Discussion of the Analysis of Self-similar Teletraffic with Long-range Dependence (LRD) at the Network Layer Level

Authors

  • Ginno Millí¡n Universidad de Santiago de Chile Departamento de Ingenierí­a Eléctrica Avda. Libertador Bernardo O’Higgins #3363. Estación Central. Santiago - Chile
  • Héctor Kaschel Universidad de Santiago de Chile Departamento de Ingenierí­a Eléctrica Avda. Libertador Bernardo O’Higgins #3363. Estación Central. Santiago - Chile
  • Gastón Lefranc Pontificia Universidad Católica de Valparaí­so Escuela de Ingenierí­a Eléctrica Avda. Brasil #2147. Valparaí­so - Chile

Keywords:

Long-range-dependent, network layer, network traffic, self-similar process

Abstract

Traffic streams, sources as well as aggregated traffic flows, often exhibit long-range-dependent (LRD) properties. This paper presents the theoretical foundations to justify that the behavior of traffic in a high-speed computer network can be modeled from a self-similar perspective by limiting its scope of analysis to the network layer, since the most relevant properties of self-similar processes are consistent for use in the formulation of traffic models when performing this specific task.

References

W. Stallings, Redes e Internet de Alta Velocidad. Rendimiento y Calidad de Servicio, 2nd ed., Madrid, Pearson - Prentice Hall, 2004, pp. 224-237.

Kleinrock, Information Flow in Large Communication Nets, Ph.D. Thesis, Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, 1961.

L. Kleinrock, Communication Nets: Stochastic Message Flow and Delay, New York, McGraw- Hill, 1964.

W.E. Leland, M.S. Taqqu, W. Willinger, and D.V. Wilson, On the Self-Similar Nature of Ethernet Traffic, in Proc. ACM SIGCOMM ?93, San Francisco, CA, pp. 183-193. http://dx.doi.org/10.1145/166237.166255

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. Netw., Vol. 2, No. 1, pp. 1-15, February 1994. http://dx.doi.org/10.1109/90.282603

A. Erramilli, R.P. Singh, and P. Pruthi, Application of Deterministic Chaotic Maps to Model Packet Traffic in Broadband Networks, in Proc. 7th ITC Specialist Seminar, Morristown, NJ, 1990.

W.E. Leland and D.V. Wilson, High Time-Resolution Measurement and Analysis of LAN Traffic: Implications for LAN Interconnections, in Proc. IEEE INFOCOM ?91, Bal Harbour, FL, pp. 1360-1361.

J. Beran, R. Sherman, M.S. Taqqu, and W. Willinger, Long-Range Dependence in Variable- Bit-Rate Video Traffic, IEEE Trans. Commun., Vol. 43, No 2/3/4, pp. 1566-1579, Feb/- Mar/Apr 1995.

B. Mandelbrot, Self-Similar Error Cluster in Communication Systems and the Concept of Conditional Stationarity, IEEE Trans. Commun. Technol., Vol. 13, No. 1, pp. 71-90, Mar. 1965. http://dx.doi.org/10.1109/TCOM.1965.1089090

http://ita.ee.lbl.gov/html/contrib/BC.html.

W. Willinger, M.S. Taqqu, R. Sherman, and D.V. Wilson, Self-Similarity Through High- Variability: Statistical Analysis of Ethernet LAN Traffic at the Source Level, in Proc. ACM SIGCOMM '95, Cambridge, MA, pp. 100-113. http://dx.doi.org/10.1109/90.554723

W. Willinger, M.S. Taqqu, R. Sherman, and D.V. Wilson, Self-Similarity Through High- Variability: Statistical Analysis of Ethernet LAN Traffic at the Source Level, IEEE/ACM Trans. Netw., Vol. 5, No. 1, pp. 71-86, Feb. 1997. http://dx.doi.org/10.1109/90.554723

M.S. Taqqu, W. Willinger, and R. Sherman, Proof of a Fundamental Result in Self-Similar Traffic Modeling, ACM SIGCOMM Computer Communication Review, Vol. 27, No. 2, pp. 5-23, Apr. 1997. http://dx.doi.org/10.1145/263876.263879

A. Adas and A. Mukherjee. (1994, Dec.).On Resource Management and QoS Guarantees for Long Range Dependent Traffic. Georgia Inst. Tech., GA. [Online]. Available: http://hdl.handle.net/1853/6797.

S.M. Klivansky and A. Mukherjee. (1995, Aug.). The NFSNET. Georgia Inst. Tech., GA. [Online]. Available: ftp://ftp.cc.gatech.edu/pub/coc/tech_reports/95/GIT-CC-95-07.ps.Z.

