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## A Markov Chain Model Checker (2000)

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Citations: | 58 - 22 self |

### Citations

1406 | Depth-first search and linear graph algorithms - TARJAN - 1972 |

1388 | Automatic Verification of Finite-State Concurrent Systems Using Temporal Logic Specifications.
- Clarke, Emerson, et al.
- 1986
(Show Context)
Citation Context ... Pp(✸t Φ) = Pp(trueUt Φ) and Pp(✷Φ) = P1−p(✸¬Φ). Semantics of CSL. Let M = (S,R, L) with proposition labels in AP. The semantics for atomic propositions, negation, and conjunction is standard =-=[11]-=-. Let Sat(Φ) = { s ∈ S | s |= Φ }. The steady-state operator is defined by: s |= Sp(Φ) iff πSat(Φ)(s) p where πS′(s) denotes the steady-state probability for S′ ⊆ S when starting in s, πS′(s) = l... |

757 | A Compositional Approach to Performance Modelling
- Hillston
- 1994
(Show Context)
Citation Context ...ticular, CTMCs are the underlying semantic model of major high-level performance modelling formalisms such as stochastic Petri nets [1], stochastic automata networks [26], stochastic process algebras =-=[24,21]-=-, Markovian queueing networks [12], and various extensions thereof. Model checking of CTMCs has been discussed in [8], introducing a (branching) temporal logic called continuous-time stochastic logic ... |

752 |
Introduction to the numerical solution of Markov chains
- Stewart
- 1994
(Show Context)
Citation Context ...r until- and steady-state formulas), and solutions of systems of Volterra integral equations (for time-bounded until). Linear systems of equations are iteratively solved by standard numerical methods =-=[27]-=-. Systems of integral equations are iteratively solved by piecewise integration after discretization. As a side result, E MC2 is also capable to model check DTMCs against properties expressed in PCT... |

370 | A Logic for Reasoning about Time and Reliability
- Hansson, Jonsson
- 1994
(Show Context)
Citation Context ...f 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 continuous-time Markov chains, the Erlangen–Twente Markov Chain Checker (E MC2), where p... |

311 |
Automatic verification of probabilistic concurrent systems.
- Vardi
- 1985
(Show Context)
Citation Context ...he resulting model boils down to a finitestate discrete-time Markov chain (DTMC). For these models, qualitative and quantitative model checking algorithms have been investigated extensively, see e.g. =-=[3,5,6,10,13,17,29]-=-. In a qualitative setting it is checked whether a property holds with probability 0 or 1; in a quantitative setting it is verified whether the probability for a certain property meets a given lower- ... |

156 | Approximate Symbolic Model Checking of ContinuousTime Markov Chains
- Baier, Katoen, et al.
- 1999
(Show Context)
Citation Context ...n 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 continuous-time Markov chains, the Erlangen–Twente Markov Chain Checker (E MC2), where properties are expressed in appropriate... |

128 | Stochastic automata network for modeling parallel systems.
- Plateau, Atif
- 1991
(Show Context)
Citation Context ...TMCs, as opposed to DTMCs.1 In particular, CTMCs are the underlying semantic model of major high-level performance modelling formalisms such as stochastic Petri nets [1], stochastic automata networks =-=[26]-=-, stochastic process algebras [24,21], Markovian queueing networks [12], and various extensions thereof. Model checking of CTMCs has been discussed in [8], introducing a (branching) temporal logic cal... |

125 | Verifying continuous time Markov chains.
- Aziz, Sanwal, et al.
- 1996
(Show Context)
Citation Context ...n 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 continuous-time Markov chains, the Erlangen–Twente Markov Chain Checker (E MC2), where properties are expressed in appropriate... |

102 | It Usually Works: The Temporal Logic of Stochastic Systems
- Aziz, Singhal, et al.
- 1995
(Show Context)
Citation Context ...he resulting model boils down to a finitestate discrete-time Markov chain (DTMC). For these models, qualitative and quantitative model checking algorithms have been investigated extensively, see e.g. =-=[3,5,6,10,13,17,29]-=-. In a qualitative setting it is checked whether a property holds with probability 0 or 1; in a quantitative setting it is verified whether the probability for a certain property meets a given lower- ... |

97 | Symbolic model checking for probabilistic processes
- Baier, Clarke, et al.
- 1997
(Show Context)
Citation Context ...f 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 continuous-time Markov chains, the Erlangen–Twente Markov Chain Checker (E MC2), where p... |

