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## Automated performance and dependability evaluation using model checking (2002)

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### Other Repositories/Bibliography

Venue: | In Performance Evaluation of Complex Systems: Techniques and Tools, Performance 2002, Tutorial Lectures |

Citations: | 21 - 2 self |

### Citations

3251 | Model checking
- Clarke, Grumberg, et al.
- 1999
(Show Context)
Citation Context ... repetitive attempt to carry out a transaction be eventually granted? Prominent formal verification techniques are theorem proving and model checking, as well as (but to a less formal extent) testing =-=[17,50,55,8]-=-. Important to note at this point is that for an ever-increasing class of systems, their “formal correctness” cannot be separated anymore from their “quantitative correctness”, e.g., in real-time syst... |

3087 |
An Introduction to Probability Theory and Its Applications,
- FELLER
- 1968
(Show Context)
Citation Context ...d continuous-time Markov chains with finite state space. The presentation is focused on the concepts needed for the understanding of the rest of this paper; for a more elaborate treatment we refer to =-=[21,43,47,48,59]-=-. We slightly depart from the standard notations by representing a Markov chain as an ordinary finite transition system where the edges are equipped with probabilistic information, and where states ar... |

2704 | Statecharts: A visual formalism for complex systems.
- Harel
- 1987
(Show Context)
Citation Context ...s model the evolution of the system while moving from one state to another. These automata are usually generated from a high-level description language such as Petri nets, Promela [41] or Statecharts =-=[27]-=-. At this point, notice the similarities with the models used for performance and dependability evaluation. ComputationalTree Logic. Required system properties can be specified in an extension of prop... |

1516 | The model checker SPIN.
- Holzmann
- 1997
(Show Context)
Citation Context ...ta, where transitions model the evolution of the system while moving from one state to another. These automata are usually generated from a high-level description language such as Petri nets, Promela =-=[41]-=- or Statecharts [27]. At this point, notice the similarities with the models used for performance and dependability evaluation. ComputationalTree Logic. Required system properties can be specified in ... |

1491 |
Symbolic Model Checking
- McMillan
- 1993
(Show Context)
Citation Context ... repetitive attempt to carry out a transaction be eventually granted? Prominent formal verification techniques are theorem proving and model checking, as well as (but to a less formal extent) testing =-=[17,50,55,8]-=-. Important to note at this point is that for an ever-increasing class of systems, their “formal correctness” cannot be separated anymore from their “quantitative correctness”, e.g., in real-time syst... |

1388 | Automatic Verification of Finite-State Concurrent Systems Using Temporal Logic Specifications.
- Clarke, Emerson, et al.
- 1986
(Show Context)
Citation Context ...ems specified as finite state automata (note that we can view a CTMC as a special type of such an automaton). Not only are suitable means available to express state-based properties, a logic like CTL =-=[16]-=- (Computational Tree Logic; see below) also allows one to express properties over state sequences. Such capabilities would also be welcome in specifying performance and dependability measures. To fulf... |

1125 |
Finite Markov Chains,
- Kemeny, Snell
- 1976
(Show Context)
Citation Context ...d continuous-time Markov chains with finite state space. The presentation is focused on the concepts needed for the understanding of the rest of this paper; for a more elaborate treatment we refer to =-=[21,43,47,48,59]-=-. We slightly depart from the standard notations by representing a Markov chain as an ordinary finite transition system where the edges are equipped with probabilistic information, and where states ar... |

757 | A Compositional Approach to Performance Modelling
- Hillston
- 1994
(Show Context)
Citation Context ...s as subsets.Automated Performance and Dependability Evaluation 285 Bisimulation (lumping) equivalence. Lumpability enables the aggregation of CTMCs and MRMs without affecting performance properties =-=[47,10,40,35]-=-. We adapt the standard notion slightly in order to deal with MRMs with statelabellings. We only sketch the concepts here, and refer to the papers [4,5] for more details. For some MRM M =(S, R,L,ρ) we... |

