Analysis Methods for Non-Markovian Models


Project Description

Traditional approaches to solve non-Markovian models use phase-type expansions, apply the method of supplementary variables or construct an embedded Markov chain. All three approaches have also been investigated in the context of queuing networks and stochastic Petri nets. The phase-type expansion approach suffers from the enlargement of the state space, whereas the method of supplementary variables and the embedded Markov chain construction require basically that non-exponentially timed activities are not concurrent. If they are concurrent this will result in multidimensional differential equations that are hard to solve. To avoid these problems more efficient techniques for the performance evaluation of computer networks like web servers or networks of embedded systems have to be developed. In such systems activity durations with large variances (file transfers) as well as deterministic durations (security aspects) arise.

We have created two new approaches to approximately evaluate the performance models of these systems; the first one is based on the method of supplementary variables and the second one deals with phase-type expansions. We are currently enhancing these approaches and it is planned to combine them for the solution of large non-Markovian models.
In cooperation with department 4 (Distributed Systems and Operating Systems) the tool WinPEPSY for performance evaluation and prediction of queueing systems was developed. It contains well known analysis methods for open and closed product form and non-product form networks (mean value analysis, Jackson-method, decomposition methods, simulation) and the new state-based analysis methods are integrated.
In a cooperation with the Telecommunications Laboratory, Communications, Electronics and Information Engineering Division of the National Technical University of Athens simulation models for embedded network processors have been developed. The goal is to enhance the above mentioned methods, so that even performance measures for these large models can be derived.

Project Period

    2001-11-01 – 2004-10-30

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