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A Markov Chain Model Checker
, 2000
"... . Markov chains are widely used in the context of performance and reliability evaluation of systems of various nature. Model checking of such chains with respect to a given (branching) temporal logic formula has been proposed for both the discrete [17, 6] and the continuous time setting [4, 8]. ..."
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Cited by 57 (22 self)
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. Markov chains are widely used in the context of performance and reliability evaluation of systems of various nature. Model checking of such chains with respect to a given (branching) temporal logic formula has been proposed for both the discrete [17, 6] and the continuous time setting [4, 8]. In this paper, we describe a prototype model checker for discrete and continuoustime Markov chains, the ErlangenTwente Markov Chain Checker (E MC 2 ), where properties are expressed in appropriate extensions of CTL. We illustrate the general benefits of this approach and discuss the structure of the tool. Furthermore we report on first successful applications of the tool to nontrivial examples, highlighting lessons learned during development and application of E T MC 2 . 1 Introduction Markov chains are widely used as simple yet adequate models in diverse areas, ranging from mathematics and computer science to other disciplines such as operations research, industrial engine...
Automated performance and dependability evaluation using model checking
 In Performance Evaluation of Complex Systems: Techniques and Tools, Performance 2002, Tutorial Lectures
, 2002
"... Abstract. Markov chains (and their extensions with rewards) have been widely used to determine performance, dependability and performability characteristics of computer communication systems, such as throughput, delay, mean time to failure, or the probability to accumulate at least a certain amount ..."
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Cited by 21 (2 self)
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Abstract. Markov chains (and their extensions with rewards) have been widely used to determine performance, dependability and performability characteristics of computer communication systems, such as throughput, delay, mean time to failure, or the probability to accumulate at least a certain amount of reward in a given time. Due to the rapidly increasing size and complexity of systems, Markov chains and Markov reward models are difficult and cumbersome to specify by hand at the statespace level. Therefore, various specification formalisms, such as stochastic Petri nets and stochastic process algebras, have been developed to facilitate the specification of these models at a higher level of abstraction. Uptill now, however, the specification of the measureofinterest is often done in an informal and relatively unstructured way. Furthermore, some measuresofinterest can not be expressed conveniently at all. In this tutorial paper, we present a logicbased specification technique to specify performance, dependability and performability measuresofinterest and show how for a given finite Markov chain (or Markov reward model) such measures can be evaluated in a fully automated way. Particular emphasis will be given to socalled pathbased measures and hierarchicallyspecified measures. For this purpose, we extend socalled model checking techniques to reason about discrete and continuoustime Markov chains and their rewards. We also report on the use of techniques such as (compositional) model reduction and measuredriven statespace generation to combat the infamous state space explosion problem. 1
Performance Trees: A New Approach to Quantitative Performance Specification
 in Proc. 14th IEEE/ACM Intl. Symposium on Modeling, Analysis and Simulation of Computer and Telecommunications Systems (MASCOTS 2006
, 2006
"... We introduce Performance Trees (PTs), a novel representation formalism for the specification of modelbased performance queries. Traditionally, stochastic logics have been the prevalent means of performance requirement expression; however, in practice, their use amongst system designers is limited o ..."
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Cited by 19 (11 self)
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We introduce Performance Trees (PTs), a novel representation formalism for the specification of modelbased performance queries. Traditionally, stochastic logics have been the prevalent means of performance requirement expression; however, in practice, their use amongst system designers is limited on account of their inherent complexity and restricted expressive power. PTs are a more accessible alternative, in which performance queries are represented by hierarchical tree structures. This allows for the convenient visual composition of complex performance questions, and enables not only the verification of stochastic requirements, but also the direct extraction of performance measures. In addition, PTs offer a superset of the expressiveness of Continuous Stochastic Logic (CSL) since all CSL formulae can be translated into PT form. Performance Trees can be used to represent passage time, transient, steadystate and higher order queries of varying levels of sophistication. While they are conceptually independent of the underlying stochastic modelling formalism, in many cases the tree operators we use are already backed up by good algorithmic and tool support for both stochastic verification and performance measure extraction. We do not therefore perceive major barriers to the integration of PTs into existing stochastic model checking tools. Indeed, we illustrate how semiMarkov passage time computation algorithms, based on numerical Laplace transform inversion, can be directly applied to the resolution of a case study PT query. 1
Model checking action and statelabelled Markov chains
 DSN’04, Proceedings of International Conference on Dependable Systems and Networks
, 2004
"... In this paper we introduce the logic asCSL, an extension of continuous stochastic logic (CSL), which provides powerful means to characterise execution paths of action and statelabelled Markov chains. In asCSL, path properties are characterised by regular expressions over actions and stateformulas ..."
