Remarks Regarding Queuing Model and Packet Loss Probability for the Traffic with Self-Similar Characteristics

Authors: Mihails Kulikovs, Ernests Petersons

Abstract:

Network management techniques have long been of interest to the networking research community. The queue size plays a critical role for the network performance. The adequate size of the queue maintains Quality of Service (QoS) requirements within limited network capacity for as many users as possible. The appropriate estimation of the queuing model parameters is crucial for both initial size estimation and during the process of resource allocation. The accurate resource allocation model for the management system increases the network utilization. The present paper demonstrates the results of empirical observation of memory allocation for packet-based services.

Keywords: Queuing System, Packet Loss Probability, Measurement-Based Admission Control (MBAC), Performanceevaluation, Quality of Service (QoS).

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1333839

References:

[1] A. Erramilli, O. Narayan, and W. Willinger. (1996). Experimental queueing analysis with long-range dependent traffic. IEEE/ACM Trans. Networking, vol. 4 , pp. 209-223.
[2] Addie, R.G., Neame, T.D. & Zukerman, M. (2002, October). Performance Evaluation of a Queue Fed by a Poisson Pareto Burst Process. Computer Networks, Vol. 40, Nº 3 , pp. 377-397.
[3] Beran, J. (1994). Statistics for Long-Memory Processes. New York: Chapman & Hall/CRC, 1 ed.
[4] B. D. Choi, B. Kim, and I.Wee, "Asymptotic behavior of loss probability in GI/M/1/K Queue as K tends to infinity, Queueing Systems, vol. 36, pp. 437-442, 2000.
[5] Carl M. Harris, Percy H. Brill , Martin J. Fischer "Internet-Type Queues with Power-Tailed Interarrival Times and Computational Methods for their Analysis", INFORMS Journal on Computing, 2000
[6] Chengyu Zhu and Oliver W. W. Yang, "A Comparison of Active Queue Management Algorithms Using the OPNET Modeler", IEEE Communications Magazine ÔÇó June 2002
[7] Crovella, M. E. & Bestravos, A. (1997, December). Self-Similarity in World Wide Web Traffic: Evidence and Possible Causes. IEEE Trans. Networking, 5(6).
[8] Downey, A. B. (2001, November). Evidence for Long-Tailed Distributions in the Internet. ACM SIGCOMM IMW 2001.
[9] Duffield, N. G. (Preprint, 1994.). Economies of scale in queues with sources having power-law large deviation scalings.
[10] F. Ferreira (speaker) and A. Pacheco, "Analysis of Pareto -Type/M/s/c finite buffer queues.", Second Workshop on New Trends in Modelling, Quantitative Methods and Measurements, Aveiro, Portugal, 24/11/2005 - 25/11/2005.
[11] Gordon, J., "Pareto Process as a Model of Self-Similar Packet Traffic", Global Telecommunications Conference, 1995. GLOBECOM '95., IEEE.
[12] G. Bolch, S. Greiner, H. Meer, K S. Trivide, "Queueing Networks and Markov Chains Modeling and Perfomance Evaluation with Computer Science Applications", 2nd Edition Wiley-Interscience 2006
[13] Guanghui He, Yuan Gao I Jennifer H Hou, Kihong Park. (2004, August). A Case for Exploiting Self-Similarity of Network Traffic in TCP Congestion Control. The International Journal of Computer and Telecommunications Networking Volume 45, Issue 6 , pp. p. 743 - 766.
[14] Hengky Susanto Byung-Guk Kim, ÔÇ×Examining Self-Similarity Network Traffic intervals".
[15] Ilkka Norros, On the use of fractional Brownian motion in the theory of connectionless networks (1995).
[16] Jeong, H.-D. J., McNickle, D. & Pawlikowski., K. "Fast Self-Similar Teletraffic Generation Based on FGN and Wavelets". IEEE ICON'99, Sept. 1999