91 | Model checking continuous-time Markov chains by transient analysis.
- Baier, Haverkort, et al.
- 2000
(Show Context)
Citation Context ...r experiments with E MC2 have shown that the checking of time-bounded until-properties requires an efficiency improvement. We are currently considering alternative ways to model check this operator =-=[7]-=-. A Markov Chain Model Checker 361 Acknowledgement The authors thank Lennard Kerber (Erlangen) for his contribution to assessing the accuracy of the tool output and Christel Baier (Bonn) for her valua... |

71 | Process algebra for performance evaluation
- Hermanns, Herzog, et al.
- 2002
(Show Context)
Citation Context ...ticular, CTMCs are the underlying semantic model of major high-level performance modelling formalisms such as stochastic Petri nets [1], stochastic automata networks [26], stochastic process algebras =-=[24,21]-=-, Markovian queueing networks [12], and various extensions thereof. Model checking of CTMCs has been discussed in [8], introducing a (branching) temporal logic called continuous-time stochastic logic ... |

69 |
Performance of Computer Communication Systems. A Model-Based Approach.
- Haverkort
- 1999
(Show Context)
Citation Context ...in practice. The major advantage of these methods is that the involved matrices do not change during the computation (i.e. fill-in is avoided), and hence the buildup of rounding errors is nonexistent =-=[19,27]-=-. In addition, direct methods are known 2 In [8] the above linear system of equations is defined in a slightly different way, by characterizing the steady-state probabilities in terms of the embedded ... |

68 | On algorithmic verification methods for probabilistic systems
- Baier
- 1998
(Show Context)
Citation Context ...he resulting model boils down to a finitestate discrete-time Markov chain (DTMC). For these models, qualitative and quantitative model checking algorithms have been investigated extensively, see e.g. =-=[3,5,6,10,13,17,29]-=-. In a qualitative setting it is checked whether a property holds with probability 0 or 1; in a quantitative setting it is verified whether the probability for a certain property meets a given lower- ... |

61 |
Stochastic Petri net models of polling systems
- Ibe, Trivedi
- 1990
(Show Context)
Citation Context ...lmost 1000 states. 4.2 A Cyclic Server Polling System In this section, we consider a cyclic server polling system consisting of d stations and a server, modelled as a GSPN.4 The example is taken from =-=[25]-=-, where a poll1 poll2 serve1 serve2 idle2 busy2 busy1idle1 λ2 λ1 µ1 γ1 µ2 γ2 skip1 skip2 detailed explanation can be found. For d = 2, i.e. a two-station polling system, the GSPN model is depicted on ... |

60 | Multi terminal binary decision diagrams to represent and analyse continuous time Markov chains
- Hermanns, Kayser, et al.
- 1999
(Show Context)
Citation Context ...s by means of the Gauß-Seidel method. All recorded execution times are wall clock times. 4.1 A Simple Tandem Queue As a first, simple example we consider a queueing network (with blocking) taken from =-=[23]-=-. It consists of a M/Cox2/1-queue sequentially composed with a M/M/1queue, see Fig. 3. Due to space constraints, we have to refer to [12] for a thorough introduction to networks of queues. Both queuei... |

53 | Compositional performance modelling with TIPPTool
- Hermanns, Herzog, et al.
- 1998
(Show Context)
Citation Context ...ism at hand and the model checker E MC2. Currently, E MC2 accepts CTMCs represented in the tra-format A Markov Chain Model Checker 351 as generated by the stochastic process algebra tool TIPPtool =-=[22]-=-, but the tool is designed in such a way that it enables a filter plug-in functionality to bridge to various other input formats. This is realized via Java’s dynamic class loading capability. 3.1 The ... |

44 | Faster and symbolic CTMC model checking - Katoen, Kwiatkowska, et al. |

39 |
Verifying temporal properties of finite-state probabilistic programs
- Courcoubetis, Yannakakis
- 1988
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Citation Context |

37 |
A Class of Generalised Stochastic Petri Nets for the Performance Evaluation of Multiprocessor Systems
- Marsan, Conte, et al.
- 1984
(Show Context)
Citation Context ... Markov chain modelling involves CTMCs, as opposed to DTMCs.1 In particular, CTMCs are the underlying semantic model of major high-level performance modelling formalisms such as stochastic Petri nets =-=[1]-=-, stochastic automata networks [26], stochastic process algebras [24,21], Markovian queueing networks [12], and various extensions thereof. Model checking of CTMCs has been discussed in [8], introduci... |

