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We present new algorithms for the solution of large structured Markov models whose infinitesimal generator can be expressed as a Kronecker expression of sparse matrices. We then compare them with the shuffle-based method commonly used in this context and show how our new algorithms can be advantageous in dealing with very sparse matrices and in supporting… (More)

The numerical analysis of various modeling formalisms (4, 10, 141 profits from a structured representation for the generator matrix Q of the underlying continuous time Markov chain, where Q is described by a sum of tensor (kronecker) products of much smaller matrices. In this paper we describe such a representation for the class of superposed generalized… (More)

This paper introduces a new approach for the construction of performance models of complex systems integrating software and hardware. Software components are speciied using hierarchical coloured GSPNs which extend the well established coloured GSPNs. Hardware components are composed of basic queues taken from queueing networks. Integration of queues into… (More)

The paper introduces a new approach to define process algebras with quantified transitions. A mathematical model is introduced which allows the definition of various classes of process algebras including the well known models of untimed, probabilistic and stochastic process algebras. For this general mathematical model a bisimulation equivalence is defined… (More)

- William J Knottenbelt, Prof P S Kritzinger, Peter Kemper, Farooq Khan, Djamal Zeghlache

This dissertation concerns analytical methods for assessing the performance of concurrent systems. More speciically, it focuses on the eecient generation and solution of large Markov chains which are derived from models of unrestricted timed transition systems. Timed transition systems may be described using several high-level formalisms, including… (More)

Markovian arrival processes are a powerful class of stochastic processes to represent stochastic workloads that include autocorrelation in performance or dependability modeling. However, fitting the parameters of a Markovian arrival process to given measurement data is non-trivial and most known methods focus on a single class case, where all events are of… (More)

Möbius is a multi-paradigm multi-solution framework to describe and analyze stochastic models of discrete-event dynamic systems. Möbius is widely used in academia and industry for the performance and dependability assessment of technical systems. It comes with a design of experiments as well as automated support for distributing a series of simulation… (More)

This paper presents a toolbox for the construction of modular tools for functional and quantitative (performance) analysis of discrete event dynamic systems (DEDS). The intention is to simplify the usage of appropriate analysis algorithms, thus supporting the development of appropriate tools. We describe concepts and contents of the toolbox together with an… (More)

This article describes a new version of the QPN-Tool now supporting speciication and analysis of hierarchically combined Queue-ing Petri nets (HQPNs). HQPNs are an extension of QPNs allowing the reenement of places by QPN subnets and/or queues. HQPNs can be analysed with respect to qualitative and quantitative aspects. Quantitative analysis is based on… (More)