## Stochastic Transition Systems (1998)

Citations: | 32 - 4 self |

### BibTeX

@INPROCEEDINGS{Alfaro98stochastictransition,

author = {Luca De Alfaro},

title = {Stochastic Transition Systems},

booktitle = {},

year = {1998},

pages = {423--438},

publisher = {Springer-Verlag}

}

### OpenURL

### Abstract

. Traditional methods for the analysis of system performance and reliability generally assume a precise knowledge of the system and its workload. Here, we present methods that are suited for the analysis of systems that contain partly unknown or unspecified components, such as systems in their early design stages. We introduce stochastic transition systems, a high-level formalism for the modeling of timed probabilistic systems. Stochastic transition systems extend current modeling capabilities by enabling the representation of transitions having unknown delay distributions, alongside transitions with zero or exponentially-distributed delay. We show how these various types of transitions can be uniformly represented in terms of nondeterminism, probability, fairness and time, yielding efficient algorithms for system analysis. Finally, we present methods for the specification and verification of long-run average properties of STSs. These properties include many relevant performance and re...

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Citation Context ...rness of [KB96], showing that the two notions are equivalent in this context. 2 Stochastic Transition Systems Stochastic transition systems (STSs) have been inspired by the fair transition systems of =-=[MP91]-=- and by the real-time probabilistic processes of [ACD92]. A stochastic transition system (STS) is a triple S = (V ; \Theta; T ), where: -- V is a finite set of typed state variables, each with finite ... |

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Citation Context ...ating an STS into a fair TPS, it is necessary to check that it is non-Zeno. A method to do this is presented in Section 6. A more sophisticated approach to the problem of time divergence, inspired by =-=[Seg95]-=-, is discussed in [dA97a]. 4 Translation and Informal Semantics Even though the formal semantics of STSs is defined by translation into fair TPSs, there is a correspondence between the proposed transl... |

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Citation Context ...lgorithms also shows that, when consider2 ing long-run average properties of finite-state systems, our notion of probabilistic fairness yields the same verification algorithms as the weak fairness of =-=[KB96]-=-, showing that the two notions are equivalent in this context. 2 Stochastic Transition Systems Stochastic transition systems (STSs) have been inspired by the fair transition systems of [MP91] and by t... |

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38 | How to specify and verify long-run average behaviour of probabilistic systems
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Citation Context ...Markov chain corresponding to the system. We specify long-run average properties of systems by attaching labels to the system states and transitions, following a simplified version of the approach of =-=[dA98]-=-. The labels specify system tasks, whose long-run average outcome or duration can be measured. This enables the specification of several reliability and performance indices, such as throughput, averag... |

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Citation Context ...alent in this context. 2 Stochastic Transition Systems Stochastic transition systems (STSs) have been inspired by the fair transition systems of [MP91] and by the real-time probabilistic processes of =-=[ACD92]-=-. A stochastic transition system (STS) is a triple S = (V ; \Theta; T ), where: -- V is a finite set of typed state variables, each with finite domain. The (finite) state space S consists of all type-... |

34 | Temporal logics for the specification of performance and reliability - Alfaro - 1997 |

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Citation Context ...t" associated to system transitions, expressed by fi; or a combination of the two. 10 In GSPN reward models [CMT91] it is possible to associate a reward rate to the places and transitions of the =-=net; [Cla96]-=- and [Ber97] propose methods for associating a reward with each state of the Markov chain generated from a PEPA or EMPA model. The r labeling discussed above serves a similar purpose; however, we also... |

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Citation Context ...sed to measure the expected time spent at system states, weighted by a function ff; the "cost" associated to system transitions, expressed by fi; or a combination of the two. 10 In GSPN rewa=-=rd models [CMT91]-=- it is possible to associate a reward rate to the places and transitions of the net; [Cla96] and [Ber97] propose methods for associating a reward with each state of the Markov chain generated from a P... |

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Citation Context ...d to system transitions, expressed by fi; or a combination of the two. 10 In GSPN reward models [CMT91] it is possible to associate a reward rate to the places and transitions of the net; [Cla96] and =-=[Ber97]-=- propose methods for associating a reward with each state of the Markov chain generated from a PEPA or EMPA model. The r labeling discussed above serves a similar purpose; however, we also introduce t... |

16 |
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Citation Context ...ed delay distributions, and by introducing the possibility of nondeterministic choice among enabled immediate transitions. STSs extend in a similar way also the probabilistic finite-state programs of =-=[PZ86]-=- and the real-time probabilistic processes of [ACD92]. The introduction of nondeterminism and of transitions with unspecified delay distributions, and the capability to deal with these features in the... |

11 |
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Citation Context ...-0096 (DARPA), by the ONR YIP award N00014-95-1-0520, by the NSF CAREER award CCR-9501708, and by the NSF grant CCR-9504469. nets [ABC84] and of stochastic process algebras such as TIPP [GHR93], PEPA =-=[Hil96]-=- and EMPA [BG96] with the introduction of nondeterminism and of transitions with unspecified delay distribution. These features enable the modeling of unknown (or imprecisely known) arrival rates and ... |