752 |
Introduction to the numerical solution of Markov chains
- Stewart
- 1994
(Show Context)
Citation Context ...d continuous-time Markov chains with finite state space. The presentation is focused on the concepts needed for the understanding of the rest of this paper; for a more elaborate treatment we refer to =-=[21,43,47,48,59]-=-. We slightly depart from the standard notations by representing a Markov chain as an ordinary finite transition system where the edges are equipped with probabilistic information, and where states ar... |

282 |
Modeling and analysis of stochastic systems.
- Kulkarni
- 1995
(Show Context)
Citation Context |

235 | Model-checking algorithms for continuous-time markov chains.
- Baier, Haverkort, et al.
- 2003
(Show Context)
Citation Context ...m, we have introduced the so-called continuous stochastic logic (CSL) that provides us ample means to specify state- as well as path-based performance measures for CTMCs in a compact and flexible way =-=[1,2,3,4,5]-=-. Moreover, due to the formal syntax and semantics of CSL, we can exploit the structure of CSL-specified measures in the subsequent evaluation process, such that typically the size of the underlying M... |

197 | SPNP: Stochastic Petri Net Package,”
- Ciardo, Muppala, et al.
- 1989
(Show Context)
Citation Context ...astic activity networks. With appropriate tools supporting these specification methods, such as, for instance, provided by TIPPtool [36], the PEPA workbench [23], GreatSPN [13], UltraSAN [56] or SPNP =-=[14]-=-, it is relatively comfortable to specify performance models of which the associated CTMCs have millions of states. In combination with state-of-the-art numerical means to solve the resulting linear s... |

193 | On evaluating the performability of degradable computing systems,”
- Meyer
- 1980
(Show Context)
Citation Context ...asures over CTMCs extended with a reward structure (Markov reward models) [4]. We showed that well-known performability measures, most notably also the performability distribution introduced by Meyer =-=[51, 52,53]-=-, can be specified using CSRL. However, CSRL allows for the specification of new measures that have not yet been addressed in the performability literature. For instance, when rewards are interpreted ... |

173 | The PEPA Workbench: A Tool to Support a Process Algebra-Based Approach to Performance Modelling
- Gilmore, Hillston
- 1994
(Show Context)
Citation Context ...ets, stochastic process algebras, and stochastic activity networks. With appropriate tools supporting these specification methods, such as, for instance, provided by TIPPtool [36], the PEPA workbench =-=[23]-=-, GreatSPN [13], UltraSAN [56] or SPNP [14], it is relatively comfortable to specify performance models of which the associated CTMCs have millions of states. In combination with state-of-the-art nume... |

156 | Approximate Symbolic Model Checking of ContinuousTime Markov Chains
- Baier, Katoen, et al.
- 1999
(Show Context)
Citation Context ... in the context of model checking performability properties expressible with CSRL to make the analysis effective. Since the first paper on algorithms for CSL model checking has been published in 1999 =-=[2]-=- the approach has been implemented in (at least) three research tools, namely the ETMCC model checker [37], the model checker Prism, and the APNN toolbox [11]. While ETMCC is a dedicated CSL model che... |

116 | Exact and ordinary lumpability in finite Markov chains.
- Buchholz
- 1994
(Show Context)
Citation Context ...eneral measures can be described. An example is the probability of reaching a certain set of states provided that all paths to these states obey certain properties. For instance, P�0.01((up3 ∨ up2) U =-=[0,10]-=- down) is valid for those states where the probability of the system going down within 10 time-units after having continuously operated with at least 2 processors is at most 0.01. Nested measures. By ... |

113 |
The randomization technique as a modeling tool and solution procedure for transient Markov processes.
- Gross, Miller
- 1984
(Show Context)
Citation Context ...abilities are then computed from a system of linear differential equations: π ′ (s, t) =π(s, t) · Q, which can be solved by standard numerical methods or by specialised methods such as uniformisation =-=[45,26,25]-=-. With uniformisation, the transient probabilities of a CTMC are computed via a uniformised DTMC which characterises the CTMC at discrete state transition epochs. Steady-state probabilities are define... |

