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Performance Analysis and Optimization with the Power-Series Algorithm

  • Computer Science
  • Mathematics


M~~~ Discussion" ~;oRe~~~h paper., o~ II III I III I I I I M I I II IIIII IIIII Nu l u lll II I I In ~ ~~ CentER for Economic Research No. 9347 PERFORI~lANCE àNALYSIS AND OPTIMIZATION WITH THE POWER-SERIES ALGORITHM by Hans (J.P.C.) Blanc July 1993 ISSN 0924-7815 :S -~,.,! .. ~- i ": L (-~ 1' `. i-f; r~U;. ~r- PERFORMANCE ANALYSIS AND OPTIMIZATION WITH THE POWER-SERIES ALGORITHM Ií~ws (J.P.C.) BLnNCt Tilburg University, The Netherlands ABSTRACT The power-series algorithm (PSA) is a tlezible device for computing perfotmattce measures for systems which can be modeled as multi-queuelmulti-server systerns with a quasi-birth-and-death structure. An overview of this technique is provided, including a motivation of the principles of the PSA, the derivation of recursive computation schemes, discussions of efficient implementa- tion of the PSA, of inethods for improving the convergence of the power series, of the numer- ical complezity of the PSA, and of the computation of derivatives with respect to system pazam- eters, and ezamples of application of the PSA. L INTRODUCTION The performance analysis and control of many computerlcornmunication systerns lead to the for- mulation and study of multi-queue models. The stochastic processes underlying these systems are generally very hard to treat by analytical methods. Therefore, it is important to develop numerical methods for computing performance measures for such systems. The power-series algorithm (PSA) is one of the available methods. It requires a Markov representation of the queueing process, possibly with the aid of some supplementary variables. [t is based on power-series expansions of the state probabilities in terms of the load of a system for solving (recursively) the global balance equations satisfied by these probabilities. It is a flexible method which is applicable to a wide class of multi-queuelmulti-server models, with Markovian Arrival Processes (MAPs) and phase-type (PH) service time distributions. The PSA is

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