[17] J. P. Buzen, "A Queueing Network Model of MVS," ACM Computing Surveys, Vol. 10, No. 3, Sept. 1978,pp. 319-331.
[18] K. Nichols, V. Jacobson, and L. Zhang. "A Two-bit Differentiated Services Architecture for the Internet", RFC 2638, IETF, July 1999. (pp 23, 25, 102, 213)
[19] Leonard Klienrock, "Queuing System", A Wiley-Interscience Publication, John Wiley & Sons, 1979
[20] Mandelbrot B.B., "Long-Run Linearity, Locally Gaussian Processes, HSpectra and Infinite Variances", International Economic Review, Vol.10, pp. 82-113, 1969.
[21] M. S. Taqqu, "A bibliographical guide to self-similar processes and long-range dependence," in Dependence in Probability and Statistics, E. Eberlein and M. S. Taqqu, Eds. Boston, MA: Birkh¨auser, 1986, pp. 137-162.
[22] N. G. Duffield and N. O-Connell. (1995). Large deviations and overflow probabilities for the general single-server queue, with applications. in Math, Proc. Cambridge Philos. Soc. , pp. 363-375.
[23] Norros, I. (1994). A storage model with self-similar input. Queueing Syst., vol. 16 , pp. 387-396.
[24] Park, J. and Park, C, Robust estimation of the Hurst parameter and selection of an onset scaling //Under revision, 2007, Web available: ttp://www.maths.lancs.ac.uk/~parkj1/paper/robusth_Dec07.pdf
[25] Park, K. Kim, G. & Crovella, M.E. (1997, November). On the Effect of Traffic Self-similarity on Network Performance. SPIE International Conference on Performance and Control of Network Systems.
[26] P. Leys, J. Potemans1, B. Van den Broeck, J. Theunis, E. Van Lil, A. Van de Capelle, "Use of the Raw Packet Generator in OPNET", OPNETWORK, (Washington, DC, 2001).
[27] P.Ulanovs, E.Petersons, "Modeling Methods of Self-Similar Traffic for Network Performance Evaluation", Scientific Proceedings of RTU. Series 7. Telecommunications and Electronics, 2002.
[28] Ramon M. Rodr─▒guez-Dagnino, "Some Remarks Regarding Asymptotic Packet Loss in the Pareto/M/1/K Queueing System, IEEE Communications Letters, VOL. 9, NO. 10, October 2005.
[29] R. Braden, L. Zhang, S. Berson, S. Herzog, and S. Jamin. "Resource ReSerVation Protocol (RSVP) ÔÇö Version 1 Functional Specification", RFC 2205, IETF, September 1997. (pp 23, 24, 85, 124, 160, 210).
[30] Sahinoglu, Z. & Tekinay, Sirin. (1999, January). On Multimedia Networks: Self-Similar Traffic and Network Performance. IEEE Comm. Mag., 37(1).
[31] Saralees Nadarajah and Samuel Kotz, ÔÇ×On the Laplace Transform of the Pareto Distribution", Queuing Systems, Volume 54, Number 4, December 2006.
[32] Stenio Fernandes, Carlos Kamienski & Djamel Sadok, "Accuracy and Computational Efficiency on the Fractal Traffic Generation".
[33] Walter Willinger, Murad S. Taqqu, Robert Sherman, and Daniel V. Wilson , "Self-Similarity Through High-Variability: Statistical Analysis of Ethernet LAN Traffic at the Source Level", IEEE/ACM Transactions on Networking, VOL. 5, NO. 1, February 1997.
[34] W. E. Leland, M. S. Taqqu, W. Willinger, and D. V. Wilson, "On the Self-similar nature of Ethernet traffic (extended version)," IEEE/ACM Trans. Networking, vol. 2, pp. 1-15, 1994.
[35] Willinger, W., Taqqu, M.S., Sherman, R. & Wilson, D.V. (1997). Self- Similarity Through High-Variability: Statistical Analisys of Ethernet LAN Traffic at the Source Level. IEEE Trans. Networking, 5(1) , pp. 71-86.
[36] Younsuk Koh and Kiseon Kim, "Loss Probability Behavior of Pareto/M/1/K Queue", IEEE Communications Letters, Vol. 7, No. 1, January 2003.
[37] Y. Bernet, R. Yavatkar, P. Ford, F. Baker, and L. Zhang. A Framework for End-to-End QoS Combining RSVP/Intserv and Differentiated Services, March 1998. Internet Draft: draft-bernet-intdiff-00.txt. (p 25).