108 | Computer-Aided Verification,
- Clarke, Kurshan
- 1996
(Show Context)
Citation Context ... control systems (traffic collision avoidance and alert system270 C. Baier et al. TCAS-II, storm surge barrier), and communication protocols (ISDN-User Part and IEEE Futurebus+); see for an overview =-=[18]-=-. 4 Stochastic Model Checking CTMCs As has become clear from the previous section, the existing approaches for formal verification using model checking and performance and dependability evaluation hav... |

99 | GreatSPN 1.7—graphical editor and analyzer for timed and stochastic Petri nets.
- Chiola, Franceschinis, et al.
- 1995
(Show Context)
Citation Context ... process algebras, and stochastic activity networks. With appropriate tools supporting these specification methods, such as, for instance, provided by TIPPtool [36], the PEPA workbench [23], GreatSPN =-=[13]-=-, UltraSAN [56] or SPNP [14], it is relatively comfortable to specify performance models of which the associated CTMCs have millions of states. In combination with state-of-the-art numerical means to ... |

91 | Model checking continuous-time Markov chains by transient analysis.
- Baier, Haverkort, et al.
- 2000
(Show Context)
Citation Context ...m, we have introduced the so-called continuous stochastic logic (CSL) that provides us ample means to specify state- as well as path-based performance measures for CTMCs in a compact and flexible way =-=[1,2,3,4,5]-=-. Moreover, due to the formal syntax and semantics of CSL, we can exploit the structure of CSL-specified measures in the subsequent evaluation process, such that typically the size of the underlying M... |

83 | Model checking continuous time Markov chains.
- Singhal, Aziz, et al.
- 2000
(Show Context)
Citation Context ...m, we have introduced the so-called continuous stochastic logic (CSL) that provides us ample means to specify state- as well as path-based performance measures for CTMCs in a compact and flexible way =-=[1,2,3,4,5]-=-. Moreover, due to the formal syntax and semantics of CSL, we can exploit the structure of CSL-specified measures in the subsequent evaluation process, such that typically the size of the underlying M... |

71 | Process algebra for performance evaluation
- Hermanns, Herzog, et al.
- 2002
(Show Context)
Citation Context ...s as subsets.Automated Performance and Dependability Evaluation 285 Bisimulation (lumping) equivalence. Lumpability enables the aggregation of CTMCs and MRMs without affecting performance properties =-=[47,10,40,35]-=-. We adapt the standard notion slightly in order to deal with MRMs with statelabellings. We only sketch the concepts here, and refer to the papers [4,5] for more details. For some MRM M =(S, R,L,ρ) we... |

70 |
Performance Analysis of Communication Systems: Modeling with Non-Markovian Stochastic Petri Nets.
- German
- 2000
(Show Context)
Citation Context ... to remark that similar processes (with mixed discrete-continuous state spaces) also emerge in the analysis of non-Markovian stochastic Petri nets (when using the supplementary variable approach, cf. =-=[22]-=-), Markov-regenerative stochastic Petri nets [9], and in fluid-stochastic Petri nets [42]. We briefly sketch three other approaches to compute Pr{Yt � r, Xt ∈ S ′ } here, which are more directly appli... |

70 | Fluid stochastic Petri nets: theory, application, and solution techniques,
- Horton, Kulkarni, et al.
- 1998
(Show Context)
Citation Context ...ge in the analysis of non-Markovian stochastic Petri nets (when using the supplementary variable approach, cf. [22]), Markov-regenerative stochastic Petri nets [9], and in fluid-stochastic Petri nets =-=[42]-=-. We briefly sketch three other approaches to compute Pr{Yt � r, Xt ∈ S ′ } here, which are more directly applicable to the problem. An Erlangian approximation. A first approach to compute Pr{Yt � r, ... |

