Remarks Regarding Queuing Model and Packet Loss Probability for the Traffic with Self-Similar Characteristics
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.
[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).
[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).
@article{"International Journal of Electrical, Electronic and Communication Sciences:56539", author = "Mihails Kulikovs and Ernests Petersons", title = "Remarks Regarding Queuing Model and Packet Loss Probability for the Traffic with Self-Similar Characteristics", 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).", volume = "2", number = "4", pages = "626-7", }