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## Beyond Model-Checking CSL for QBDs: Resets, Batches and Rewards

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894 |
Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach
- Neuts
- 1981
(Show Context)
Citation Context ...as shown in Figure 1(b). Q describes an infinite-state CTMC, {Xt ∈ S | t/geq0}. The steady-state probabilities of a QBD can be calculated in a level-wise fashion, using e.g., matrix-geometric methods =-=[9, 11]-=-, which exploit the repetitive structure in the generator matrix. To compute transient state probabilities for the infinite-state QBDs, we developed an uniformization-based approach [12]. Continuous s... |

235 | Model-checking algorithms for continuous-time markov chains.
- Baier, Haverkort, et al.
- 2003
(Show Context)
Citation Context ...of performance or dependability measures for finite Markov chains [4, 1, 7]. Furthermore, efficient uniformization-based algorithms have been proposed to make such model checking practically feasible =-=[2]-=-. The logic CSRL (continuous stochastic reward logic) has been proposed to reason about time and rewards in finite Markov chains [3]. As such, CSRL comprises a natural way of specifying performability... |

186 |
Introduction to Matrix-Analytic Methods
- Latouche, Ramaswami
- 1999
(Show Context)
Citation Context ...as shown in Figure 1(b). Q describes an infinite-state CTMC, {Xt ∈ S | t/geq0}. The steady-state probabilities of a QBD can be calculated in a level-wise fashion, using e.g., matrix-geometric methods =-=[9, 11]-=-, which exploit the repetitive structure in the generator matrix. To compute transient state probabilities for the infinite-state QBDs, we developed an uniformization-based approach [12]. Continuous s... |

156 | Approximate Symbolic Model Checking of ContinuousTime Markov Chains
- Baier, Katoen, et al.
- 1999
(Show Context)
Citation Context ... algorithms for finite Markov chains. The logic CSL (continuous stochastic logic) has been shown to be suitable for the specification of performance or dependability measures for finite Markov chains =-=[4, 1, 7]-=-. Furthermore, efficient uniformization-based algorithms have been proposed to make such model checking practically feasible [2]. The logic CSRL (continuous stochastic reward logic) has been proposed ... |

91 | Model checking continuous-time Markov chains by transient analysis.
- Baier, Haverkort, et al.
- 2000
(Show Context)
Citation Context ... algorithms for finite Markov chains. The logic CSL (continuous stochastic logic) has been shown to be suitable for the specification of performance or dependability measures for finite Markov chains =-=[4, 1, 7]-=-. Furthermore, efficient uniformization-based algorithms have been proposed to make such model checking practically feasible [2]. The logic CSRL (continuous stochastic reward logic) has been proposed ... |

60 |
Spectral expansion solution for a class of Markov models: Application and comparison with the matrix-geometric method. Performance Evaluation,
- Mitrani, Chakka
- 1995
(Show Context)
Citation Context ...ut regrouping. This can be done with specialized matrix-geometric algorithms algorithms for M|G|1 and G|M|1 processes with batch arrivals and services [9], [13], or with the spectral expansion method =-=[10]-=-. Whether this is computationally more attractive has to be established. Uniformization can be done as for standard QBDs, we just have to consider that one uniformization step possibly crosses more th... |

52 | On the Logical Characterisation of Performability Properties”,
- Baier, Haverkort, et al.
- 2000
(Show Context)
Citation Context ...have been proposed to make such model checking practically feasible [2]. The logic CSRL (continuous stochastic reward logic) has been proposed to reason about time and rewards in finite Markov chains =-=[3]-=-. As such, CSRL comprises a natural way of specifying performability properties of systems. In [6] we proposed a number of numerical algorithms to efficiently model check finite Markov-reward models. ... |

38 |
On the use of model checking techniques for dependability evaluation.
- Haverkort, Hermanns, et al.
- 2000
(Show Context)
Citation Context ... algorithms for finite Markov chains. The logic CSL (continuous stochastic logic) has been shown to be suitable for the specification of performance or dependability measures for finite Markov chains =-=[4, 1, 7]-=-. Furthermore, efficient uniformization-based algorithms have been proposed to make such model checking practically feasible [2]. The logic CSRL (continuous stochastic reward logic) has been proposed ... |

36 | Model checking performability properties. In:
- Haverkort, Cloth, et al.
- 2003
(Show Context)
Citation Context ...s stochastic reward logic) has been proposed to reason about time and rewards in finite Markov chains [3]. As such, CSRL comprises a natural way of specifying performability properties of systems. In =-=[6]-=- we proposed a number of numerical algorithms to efficiently model check finite Markov-reward models. Recently, we considered the step of applying CSL model checking algorithms for infinitestate Marko... |

17 | Model checking infinite-state Markov chains.
- Remke, Haverkort, et al.
- 2005
(Show Context)
Citation Context ...Ds: Resets, Batches and Rewards Abstract We propose and discuss a number of extensions to quasibirth-death models (QBDs) for which CSL model checking is still possible, thus extending our recent work =-=[12]-=- on CSL model checking of QBDs. We then equip the QBDs with rewards, and discuss algorithms and open research issues for model checking CSRL for QBDs with rewards. 1 Introduction Over the last few yea... |

14 | Steady-state analysis of infinite stochastic Petri nets: A comparison between the spectral expansion and the matrix-geometric method
- Haverkort, Ost
- 1997
(Show Context)
Citation Context ...ntering or leaving a level are restricted to neighboring levels only, we can transform the QBD with batches to a standard QBD. This procedure always works, as long as the maximum batch size is finite =-=[8]-=-. With regrouping, the level size is multi, for every possible batch size i. A(1) 0 just equals A0sB0,1 A0 A0 A0 0 1 2 3 B 0,0 B 0,2 B 1,0 A 2 A 2 B 1,1 A 1 A 1 (a) batch arrivals of size 2 A 2 . . . ... |

12 | Model checking Markov Reward Models with Impulse Rewards. - Cloth, Katoen, et al. - 2005 |

12 | Aggregate Matrix-analytic Techniques and their Applications - Riska - 2002 |