70 |
Software reliability methods.
- Peled
- 2001
(Show Context)
Citation Context ... repetitive attempt to carry out a transaction be eventually granted? Prominent formal verification techniques are theorem proving and model checking, as well as (but to a less formal extent) testing =-=[17,50,55,8]-=-. Important to note at this point is that for an ever-increasing class of systems, their “formal correctness” cannot be separated anymore from their “quantitative correctness”, e.g., in real-time syst... |

69 |
Performance of Computer Communication Systems. A Model-Based Approach.
- Haverkort
- 1999
(Show Context)
Citation Context ... if E(s) = 0; in this case we define P(s, s ′) = 0). The matrix P describes an embedded DTMC of the CTMC. Example 1. As a running example we address a triple modular redundant system (TMR) taken from =-=[28]-=-, a fault-tolerant computer system consisting of three processors and a single (majority) voter. We model this system as a CTMC where state si,j models that i (0 � i<4) processors and j (0 � j � 1) vo... |

69 | The UltraSAN modeling environment
- Sanders, Obal, et al.
- 1995
(Show Context)
Citation Context ...as, and stochastic activity networks. With appropriate tools supporting these specification methods, such as, for instance, provided by TIPPtool [36], the PEPA workbench [23], GreatSPN [13], UltraSAN =-=[56]-=- or SPNP [14], it is relatively comfortable to specify performance models of which the associated CTMCs have millions of states. In combination with state-of-the-art numerical means to solve the resul... |

67 |
Performance-Related Reliability Measures for Computing Systems.
- Beaudry
- 1978
(Show Context)
Citation Context ...re, i.e., ρ(s) > 0 for each state s. The basic idea behind the duality phenomenon is that the progress of time can be regarded as the earning of reward and vice versa. This observation is inspired by =-=[7]-=-. To make it concrete, we define an MRM M −1 =(S, R ′ ,L,ρ ′ ) that results from M by – rescaling the transition rates by the reward of their originating state, i.e., R ′ (s, s ′ )=R(s, s ′ )/ρ(s) and... |

58 | A Markov Chain Model Checker.
- Hermanns, Katoen, et al.
- 2000
(Show Context)
Citation Context ... state space becomes larger (above 10,000 states), or when the required accuracy becomes higher, e.g., between 10 −6 and 10 −9 . Numerical stability is another issue of concern when using this method =-=[37]-=-.Automated Performance and Dependability Evaluation 275 An alternative method is to reduce the problem of computing Prob(s, Φ U [0,t] Ψ) to a transient analysis problem for which well-known and effic... |

53 | Compositional performance modelling with TIPPTool
- Hermanns, Herzog, et al.
- 1998
(Show Context)
Citation Context ...sed on stochastic Petri nets, stochastic process algebras, and stochastic activity networks. With appropriate tools supporting these specification methods, such as, for instance, provided by TIPPtool =-=[36]-=-, the PEPA workbench [23], GreatSPN [13], UltraSAN [56] or SPNP [14], it is relatively comfortable to specify performance models of which the associated CTMCs have millions of states. In combination w... |

53 | Performability: a retrospective and some pointers to the future,”
- Meyer
- 1992
(Show Context)
Citation Context ...asures over CTMCs extended with a reward structure (Markov reward models) [4]. We showed that well-known performability measures, most notably also the performability distribution introduced by Meyer =-=[51, 52,53]-=-, can be specified using CSRL. However, CSRL allows for the specification of new measures that have not yet been addressed in the performability literature. For instance, when rewards are interpreted ... |

52 | On the Logical Characterisation of Performability Properties”,
- Baier, Haverkort, et al.
- 2000
(Show Context)
Citation Context ...ame as for CSL, and only the path operators XJ , UJ need specific considerations. To calculate the probability of satisfiying such a path formula we rely on a general duality result for MRMs and CSRL =-=[4]-=-. Duality. Assume an MRM M =(S, R,L,ρ) with positive reward structure, i.e., ρ(s) > 0 for each state s. The basic idea behind the duality phenomenon is that the progress of time can be regarded as the... |