V. Paxson and S. Floyd, Wide-Area Traffic: The Failure of Poisson Modeling, IEEE/ACM Trans. Netw., Vol. 3, No. 3, pp. 226-244, Jun. 1995. http://dx.doi.org/10.1109/90.392383

M.E. Crovella and A. Bestavros. (1995, Oct.). Explaining World Wide Web Traffic Self- Similarity. Boston Univ., MA. [Online]. Available: http://www.cs.bu.edu/techreports.

M.E. Crovella and A. Bestavros, Self-Similarity in World Wide Web Traffic: Evidence and Possible Causes, IEEE/ACM Trans. Netw., Vol. 5, No. 6, pp. 835-846. Dec. 1997. http://dx.doi.org/10.1109/90.650143

M. Arlitt, R. Friedrich, and T. Jin, Workload Characterization of a Web Proxy in a Cable Model Environments, Performance Evaluation Review, Vol. 27, No. 2, pp. 25-36, Sep. 1999. http://dx.doi.org/10.1145/332944.332951

D.E. Duffy, A.A. Mc Intosh, M. Rosenstein, and W. Willinger, Statistical Analysis of CCSN/ SS7 Traffic Data from Working CCS Subnetworks, IEEE J. Sel. Areas Commun., Vol. 12, No. 3, pp. 544-551, Apr. 1994. http://dx.doi.org/10.1109/49.285297

P. Pruthi and A. Erramilli, Heavy-Tailed ON/OFF Source Behavior and Self-Similar Traffic, in Proc. 1995 IEEE International Conference on Communications, Seattle, WA, Vol. 1, pp. 445-450. http://dx.doi.org/10.1109/ICC.1995.525209

G. Rufa, Developments in Telecommunications. Whit a Focus on SS7 Network Reliability, Berlin, Germany: Springer-Verlag, 2008.

M.W. Garrett and W. Willinger, Analysis, Modeling and Generation of Self-Similar VBR Video Traffic, Computer Communication Review, Vol. 24, No. 4, pp. 269-280, Oct. 1994. http://dx.doi.org/10.1145/190809.190339

B. Tsybakov and N.D. Georganas, On Self-Similar Traffic in ATM Queues: Definitions, Overflow Probability Bound and Cell Delay Distribution, IEEE/ACM Trans. Netw., Vol. 5, No. 3, pp. 397-409, Jun. 1997. http://dx.doi.org/10.1109/90.611104

L. Yellanki, Performance Evaluation of VBR Video Traffic Models, M.Sc. Thesis, Dept. Comput. Sci., Univ. Saskatchewan, Saskatoon, SK, Canada, 1999.

M. Zhonghua, Analysis of Wireless Data Network Traffic, M.Sc. Thesis, School of Engineering Science, Simon Fraser Univ., Burnaby, BC, Canada, 2000.

D.R. Basgeet, J. Irvine, A. Munro, P. Dugenie, D. Kaleshi, and O. Lazaro, Impact of Mobility on Aggregate Traffic in Mobile Multimedia System, in the 5th International Symposium on Wireless Personal Multimedia Communications, Honolulu, HI, 2002, Vol. 2, pp. 333-337.

Q. Liang, Ad Hoc Wireless Network Traffic-Self-Similar and Forecasting, IEEE Commun. Lett., Vol. 6, No. 7, pp. 297-299, Jul. 2002. http://dx.doi.org/10.1109/LCOMM.2002.801327

T. Janevski, Characterization and classification of IP traffic, in Traffic Analysis and Design of Wireless IP Networks, Norwood, MA: Artech House, Inc., 2002, ch. 5, pp. 135-165.

J. Yu, Modeling of High-Speed Wireline and Wireless Network Traffic, Ph.D. Dissertation, Elect. Comput. Eng. Dept., Drexel Univ., Philadelphia, PA, 2005.

X. Yang, Impulsive Self-Similar Processes, with Applications in Broadband Communication System Modeling, Ph.D. Dissertation, Elect. Comput. Eng. Dept., Drexel Univ., Philadelphia, PA, 2001.

