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DFG-Project: Markovian and Rational Arrival and Service Processes for Performance and Reliability Analysis (2008-2014)

Stochastic models are widely used for the analysis of performance, security and reliability of systems. In these models time consumption has to be modelled by probability distributions or stochastic processes. In most approaches used so far time consumption is described by probability distributions being independent and identically distributed. However, experience shows that many parameters of a model are highly correlated and that this correlation is observable over a long period of time. Ignoring correlations can lead to significant errors in performance measures as illustrated by various examples.

Therefore stochastic models need to be found that are capable of capturing correlations. Furthermore the models have to be parameterizable such that they reflect the characteristics of a measured trace accurately and still result in an analysable model. An attractive model class is Markovian Arrival Processes (MAPs) which are considered in the first project term (2008 - 2011).

For specific correlation structures the use of MAPs is limited due to state explosion. The second project term (2011 - 2014) considers the investigation of matrix exponential distributions and rational arrival processes (RAPs), which are an extension of MAPs. Although the theory on RAPs is not as elaborated as the one on MAPs, recent results indicate that methods for Markovian processes might also be applicable for RAPs.



Demands on models for performance and reliability analysis are growing constantly, since due to the increasing complexity, experiments with real systems are either not realisable or would require an unacceptable effort. Moreover the demands on the quality of the results are rising simultaneously, so that real processes and the associated correlations have to be modelled sufficiently accurate.

Existing approaches for fitting the parameters of a MAP to real traces still have some shortcomings impeding their use in practical applications. The key activities of this project aim at eliminating or at least reducing these shortcomings with the objective to make parameter fitting of MAPs similarly efficient and robust as it is possible with methods developed in the recent years for the fitting of phase type distributions. The second project term is devoted to the extension of parameter fitting methods for MAPs to RAPs. Further information on the key aspects of the project can be found by selecting the menu item Objectives.