45 |
Finding Transient Solutions in Markovian Event Systems Through Randomization.
- Grassmann
- 1991
(Show Context)
Citation Context ...abilities are then computed from a system of linear differential equations: π ′ (s, t) =π(s, t) · Q, which can be solved by standard numerical methods or by specialised methods such as uniformisation =-=[45,26,25]-=-. With uniformisation, the transient probabilities of a CTMC are computed via a uniformised DTMC which characterises the CTMC at discrete state transition epochs. Steady-state probabilities are define... |

44 |
Markov regenerative SPN with non-overlapping activity cycles
- Bobbio, Telek
- 1995
(Show Context)
Citation Context ...crete-continuous state spaces) also emerge in the analysis of non-Markovian stochastic Petri nets (when using the supplementary variable approach, cf. [22]), Markov-regenerative stochastic Petri nets =-=[9]-=-, and in fluid-stochastic Petri nets [42]. We briefly sketch three other approaches to compute Pr{Yt � r, Xt ∈ S ′ } here, which are more directly applicable to the problem. An Erlangian approximation... |

44 | Faster and symbolic CTMC model checking
- Katoen, Kwiatkowska, et al.
(Show Context)
Citation Context ...y measures as logical formulas over CTMCs, we describe in this section CSL [1,2], a stochastic variant of CTL, and explain how model checking this logic can be performed, summarising work reported in =-=[2,3,46]-=-. Syntax. CSL extends CTL with two probabilistic operators that refer to the steady-state and transient behaviour of the system being studied. Whereas the steady-state operator refers to the probabili... |

44 |
Closed-form solutions of performability,”
- Meyer
- 1982
(Show Context)
Citation Context ...asures over CTMCs extended with a reward structure (Markov reward models) [4]. We showed that well-known performability measures, most notably also the performability distribution introduced by Meyer =-=[51, 52,53]-=-, can be specified using CSRL. However, CSRL allows for the specification of new measures that have not yet been addressed in the performability literature. For instance, when rewards are interpreted ... |

36 | Model checking performability properties. In:
- Haverkort, Cloth, et al.
- 2003
(Show Context)
Citation Context ...mulated reward) below a certain threshold. We have introduced CSL and CSRL (including its complete syntax and formal semantics) in a much more theoretical context as we do in this tutorial paper (cf. =-=[2,3,4,5,33]-=-).Automated Performance and Dependability Evaluation 263 The rest of the paper is organised as follows. In Section 2 and Section 3 we present the two system evaluation techniques that will be merged ... |

36 | Bisimulation Algorithms for Stochastic Process Algebras and Their BDDBased Implementation.
- Hermanns, Siegle
- 1999
(Show Context)
Citation Context ...(and CSL, and CRL) on the quotient state space with respect to lumpability. This lumped state space is often much smaller than the original one. It can be computed by a partition refinement algorithm =-=[39,20]-=-. 7 Conclusions and Future Outlook In this paper we have tried to give a tutorial style overview on the model checking approach to continuous time Markov chains and Markov reward models. While the log... |

31 | Continous Stochastic Logic Characterizes Bisimulation of Continuous-time Markov Processes. The Journal of Logic and Algebraic Programming
- Desharnais, Panangaden
- 2003
(Show Context)
Citation Context ...ell as steady state probabilities on the lumped MRM M/R if one is only interested in probabilities of equivalence classes. For a given MRM it is therefore possible to establish the following property =-=[4,19,5]-=-: s |= Φ iff s ′ |= Φ if and only if for all CSRL formulas Φ s and s ′ are bisimilar. In other words, CSRL cannot distinguish between lumping equivalent states, but non-equivalent states can always be... |

30 | Beyond Memoryless Distributions: Model Checking Semi-Markov Chains
- López, Hermanns, et al.
- 2001
(Show Context)
Citation Context ...ope [34]. Among work that extends the basic stochastic model checking approach to a broader context, we are aware of the extension of CSL to process algebra specifications [38], to semi-Markov chains =-=[44]-=- and to random time bounds [49]. More work is foreseen in many exciting areas extending what has been described in this tutorial paper, ranging from research on the inclusion of nondeterminism, to eff... |