J. Ridoux, A. Nucci, and D. Veitch, Seeing the Difference in IP Traffic: Wireless Versus Wireline, in Proc. 25th IEEE International Conference on Computer Communications, Barcelona, Spain, 2006, pp. 1-12. http://dx.doi.org/10.1109/infocom.2006.292

N. Hohn, D. Veitch, and P. Abry, Does Fractal Scaling at the IP Level Depend on TCP Flow Arrival Processes?, in Proc. 2nd ACM SIGCOMM Workshop on Internet Measurement, Marseille, 2002, pp. 63-68. http://dx.doi.org/10.1145/637201.637208

N. Hohn, D. Veitch, and P. Abry, Cluster Processes, a Natural Language for Network Traffic, IEEE Trans. Signal Process., Vol. 51, No. 8, pp. 2229-2244, Aug. 2003. http://dx.doi.org/10.1109/TSP.2003.814460

N. Hohn, D. Veitch, and P. Abry, The Impact of the Flow Arrival Process in Internet Traffic, in Proc. IEEE Int. Conf. Acoustics, Speech, and Signal Processing, Hong Kong, 2003, Vol. 6, pp. VI-37-40.

R. Fantacci and D. Tarchi, Bridging Solutions for a Heterogeneous WiMAX-WiFi Scenario, Journal of Communications and Networks, Vol. 8, No. 4, pp. 369-377, Dec. 2006. http://dx.doi.org/10.1109/JCN.2006.6182785

A. Erramilli, M. Roughan, D. Veitch, and W. Willinger, Self-Similar Traffic and Network Dynamics, in Proc. of the IEEE, Vol. 90, No. 5, pp. 800-819, May. 2002. http://dx.doi.org/10.1109/jproc.2002.1015008

J.P. Gianvittorio and Y. Rahmat-Samil, Fractal Antennas: A Novel Antenna Miniaturization Technique, and Applications, IEEE Antennas Propagat. Mag., Vol. 44, No. 1, pp. 20-36, Feb. 2002. http://dx.doi.org/10.1109/74.997888

R. Azaro, E. Zeni, M. Donelli, and A. Massa, Fractal-based methodologies for WiMAX antenna synthesis, in WiMAX: Technologies, Performance Analysis, and QoS, S. Ahson and M. Ilyas, Eds. Boca Raton, FL: CRC Press, 2008, ch. 2, pp. 21-39.

G. Kramer, Ethernet Passive Optical Networks, USA, McGraw-Hill, 2005.

A. Huang, B. Mukherjee, L. Xie, and Z. Li, Time-Space Label Switching Protocol (TSLSP), in High-Performance Packet Switching Architectures, I. Elhanany and M. Hamdi, Eds., Germany: Springer-Verlag, 2007, ch. 9, pp. 197-210. http://dx.doi.org/10.1007/1-84628-274-8_9

M. Maier, Optical Switching Networks, New York: Cambridge University Press, 2008.

M. Grossglauser and J-C Bolot, On the Relevance of Long-Range Dependence in Network Traffic, IEEE/ACM Trans. Netw., vol. 7, no. 5, pp. 629-640, Oct. 1999. http://dx.doi.org/10.1109/90.803379

J.-Y. Le Boudec and P. Thiran, Network Calculus. A Theory of Deterministic Queuing Systems for the Internet, Germany: Springer-Verlag, 2004, pp. 3-6.

A. Adas, Traffic Models in Broadband Network, IEEE Commun. Mag., Vol. 35, No. 7, pp. 82-89, Jul. 1997. http://dx.doi.org/10.1109/35.601746

D.P Heyman and T.V. Lakshman, What are the Implications of Long-Range Dependence for VBR-Video Traffic Engineering?, IEEE/ACM Trans. Netw., Vol. 4, No. 3, pp. 301-317, Jun. 1996. http://dx.doi.org/10.1109/90.502230

K. Sriram and W. Whitt, Characterizing Superposition Arrival Processes in Packet Multiplexers for Voice and Data, IEEE J. Sel. Areas Commun., Vol. 4, No. 6, pp. 833-846, Sep. 1986. http://dx.doi.org/10.1109/JSAC.1986.1146402

B.K. Ryu and A. Elwaid, The Importance of Long-Range Dependence of VBR Video Traffic in ATM Traffic Engineering: Myths and Realities, Computer Communication Review, vol. 26, no. 4, pp. 3-14, Oct. 1996. http://dx.doi.org/10.1145/248157.248158

B.K Ryu and A. Elwaid, The Relevance of Short Range and Long-Range Dependence of VBR Video Traffic to Real-Time Traffic Engineering, unpublished.

K. Chandra and A.R. Reibman, Modeling One-and Two-Layer Variable Bit Rate Video, IEEE/ACM Trans. Netw., Vol. 7, No. 3, pp. 398-417, Jun. 1999. http://dx.doi.org/10.1109/90.779209

J. Yu and A. Petropulu, Is High-Speed Wireless Network Traffic Self-Similar?, in Proc. of IEEE Int. Conf. Acoustics, Speech, and Signal Processing, Montreal, Canada, 2004, Vol. 2, pp. II-425-428.

