Transient analysis of deterministic and stochastic Petri nets

Choi, Hoon; Kulkarni, Vidyadhar G.; Trivedi, Kishor S.

doi:10.1007/3-540-56863-8_46

Cited by 66 publications

(27 citation statements)

References 9 publications

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“…The motivation for the mean-field approach is the same as in the continuoustime Markov chain (CTMC) case -unsurprisingly, GSMP models with many components also become computationally intractable to explicit state techniques [7,9] rapidly as a result of the familiar state-space explosion problem. Our approach is based on the derivation of delay differential equations (DDEs) from PGSMP models and generalises the traditional mean-field approach as applied to CTMC models based on ordinary differential equations (ODEs) [1,13,4,17].…”

Section: Introductionmentioning

confidence: 99%

Mean Field for Performance Models with Generally-Distributed Timed Transitions

Hayden

Horváth²,

Telek

2014

Quantitative Evaluation of Systems

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Section: Introductionmentioning

confidence: 99%

Mean Field for Performance Models with Generally-Distributed Timed Transitions

Hayden

Horváth²,

Telek

2014

Quantitative Evaluation of Systems

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“…However, the application of these techniques imposes various restrictions which exclude models allowing multiple concurrent non-exponential clocks [2] [14] [15] [11], or models where timing constraints are essential to keep the set of reachable markings finite [24] [10].…”

Section: Introductionmentioning

confidence: 99%

Introducing probability within state class analysis of dense-time-dependent systems

Bucci¹,

Piovosi²,

Sassoli³

et al. 2005

Second International Conference on the Quantitative Evaluation of Systems (QEST'05)

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Abstract-Several techniques have been proposed for symbolic enumeration and analysis of the state space of reactive systems with non-deterministic temporal parameters taking values within a dense domain. In a large part of these techniques, the state space is covered by collecting states within equivalence classes each comprised of a discrete logical location and a dense variety of clock valuations encoded as a Difference Bounds Matrix (DBM). The reachability relation among such classes enables qualitative verification of properties pertaining the ordering of events along critical runs and the satisfaction of stimulus/response deadlines. However, up to now, no results have been proposed which extend state class enumeration so as to combine the verification of the possibility of critical behaviors with a quantitative evaluation of their probability.In this paper, we extend the concept of equivalence classes based on DBM encoding with a density function which provides a measure for the probability associated with individual states collected in the class itself. To this end, we extend the formalism of Time Petri Nets by associating the static firing interval of each transition with a probability density function. We then expound how this probabilistic information determines a probability for the states collected within a class and how this probability evolves in the enumeration of the reachability relation among state classes. This opens the way to characterizing the possibility of critical behaviors with a quantitative measure of probability.

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“…Previous work on transient analysis of DSPNs was always based on the restriction that deterministic transitions are not concurrently enabled. In [2] it has been show that, with this restriction, the stochastic process underlying a DSPN is a Markov regenerative stochastic process. Based on this result, a numerical method for the transient analysis of such DSPN is proposed.…”

Section: Introductionmentioning

confidence: 99%