Stochastic models are used to analyze performance, safety and reliability of systems, especially computer systems. In these models, real time consumptions have to be modeled by stochastic distributions or stochastic processes. Approaches used so far are based on the description of the required times by distributions, so that the individual times are independently and identically distributed. In practice, however, it is shown that many quantities are strongly correlated and this correlation can also be observed over long periods of time. Examples can be used to demonstrate that neglecting the correlation can lead to significant distortion of the results.
Consequently, stochastic models have to be found that can reproduce correlations. The models must be parameterizable in such a way that they reproduce measured event streams sufficiently accurately and the resulting system models remain analyzable. Markovian arrival processes (MAPs), which were investigated in the first project phase (2008 - 2011), are particularly suitable as models.
However, it has also been shown that Markov models reach their limits when the density function or correlation exhibits certain structures that can only be represented with very many states in the Markov process. Therefore, in the second project phase (2011 - 2014), the considered model class will also be extended to matrix exponential distributions and the associated rational processes (RAPs). For these model classes no comprehensive theory exists yet, as for Markov processes, but recent results give reason to hope that many methods known from Markov processes can be transferred to the more general models.
The demands on models for performance and reliability analysis are constantly increasing, as the increasing complexity of real systems makes experiments on the system infeasible or would require an unreasonable effort. At the same time, however, the demands on the quality of results to be achieved are also increasing, so that real processes and thus also correlations must be modeled with sufficient accuracy.
The approaches available so far for adapting the parameters of a MAP to real traces still have some deficits for practical use. These deficits shall be eliminated or at least reduced within the scope of this project. The goal is to perform parameter fitting of MAPs as efficiently and robustly as is possible with the methods for phase distributions developed in recent years.
The second phase of the project focuses on extending the developed methods for parameter fitting of MAPs to RAPs in order to extend the class of models that can be analyzed with numerical methods beyond Markov processes without having to introduce fundamentally new analysis techniques.
For further information on the main focus of the project, please refer to the menu item Objectives.