S. Bregni, P. Giacomazzi, and G. Saddemi, Transport of Long-Range Dependent Traffic in Single-Hop and Multi-Hop IEEE 802.3e Networks, in Proc. IEEE Global Telecommunications Conference, New Orleans, LA, 2008, pp. 1-6.

A. Ge, F. Callegati, and L.S. Tamil, On Optical Burst Switching and Self-Similar Traffic, IEEE Commun. Lett., Vol. 4, No. 3, pp. 98-100, Mar. 2000. http://dx.doi.org/10.1109/4234.831037

D.I. Sheluhin, S.M. Smolskiy, and A.V. Osin, Self-Similar Processes in Telecommunications, Chichester, UK: John Wiley & Sons, Ltd., 2007, ch.​1, pp. 8-9. http://dx.doi.org/10.1002/9780470062098

X. Yang, Impulsive Self-Similar Processes, with Applications in Broadband Communication System Modeling, Ph.D. Dissertation, Elec. Comput. Eng. Dept., Drexel Univ., Philadelphia, PA, 2001.

F. M. Dekking, C. Kraaikamp H. P. Lopuhaä, and L. E. Meester, The central limit theorem, in A Modern Introduction to Probability and Statistics. Understanding Why and Wow. Springer-Verlag, 2005, ch. 14, pp. 195-202.

M. Parulekar and A.M. Makowski, Tail Probabilities for a Multiplexer with Self-Similar Traffic, in Fifteenth Annual Joint Conf. IEEE Computer Societies. Networking the Next generation, San Francisco, CA, 1996, vol. 3, pp. 1452-1459.

M. Parulekar and A.M. Makowski. (1996). M/G/∞ Input Process: A Versatile Class of Models for Network Traffic, Univ. Maryland, College Park, MD, [Online]. Available: http://hdl.handle.net/1903/5778.

B. Mandelbrot and W. Van Ness, Fractional Brownian Motions, Fractional Noises and Applications, SIAM Review, Vol. 10, No. 4, pp. 422-437, Oct. 1968. http://dx.doi.org/10.1137/1010093

J. Beran, Statistical Methods for Data with Long-Range Dependence, Statistical Science, Vol. 7, No. 4, pp. 404-416, Nov. 1992. http://dx.doi.org/10.1214/ss/1177011122

H. Rinne, The Weibull Distribution. A Handbook, Boca Raton, FL: Chapman & Hall/CRC, 2009.

M. Parulekar and A.M. Makowski. (1995). Buffer Overflow Probabilities for a Multiplexer with Self-Similar Traffic. Univ. Maryland. College Park, MD, [Online]. Available: http://hdl.handle.net/1903/5727.

M. Parulekar and A.M. Makowski (1996). Tail Probabilities for M|G|∞ Input Processes (I): Preliminary Asymtotics. Univ. Maryland. College Park, MD, [Online]. Available: http://hdl.handle.net/1903/5760.

A. Patel and C. Williamson, Statistical Multiplexing of Self-Similar Traffic: Theoretical and Simulation Results, unpublished.

R. Ritke, X. Hong, and M. Gerla, Contradictory Relationship Between Hurst Parameter and Queuing Performance (extended version), Telecommunication Systems, Vol. 16, No. 1-2, pp. 159-175, Jan. 2001. http://dx.doi.org/10.1023/A:1009063114616

B.K. Ryu and S.B. Lowen, Point Process Approaches for Modeling and Analysis of Self- Similar Traffic: Part I: Model Construction, in Proc. Fifteenth Annual Joint Conference of the IEEE Computer Societies. Networking the Next Generation, San Francisco, CA, 1996, vol. 3, pp. 1468-1475.

B.K. Ryu and S.B. Lowen, Point Process Approaches for Modeling and Analysis of Self- Similar Traffic: Part II: Applications, in Proc. 5th International Conference on Telecommunication Systems, Modeling, and Analysis, Nashville, TN, 1997, pp. 62-70.

S.B. Lowen and M.C. Teich, Estimation and Simulation of Fractal Stochastic Point Processes, Fractals. Complex Geometry Patterns and Scaling in Nature and Society, vol. 3, no. 1, pp. 183-210, Mar. 1995. http://dx.doi.org/10.1142/s0218348x95000151

Published

2010-12-01

Most read articles by the same author(s)

Obs.: This plugin requires at least one statistics/report plugin to be enabled. If your statistics plugins provide more than one metric then please also select a main metric on the admin's site settings page and/or on the journal manager's settings pages.