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72
Modelchecking algorithms for continuoustime Markov chains
 IEEE TRANSACTIONS ON SOFTWARE ENGINEERING
, 2003
"... Continuoustime Markov chains (CTMCs) have been widely used to determine system performance and dependability characteristics. Their analysis most often concerns the computation of steadystate and transientstate probabilities. This paper introduces a branching temporal logic for expressing realt ..."
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Cited by 235 (47 self)
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Continuoustime Markov chains (CTMCs) have been widely used to determine system performance and dependability characteristics. Their analysis most often concerns the computation of steadystate and transientstate probabilities. This paper introduces a branching temporal logic for expressing realtime probabilistic properties on CTMCs and presents approximate model checking algorithms for this logic. The logic, an extension of the continuous stochastic logic CSL of Aziz et al., contains a timebounded until operator to express probabilistic timing properties over paths as well as an operator to express steadystate probabilities. We show that the model checking problem for this logic reduces to a system of linear equations (for unbounded until and the steadystate operator) and a Volterra integral equation system (for timebounded until). We then show that the problem of modelchecking timebounded until properties can be reduced to the problem of computing transient state probabilities for CTMCs. This allows the verification of probabilistic timing properties by efficient techniques for transient analysis for CTMCs such as uniformization. Finally, we show that a variant of lumping equivalence (bisimulation), a wellknown notion for aggregating CTMCs, preserves the validity of all formulas in the logic.
Model checking continuoustime Markov chains by transient analysis
, 2000
"... . The verification of continuoustime Markov chains (CTMCs) against continuous stochastic logic (CSL) [3, 6], a stochastic branchingtime temporal logic, is considered. CSL facilitates among others the specification of steadystate properties and the specification of probabilistic timing properties o ..."
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Cited by 89 (20 self)
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. The verification of continuoustime Markov chains (CTMCs) against continuous stochastic logic (CSL) [3, 6], a stochastic branchingtime temporal logic, is considered. CSL facilitates among others the specification of steadystate properties and the specification of probabilistic timing properties of the form P# #p(#1 U I #2 ), for state formulas #1 and #2 , comparison operator ##, probability p, and real interval I. The main result of this paper is that model checking probabilistic timing properties can be reduced to the problem of computing transient state probabilities for CTMCs. This allows us to verify such properties by using e#cient techniques for transient analysis of CTMCs such as uniformisation. A second result is that a variant of ordinary lumping equivalence (i.e., bisimulation), a wellknown notion for aggregating CTMCs, preserves the validity of all CSLformulas. In 12th Annual Symposium on Computer Aided Verification, CAV 2000, c # SpringerVerlag 2000 Chicago,...
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 58 (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...
On combining functional verification and performance evaluation using CADP
 FME 2002: International Symposium of Formal Methods Europe, volume 2391 of LNCS
, 2002
"... Abstract. Considering functional correctness and performance evaluation in a common framework is desirable, both for scientific and economic reasons. In this paper, we describe how the Cadp toolbox, originally designed for verifying the functional correctness of Lotos specifications, can also be use ..."
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Cited by 39 (8 self)
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Abstract. Considering functional correctness and performance evaluation in a common framework is desirable, both for scientific and economic reasons. In this paper, we describe how the Cadp toolbox, originally designed for verifying the functional correctness of Lotos specifications, can also be used for performance evaluation. We illustrate the proposed approach by the performance study of the Scsi2 bus arbitration protocol. 1
Performance Evaluation of Componentbased Software Systems: A Survey
, 2010
"... Performance prediction and measurement approaches for componentbased software systems help software architects to evaluate their systems based on component performance specifications created by component developers. Integrating classical performance models such as queueing networks, stochastic Petr ..."
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Cited by 38 (10 self)
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Performance prediction and measurement approaches for componentbased software systems help software architects to evaluate their systems based on component performance specifications created by component developers. Integrating classical performance models such as queueing networks, stochastic Petri nets, or stochastic process algebras, these approaches additionally exploit benefits of componentbased software engineering, such as reuse and division of work. Although researchers have proposed many approaches into this direction during the last decade, none of them has attained widespread industrial use. On this behalf, we have conducted a comprehensive stateoftheart survey of more than 20 of these approaches assessing their applicability. We classified the approaches according to the expressiveness of their component performance modelling languages. Our survey helps practitioners to select an appropriate approach and scientists to identify interesting topics for future research.