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Cited by 15 (2 self)
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In this paper we introduce the logic asCSL, an extension of continuous stochastic logic (CSL), which provides powerful means to characterise execution paths of action and statelabelled Markov chains. In asCSL, path properties are characterised by regular expressions over actions and stateformulas. Thus, the executability of a path not only depends on the available actions but also on the validity of certain state formulas in intermediate states. Our main result is that the model checking problem for asCSL can be reduced to CSL model checking on a modified Markov chain, which is obtained through a product automaton construction. We provide a case study of a scalable cellular phone system which shows how the logic asCSL and the model checking procedure can be applied in practice. 1.
Performance Trees: Expressiveness and Quantitative Semantics
"... Performance Trees are a recentlyproposed mechanism for the specification of performance properties and measures. They represent an attractive alternative to stochastic logics, since they support traditional stochastic model checking queries, while also allowing for the direct extraction of a wide ..."
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Cited by 11 (8 self)
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Performance Trees are a recentlyproposed mechanism for the specification of performance properties and measures. They represent an attractive alternative to stochastic logics, since they support traditional stochastic model checking queries, while also allowing for the direct extraction of a wide range of quantitative measures. In this paper we illustrate differences in expressiveness between Performance Trees and Continuous Stochastic Logic (CSL), and present quantitative semantics showing the mathematical basis underlying Performance Tree operators. As a running example, we demonstrate performance query specification with Performance Trees on a stochastic Petri net model of a healthcare system.
Advances in Model Representations
 Proc. PAPM/PROBMIV 2001, Available as Volume 2165 of LNCS (2001
, 2001
"... We review highlevel specification formalisms for Markovian performability models, thereby emphasising the role of structuring concepts as realised par excellence by stochastic process algebras. Symbolic representations based on decision diagrams are presented, and it is shown that they quite id ..."
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Cited by 9 (4 self)
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We review highlevel specification formalisms for Markovian performability models, thereby emphasising the role of structuring concepts as realised par excellence by stochastic process algebras. Symbolic representations based on decision diagrams are presented, and it is shown that they quite ideally support compositional model construction and analysis.
Performance specification and evaluation with Unified Stochastic Probes and fluid analysis
"... Abstract—Rapid and accessible performance evaluation of complex software systems requires two critical features: the ability to specify useful performance metrics easily and the capability to analyse massivelydistributed architectures, without recourse to large compute clusters. We present the unif ..."
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Cited by 6 (2 self)
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Abstract—Rapid and accessible performance evaluation of complex software systems requires two critical features: the ability to specify useful performance metrics easily and the capability to analyse massivelydistributed architectures, without recourse to large compute clusters. We present the unified stochastic probe, a performance specification mechanism for process algebra models that combines many existing ideas: state and actionbased activation, locationbased specification, manyprobe specification and immediate signalling. These features, between them, allow the precise and compositional construction of complex performance measurements. The paper shows how a subset of the stochastic probe language can be used to specify common responsetime measures in massive process algebra models. The second contribution of the paper is to show how these responsetime measures can be analysed using socalled fluid techniques to produce rapid results. In doing this, we extend the fluid approach to incorporate immediate activities and a new type of responsetime measure. Finally, we calculate various responsetime measurements on a complex distributed wireless network of O(10 129) states in size. Index Terms—Performance modelling, performance evaluation tools, stochastic process algebra, measurement probes, fluid approximation, passagetime analysis I.
Performance Evaluation With Temporal Rewards
 Journal of Performance Evaluation
, 2002
"... Today many formalisms exist for specifying complex Markov chains. In contrast, formalisms for specifying rewards, enabling the analysis of longrun average performance properties, have remained quite primitive. Basically, they only support the analysis of relatively simple performance metrics that c ..."
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Cited by 6 (4 self)
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Today many formalisms exist for specifying complex Markov chains. In contrast, formalisms for specifying rewards, enabling the analysis of longrun average performance properties, have remained quite primitive. Basically, they only support the analysis of relatively simple performance metrics that can be expressed as longrun averages of atomic rewards, i.e. rewards that are deductible directly from the individual states of the initial Markov chain specification. To deal with complex performance metrics that are dependent on the accumulation of atomic rewards over sequences of states, the initial specification has to be extended explicitly to provide the required state information.
Implementing a Model Checker for Performability Behaviour
, 2001
"... We describe a novel model checking algorithm for analysing the behaviour of stochastic systems with respect to their performability. Systems are modelled as actionlabelled CTMCs, and the properties to be veri#ed are speci#ed with the help of the actionbased temporal logic aCSL. ..."
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Cited by 6 (3 self)
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We describe a novel model checking algorithm for analysing the behaviour of stochastic systems with respect to their performability. Systems are modelled as actionlabelled CTMCs, and the properties to be veri#ed are speci#ed with the help of the actionbased temporal logic aCSL.