An Efficient Algorithm for the Exact Analysis of Multiclass Queueing ：对于多类排队的精确分析的一种有效算法.pptVIP

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An Efficient Algorithm for the Exact Analysis of Multiclass Queueing ：对于多类排队的精确分析的一种有效算法.ppt

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An Efficient Algorithm for the Exact Analysis of Multiclass Queueing ：对于多类排队的精确分析的一种有效算法

Outline Motivations Review of MAP Fitting Algorithms from fitting counts to interarrival times (IAT) fitting observations on eigenvalue-based methods Jordan characterization of MAP moments and autocorrelations analysis of small MAPs Composition of large MAPs MAP fitting using higher-order correlations Motivation MAP/MMPP Model Parameterization Markovian models of network traffic MAP closed queueing networks (see slides E. Smirni)? MAP fitting is not fully understood E.g., some questions: Fit the counting process or the interarrival process? How many moments? Which correlation coeffs? How fitting decisions affect queueing prediction? Is nonlinear optimization appropriate? MMPP Counting Process Fitting Measuring counts in networks can be often easier than measuring interarrival times S. Li C.L. Hwang, 1992, 1993: Circulant matrices to impose MMPP power spectrum A.T. Andersen B.F. Nielsen, 1998: Superposition of MMPP(2)s (Kronecker sum)? Matching of the Hurst parameter Degrees of freedom for optional least-square fitting of the interarrival time (IAT) autocorrelations (ACF)? Good accuracy on the Bellcore Aug89/Oct89 traces MAP Counting Process Fitting A. Horváth M. Telek, 2002: Multifractal traffic model, e.g., Riedi et al., 1999 Traffic analysis based on Haar wavelet transform Each MAP(2) describes variability in the Haar wavelet coefficients at a specific time scale Almost optimal fitting of the BC-Aug89 trace Further improvements may not be easy: Higher-order moments of counts hard to manipulate MAP Interarrival Process Two-phase fitting fitting of PH-type distribution followed by fitting of IAT ACF Feasible manipulation of higher-order moments P. Buchholz et al., 2003, 2004: Expectation Maximization (EM) algorithms Support for two-phase fitting Scalability of EM rapidly increasing (Panchenko Thümmler, 2007)? MAP Interarrival Process Moment and ACF Analytical Fitting: Results only for MMPP(2), MAP(2), MAP(3)? G. Horváth, M. Telek P. Buchholz, 2005: Two-