PMaude: Rewritebased specification language for probabilistic object systems
 In Proc. 3rd Workshop on Quantitative Aspects of Programming Languages (QAPL’05
, 2005
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Decision Algorithms for Probabilistic Bisimulation
, 2002
"... We propose decision algorithms for bisimulation relations de ned on probabilistic automata, a model for concurrent nondeterministic systems with randomization. The algorithms decide both strong and weak bisimulation relations based on deterministic as well as randomized schedulers. These algori ..."
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Cited by 33 (3 self)
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We propose decision algorithms for bisimulation relations de ned on probabilistic automata, a model for concurrent nondeterministic systems with randomization. The algorithms decide both strong and weak bisimulation relations based on deterministic as well as randomized schedulers. These algorithms extend and complete other known algorithms for simpler relations and models. The algorithm we present for strong probabilistic bisimulation has polynomial time complexity, while the algorithm for weak probabilistic bisimulation is exponential; however we argue that the latter is feasible in practice.
Towards Model Checking Stochastic Process Algebra
, 2000
"... . Stochastic process algebra have been proven useful because they allow behaviouroriented performance and reliability modelling. As opposed to traditional performance modelling techniques, the behaviouroriented style supports composition and abstraction in a natural way. However, analysis of stocha ..."
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Cited by 26 (10 self)
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. Stochastic process algebra have been proven useful because they allow behaviouroriented performance and reliability modelling. As opposed to traditional performance modelling techniques, the behaviouroriented style supports composition and abstraction in a natural way. However, analysis of stochastic process algebra models is stateoriented, because standard numerical analysis is typically based on the calculation of (transient and steady) state probabilities. This shift of paradigms hampers the acceptance of the process algebraic approach by performance modellers. In this paper, we develop an entirely behaviouroriented analysis technique for stochastic process algebra. The key contribution is an actionbased temporal logic to describe behavioursofinterest, together with a model checking algorithm to derive the probability with which a stochastic process algebra model exhibits a given behaviourofinterest. 1 Introduction The analysis of systems with respect to their performance...
On the use of MTBDDs for performability analysis and verification of stochastic systems
"... This paper describes how to employ Multi Terminal Binary Decision Diagrams (MTBDD) for the construction and analysis of a general class of models that exhibit stochastic, probabilistic and nondeterministic behaviour. It is shown how the notorious problem of state space explosion can be circumvented ..."
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Cited by 24 (11 self)
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This paper describes how to employ Multi Terminal Binary Decision Diagrams (MTBDD) for the construction and analysis of a general class of models that exhibit stochastic, probabilistic and nondeterministic behaviour. It is shown how the notorious problem of state space explosion can be circumvented by compositionally constructing symbolic (i.e. MTBDDbased) representations of complex systems from smallscale components. We emphasise, however, that compactness of the representation can only be achieved if heuristics are applied with insight into the structure of the system under investigation. We report on our experiences concerning compact representation, performance analysis and verification of performability properties.
ModelChecking Large Structured Markov Chains
, 2002
"... This paper presents algorithms and experimental results for modelchecking continuous time Markov chains (CTMCs) based on a structured analysis approach. In this approach, a CTMC is represented as a term in Kronecker algebra that reects the component structure of the system model. Such representati ..."
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Cited by 24 (5 self)
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This paper presents algorithms and experimental results for modelchecking continuous time Markov chains (CTMCs) based on a structured analysis approach. In this approach, a CTMC is represented as a term in Kronecker algebra that reects the component structure of the system model. Such representations can be obtained in a natural way from various highlevel speci cation formalisms, such as stochastic extensions of Petri nets, process algebras or activity networks. Properties are expressed in Continuous Stochastic Logic (CSL) which includes means to express transient, steadystate and path performance measures. This paper describes novel modelchecking algorithms for CSL that fully exploit the compositional description of the CTMC. This yields an eective way to combat the statespace explosion problem and enables the modelchecking of fairly large Markov chains. Furthermore, we show how statespace aggregation (modulo bisimulation) and the elimination of vanishing states can be done in a componentwise manner. To demonstrate the applicability of the approach, and to assess the eciency of our algorithms, we analyze a stochastic Petri netmodel of a workstation cluster system and a simple queueing network.