self-similar("fractal") input traffic N. Kikhanov;B. Tsybakov;N. D. Georganas
  16. Journal of Applied Probability v.36 Cell Loss Asymptotics for Buffers fed with a large number of independent stationary sources N. Likhanov;R. Mazumdar https://doi.org/10.1239/jap/1032374231
  17. IEEE Trans. on Comm. A General Solution Technique for Discrete Queueing Analysis of Multi-Media Traffic on ATM S. Q. Li
  18. Journal of Applied Probability v.36 Asymptotic Behavior of a Multiplexer fed by a Long-range Dependent Process Z. Liu;P. Nain;D. Towsley;Z. L. Zhang
  19. IEEE/ACM Transactions on networking v.2 On the self-similar nature of Ethernet traffic (extended version) W. E. Leland;M. S. Taqqu;W. Willinger;D. V. Wilson https://doi.org/10.1109/90.282603
  20. Self-Similar Network Traffic and Performance Evaluation Buffer Asymptotics for M/G/∞ input processes A. M. Makowski;M. Parulekar;K. Park(ed.);W. Willinger(ed.)
  21. Structured stochastic matrices of M/G/1 type and their applications M. F. Neuts
  22. Translations of Mathematical Monographs v.107 Selected Problems in Real Analysis B. M. Makarov;M. G. Goluzia;A. A. Lodkin;A. N. Podkorytov
  23. QUESTA v.27 Tail Probabilities for a Multiplexer driven by M/G/∞ input process (Ⅰ): Preliminary Asymptotics M. Parulekar;A. M. Makowski
  24. INFOCOM'96 Tail Probabilities for a Multiplexer with Self-similar Traffic M. Parulekar;A. M. Makowski
  25. INFOCOM'97 M/G/∞ input processes: A Versatile Class of Models for Traffic Network M. Parulekar;A. M. Makowski
  26. INFOCEM '93 On the theory of general ON-OFF sources with applications in high-speed networks K. Sohraby
  27. Annals of Operations Research v.49 On the asymptotic analysis of statistical multiplexers with hyper-bursty arrivals K. Sohraby https://doi.org/10.1007/BF02031602
  28. Performance Evaluation v.22 A simple approach to obtain tight upper bounds for the asymptotic queueing behavior of statistical multiplexers with heterogeneous traffic Y. Xiong, Bruneel https://doi.org/10.1016/0166-5316(93)E0057-C