Recent developments of matrix analytic methods make phase type distributions (PHs) and Markov Arrival Processes (MAPs) promising stochastic model candidates for capturing traffic trace behaviour and for efficient usage in queueing analysis. After introducing basics of these sets of stochastic models, the paper discusses the following subjects in detail: (i) PHs and MAPs have different representations. For efficient use of these models, sparse (defined by a minimal number of parameters) and unique representations of discrete time PHs and MAPs are needed, which are commonly referred to as canonical representations. The paper presents new results on the canonical representation of discrete PHs and MAPs. (ii) The canonical representation allows a direct mapping between experimental moments and the stochastic models, referred to as moment matching. Explicit procedures are provided for this mapping. (iii) Moment matching is not always the best way to model the behavior of traffic traces. Model fitting based on appropriately chosen distance measures might result in better performing stochastic models. We also demonstrate the efficiency of fitting procedures with experimental results.
Alfa, A. (2002). Discrete time queues and matrix-analytic methods, Top 10(2): 147-185.
Bodrog, L., Heindl, A., Horváth, G. and Telek, M. (2008). A Markovian canonical form of second-order matrix-exponential processes, European Journal of Operation Research 190: 459-477.
Horváth, G. and Telek, M. (2007). A canonical representation of order 3 phase type distributions, in K. Volter (Ed.), Formal Methods and Stochastic Models for Performance Evaluation, Springer, Berlin/Heidelberg, pp. 48-62.
Financed by the National Centre for Research and Development under grant No. SP/I/1/77065/10 by the strategic scientific research and experimental development program:
SYNAT - “Interdisciplinary System for Interactive Scientific and Scientific-Technical Information”.