Back
 AM  Vol.5 No.3 , February 2014
Study of Delay and Loss Behavior of Internet Switch-Markovian Modelling Using Circulant Markov Modulated Poisson Process (CMMPP)
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.
Cite this paper: R. Donthi, R. Renikunta, R. Dasari and M. Perati, "Study of Delay and Loss Behavior of Internet Switch-Markovian Modelling Using Circulant Markov Modulated Poisson Process (CMMPP)," Applied Mathematics, Vol. 5 No. 3, 2014, pp. 512-519. doi: 10.4236/am.2014.53050.
References

[1]   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

[2]   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

[3]   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

[4]   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

[5]   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

[6]   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.

[7]   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.

[8]   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.

[9]   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.

[10]   C. Blondia, “The N/G/l Finite Capacity Queue,” Communications in Statistics: Stochastic Models, Vol. 5, 1989, pp. 273-294.

[11]   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.

[12]   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

 
 
Top