28 |
Markov chains as an aid in the study of Markov processes.
- Jensen
- 1953
(Show Context)
Citation Context ...abilities are then computed from a system of linear differential equations: π ′ (s, t) =π(s, t) · Q, which can be solved by standard numerical methods or by specialised methods such as uniformisation =-=[45,26,25]-=-. With uniformisation, the transient probabilities of a CTMC are computed via a uniformised DTMC which characterises the CTMC at discrete state transition epochs. Steady-state probabilities are define... |

27 | State-Space Support for Path-Based Reward Variables
- Obal, Sanders
- 1999
(Show Context)
Citation Context ...tate sequences. Stated differently, we would also like to be able to express measures that address the probability on particular paths through the CTMC. Except for the recent work by Obal and Sanders =-=[54]-=-, we are not aware of suitable mechanisms to express such measures. In the sequel, we will specifically address this issue. s ′Automated Performance and Dependability Evaluation 267 3 Formal Verifica... |

27 | Sojourn times in Markov processes
- Sericola, Rubino
- 1989
(Show Context)
Citation Context ...complexity is O(|S|·r/d). As the computational effort is proportional to d −2 , the computation time grows rapidly when a higher accuracy is required. Occupation time distributions. In 2000, Sericola =-=[57]-=- derived a result for the distribution of occupation times in CTMCs prior to a given point in time t. The approach is based on uniformisation, and (as with uniformisation) it is possible to calculate ... |

26 | Specifying Performance Measures for PEPA”,
- Clark, Gilmore, et al.
- 1999
(Show Context)
Citation Context ...loring of the model. In the context of the stochastic process algebra PEPA, Clark et al. recently proposed the use of a probabilistic modal logic to ease the specification of reward structures of MRM =-=[15]-=-, as opposed to the specification of reward-based measures, aswedo. 5.2 A Logic for Performability The addition of rewards on the model level raises the question how they can be reflected on the measu... |

26 | Towards Model Checking Stochastic Process Algebra
- Hermanns, Katoen, et al.
- 2000
(Show Context)
Citation Context ...y of the Hubble space telescope [34]. Among work that extends the basic stochastic model checking approach to a broader context, we are aware of the extension of CSL to process algebra specifications =-=[38]-=-, to semi-Markov chains [44] and to random time bounds [49]. More work is foreseen in many exciting areas extending what has been described in this tutorial paper, ranging from research on the inclusi... |

23 | On the verification of qualitative properties of probabilistic processes under fairness constraints - Baier, Kwiatkowska - 1998 |

23 | Modelchecking large structured Markov chains
- Buchholz, Katoen, et al.
(Show Context)
Citation Context ... model checking has been published in 1999 [2] the approach has been implemented in (at least) three research tools, namely the ETMCC model checker [37], the model checker Prism, and the APNN toolbox =-=[11]-=-. While ETMCC is a dedicated CSL model checker based on sparse matrix data structures, Prism employs BDD based techniques to combat the state space explosion problem. The APNN toolbox uses Kronecker r... |

17 | Performability Modeling Tools and Techniques.
- Haverkort, Marie, et al.
- 2001
(Show Context)
Citation Context ... awkward to specify “by hand” and are therefore generated automatically from high-level description/modelling languages such as stochastic Petri nets, stochastic process algebras or queueing networks =-=[30]-=-. The steps in the process from a system to a useful dependability or performance evaluation are illustrated in the model-based performance and dependability evaluation cycle in Fig. 1. It remains to ... |

16 |
Performability analysis of computer systems: from model specification to solution. Performance Evaluation
- Silva, Gail
(Show Context)
Citation Context ...ire the summation of the Φ-conforming steady-state or transient state probabilities multiplied with the corresponding rewards. The operator CI J (Φ) can be evaluated using a variant of uniformisation =-=[28,58]-=-. Some example properties are now: EJ(¬F), which expresses the expected reward rate, e.g., the system’s capacity, for an operational system, E t J (true) expresses the expected instantaneous reward ra... |

