Research ArticleOpen AccessGoogle Scholar indexed
Study of Delay and Loss Behavior of Internet Switch-Markovian Modelling Using Circulant Markov Modulated Poisson Process (CMMPP)
Department of Mathematics, Medak College of Engineering and Technolgy, Medak, India
Department of Mathematics, Kakatiya Institute of Technology and Science, Warangal, India
Department of Mathematics, Kakatiya University, Warangal, India
Department of Mathematics, Kakatiya University, Warangal, India
- 1 Department of Mathematics, Medak College of Engineering and Technolgy, Medak, India
- 2 Department of Mathematics, Kakatiya Institute of Technology and Science, Warangal, India
- 3 Department of Mathematics, Kakatiya University, Warangal, India
- 4 Department of Mathematics, Kakatiya University, Warangal, India
Applied Mathematics·Volume 05 (2014)·Pages 512–519·Published 7 February 2014·DOI10.4236/am.2014.53050
Copy link · social · email
Abstract
Most of the classical self-similar traffic models are asymptotic in nature. Therefore, it is crucial for an appropriate buffer design of a switch and queuing based performance evaluation. In this paper, we investigate delay and loss behavior of the switch under self-similar fixed length packet traffic by modeling it as CMMPP / D /1 and CMMPP / D /1/ K , respectively, where Circulant Markov Modulated Poisson Process (CMMPP) is fitted by equating the variance of CMMPP and that of self-similar traffic. CMMPP model is already the validated one to emulate the self-similar characteristics. We compare the analytical results with the simulation ones.
KeywordsCMMPPSelf-Similar TrafficMean Waiting TimePacket Loss ProbabilityTraffic IntensityHurst ParameterTime-Scale
- W. E. Leland, M. S. Taqqu, W. Willinger and W. V. Wilson, “On the Self-Similar Nature of Ethernet Traffic (Extended Version),” IEEE/ACM Transactions on Networking, Vol. 2, No. 1, 1994, pp. 1-15. http://dx.doi.org/10.1109/90.282603
- V. Paxson and S. Floyd, “Wide Area Traffic: The Failure of Poisson Modelling,” IEEE/ACM Transactions on Networking, Vol. 3, No. 3, 1995, pp. 226-244. http://dx.doi.org/10.1109/90.392383
- M. Crovella and A. Bestavros, “Self-Similarity in World Wide Web Traffic: Evidence and Possible Causes,” IEEE/ACM Transactions on Networking, Vol. 5, No. 6, 1997, pp. 835-846. http://dx.doi.org/10.1109/90.650143
- A. Andersen and B. Nielsen, “A Markovian Approach for Modeling Packet Traffic with Long-Range Dependence,” IEEE Journal on Selected Areas in Communications, Vol. 16, No. 5, 1998, pp. 719-773. http://dx.doi.org/10.1109/49.700908
- T. Yoshihara, S. Kasahara and Y. Takahashi, “Practical Time-Scale Fitting of Self-Similar Traffic With Markov Modulated Poisson Process,” Telecommunication Systems, Vol. 17, No. 1-2, 2001, pp. 185-211. http://dx.doi.org/10.1023/A:1016616406118
- S. Kasahara, “Internet Traffic Modelling: Markovian Approach to Self-Similar Traffic and Prediction of Loss Probability for Finite Queues,” IEICE Transactions on Communication Special Issue on Internet Technology, Vol. E84-B, No. 8, 2001, pp. 2134-2141.
- S. K. Shao, P. Malla Reddy, M. G. Tsai, H. W. Tsao and J. Wu, “Generalized Variance-Based Markovian Fitting for Self-Similar Traffic Modeling,” IEICE Transactions on Communication, Vol. E88-B, No. 12, 2005, pp. 4659-4663.
- K. De and Cockand Bart DeMoor, “Identication of the First Order Parameters of a Circulant Modulated Poisson Process,” Proceedings of the International Conference on Telecommunications (ICT’98), Porto Carras, Vol. II, 1998, pp. 420-424.
- K. De Cock, T. Van Gestel and B. De Moo, “Identification of Circulant Modulated Poisson Process a Time Domain Approach,” Proceedings of MTNS, 1998, pp. 739-742.
- C. Blondia, “The N/G/l Finite Capacity Queue,” Communications in Statistics: Stochastic Models, Vol. 5, 1989, pp. 273-294.
- D. Ranadheer, R. Ramesh, D. Rajaiah and P. Malla Reddy, “Self-Similar Network Traffic Modeling Using Circulant Markov Modulated Poisson Process (CMMPP) (Manuscript),” Communicated to International Conference on Fractals and Wavelets, 2013.
- W. Fisher and K. S. Meier-Hellstern, “The Markov-Modulated Poisson Process (MMPP) Cookbook,” Performance Evaluation, Vol. 18, No. 2, 1992, pp. 149-171. http://dx.doi.org/10.1016/0166-5316(93)90035-S