34 | Symbolic model checking of probabilistic processes using mtbdds and the Kronecker representation - Alfaro, Kwiatkowska, et al. - 2000 |

27 |
Queuing Networks - Exact Computational Algorithms: A Unified Theory Based on Decomposition and Aggregation
- Conway, Georganas
- 1989
(Show Context)
Citation Context ...antic model of major high-level performance modelling formalisms such as stochastic Petri nets [1], stochastic automata networks [26], stochastic process algebras [24,21], Markovian queueing networks =-=[12]-=-, and various extensions thereof. Model checking of CTMCs has been discussed in [8], introducing a (branching) temporal logic called continuous-time stochastic logic (CSL) to express properties over C... |

27 | An efficient disk-based tool for solving very large Markov models
- Deavours, Sanders
- 1997
(Show Context)
Citation Context ...DTMC. 352 Holger Hermanns et al. to be only practical for state spaces of up to a few hundred states, while iterative methods have successfully been applied for much larger systems (up to 107 states) =-=[14]-=-. For these reasons, E MC2 supports all of the above mentioned iterative methods to solve (1). Probabilistic path-formulas. Calculating the probabilities Prob(s, ϕ) proceeds as in the discrete-time ... |

26 | Towards Model Checking Stochastic Process Algebra - Hermanns, Katoen, et al. - 2000 |

23 | On the verification of qualitative properties of probabilistic processes under fairness constraints
- Baier, Kwiatkowska
- 1998
(Show Context)
Citation Context ...probability 0. In a similar way, we compute the set of states for which the probability of these properties will be 1. This is done by computing the set of states Sat(∀(Φ1 U Φ2)) (up to fairness, cf. =-=[9]-=-) in the usual iterative way [17]. As a result, the actual computation, being it the solution of the linear system of equations in case of an unbounded until, or the solution of the system of Volterra... |

21 | ProbVerus: Probabilistic symbolic model checking - Hartonas-Garmhausen, Campos, et al. - 1999 |

17 | Performability Modeling Tools and Techniques.
- Haverkort, Marie, et al.
- 2001
(Show Context)
Citation Context ...be linked to a wide range of existing high-level modelling tools based on, for instance, stochastic process algebras, stochastic Petri nets, or queueing networks. A whole variety of such tools exists =-=[20]-=-, most of them using dedicated formats to store the rate matrix R that is obtained from the high-level specification. The matrix R, together with the proposition-labelling function L, constitutes the ... |

7 | Performability modelling tools and techniques. Performance evaluation - Haverkort, Niemegeers - 1996 |

7 | J.-P.: On the use of model checking techniques for quantitative dependability evaluation - Haverkort, Hermanns, et al. - 2000 |

6 | An ecient disk-based tool for solving very large Markov models - Deavours, Sanders - 1997 |

6 | Implementing a Model Checker for Performability Behaviour - Hermanns, Katoen, et al. - 2001 |

5 | The timing and probability workbench: a tool for analysing timed processes
- Fredlund
- 1994
(Show Context)
Citation Context ... of a cyclic server system and of a tandem queueing network. Other model checkers for probabilistic systems are the DTMC-model checkers ProbVerus [18] and TPWB (the Timing and Probability Work-Bench) =-=[15]-=-, 1 DTMCs are mostly applied in strictly synchronous scenarios, while CTMCs have shown to fit well to (interleaving) asynchronous scenarios. A Markov Chain Model Checker 349 and the recent symbolic mo... |

5 |
Markovian analysis of large finite-state machines
- Hachtel, Macii, et al.
- 1996
(Show Context)
Citation Context ...lisms for CTMCs and model checking. E MC2 is a prototype, in particular for the moment it does not use symbolic, i.e. (MT)BDD-based, data structures. Although our own experience (and of others, cf. =-=[16]-=-) has shown that very compact encodings of Markov chains are possible with MTBDDs and similar data structures [23], and symbolic model checking algorithms for CTMCs do exist [8], we favor a separation... |

3 | Performance and reliability model checking and model construction - Hermanns - 2000 |

3 |
Reasoning about safety and liveness properties for probabilistic systems
- Christoff, Christoff
- 1992
(Show Context)
Citation Context |

2 | Reasoning about safety and liveness properties for probabilistic systems - Christo, Christo - 1992 |

2 | DaNAMiCS - a Petri Net Editor. http://www.cs.uct.ac.za/Research/DNA/DaNAMiCS - Changuion, Davies, et al. |