14 |
A Measure of Guaranteed Availability and its Numerical Evaluation
- Goyal, Tantawi
- 1988
(Show Context)
Citation Context ...an [60] proposed a discretisation method for computing the transient distribution of the accumulated reward in an MRM. Their algorithm is a generalisation of an earlier algorithm by Goyal and Tantawi =-=[24]-=- for MRMs with only 0- and 1-rewards. The basic idea is to discretise both the time and the accumulated reward as multiples of the same step size d,Automated Performance and Dependability Evaluation ... |

11 |
Dynamic Probabilistic Systems; Volume 1: Markov Models
- Howard
- 1971
(Show Context)
Citation Context |

11 |
A fast algorithm for the transient reward distribution in continuous-time Markov chains
- Tijms, Veldman
(Show Context)
Citation Context ...additional constraints that earned cumulative reward r at the time of reaching some Φ2-state lies in J, i.e., r ∈ J.278 C. Baier et al. Example 4. As an example property for the TMR system, P�0.95(✸ =-=[60,60]-=- [0,200] true) denotes that with probability of at least 0.95 the cumulative reward, e.g., the incurred costs of the system for reward structure ρ3, at time instant 60 is at most 200. Given that the r... |

7 |
J.-P.: On the use of model checking techniques for quantitative dependability evaluation
- Haverkort, Hermanns, et al.
- 2000
(Show Context)
Citation Context ...hieve better space efficiency. So far, we (and others) have applied stochastic model checking to various small and medium size case studies, including the analysis of a dependable workstation cluster =-=[31]-=-, the verification of the performance of the plain ordinary telephone system protocol [3], the estimation of power consumption in mobile ad hoc networks [33], and the assessment of the survivability o... |

7 | Model checking CSL until formulae with random time bounds.
- Kwiatkowska, Norman, et al.
- 2002
(Show Context)
Citation Context ...ds the basic stochastic model checking approach to a broader context, we are aware of the extension of CSL to process algebra specifications [38], to semi-Markov chains [44] and to random time bounds =-=[49]-=-. More work is foreseen in many exciting areas extending what has been described in this tutorial paper, ranging from research on the inclusion of nondeterminism, to efforts to improve the effectivene... |

4 |
Model checking CSRL-specified performability properties
- Haverkort, Cloth, et al.
- 2001
(Show Context)
Citation Context ... swapthe model and swapthe formula. 5.5 ModelChecking CSRL-Specified Measures For the general case of CSRL, model checking algorithms are more involved, and research on their effectiveness is ongoing =-=[32,33]-=-. In this section we describe the basic strategy and sketch three algorithms implementing this strategy. A more detailed comparison of the algorithmic intricacies can be found in [33]. Given an MRM M ... |

1 |
Systems and Software Verification
- Schnoebelen
- 2001
(Show Context)
Citation Context |

1 |
Optimal state space lumping in Markov models. 2002. submitted for publication
- Derisavi, Hermanns, et al.
(Show Context)
Citation Context ...lid in those states that guarantee that in equilibrium with probability at least 0.9 the probability that the system will not go down within 10 time units is at least 0.8. Conversely, P�0.5((¬down) U =-=[10,20]-=- S�0.8((up 3 ∨ up 2))) is valid for those states that with probability at least 0.5 will reach a state s between 10 and 20 time-units, which guarantees the system to be operational with at least 2 pro... |

1 |
Construction and verfication of performance and reliability models
- Hermanns
- 2001
(Show Context)
Citation Context ...formance of the plain ordinary telephone system protocol [3], the estimation of power consumption in mobile ad hoc networks [33], and the assessment of the survivability of the Hubble space telescope =-=[34]-=-. Among work that extends the basic stochastic model checking approach to a broader context, we are aware of the extension of CSL to process algebra specifications [38], to semi-Markov chains [44] and... |