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Generalized VarianceBased Markovian Fitting for SelfSimilar Traffic Modelling
ShouKuo SHAO Malla REDDY PERATI MengGuang TSAI HenWai TSAO Jingshown WU
Publication
IEICE TRANSACTIONS on Communications
Vol.E88B
No.4
pp.14931502 Publication Date: 2005/04/01 Online ISSN:
DOI: 10.1093/ietcom/e88b.4.1493 Print ISSN: 09168516 Type of Manuscript: Special Section PAPER (Special Section on Internet Technology V) Category: Keyword: index of dispersion for counts, MMPP, selfsimilarity, variancetime,
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Summary:
Most of the proposed selfsimilar traffic models are asymptotic in nature. Hence, they are less effective in queueingbased performance evaluation when the buffer sizes are small. In this paper, we propose a short range dependent (SRD) process modelling by a generalized variancebased Markovian fitting to provide effective queueingbased performance measures when buffer sizes are small. The proposed method is to match the variance of the exact secondorder selfsimilar processes. The fitting procedure determines the related parameters in an exact and straightforward way. The resultant traffic model essentially consists of a superposition of several twostate Markovmodulated Poisson processes (MMPPs) with distinct modulating parameters. We present how well the resultant MMPP could emulate the variance of original selfsimilar traffic in the range of the specified time scale, and could provide more accurate bounds for the queueingbased performance measures, namely tail probability, mean waiting time and loss probability. Numerical results show that both the secondorder statistics and queueingbased performance measures when buffer capacity is small are more accurate than that of the variancebased fitting where the modulating parameters of each superposed twostate MMPP are equal. We then investigate the relationship between time scale and the number of superposed twostate MMPPs. We found that when the performance measures pertaining to larger time scales are not better than that of smaller ones, we need to increase the number of superposed twostate MMPPs to maintain the accurate and reliable queueingbased performance measures. We then conclude from the extensive numerical examples that an exact secondorder selfsimilar traffic can be well represented by the proposed model.

