A stochastic Petri net is a five-tuple SPN = (P, T, F, M0, Λ) where:
P is a set of states, called places.
T is a set of transitions.
F where F ⊂ (P × T) ∪ (T × P) is a set of flow relations called "arcs" between places and transitions (and between transitions and places).
M0 is the initial marking.
Λ = is the array of firing rates λ associated with the transitions. The firing rate, a random variable, can also be a function λ(M) of the current marking.
Correspondence to Markov processedit
The reachability graph of stochastic Petri nets can be mapped directly to a Markov process. It satisfies the Markov property, since its states depend only on the current marking. Each state in the reachability graph is mapped to a state in the Markov process, and the firing of a transition with firing rate λ corresponds to a Markov state transition with probability λ.
^Dingle, N. J.; Knottenbelt, W. J.; Suto, T. (2009). "PIPE2". ACM SIGMETRICS Performance Evaluation Review. 36 (4): 34. doi:10.1145/1530873.1530881. S2CID 3265173.
^Carnevali, L.; Ridi, L.; Vicario, E. (2013). "A Quantitative Approach to Input Generation in Real-Time Testing of Stochastic Systems". IEEE Transactions on Software Engineering. 39 (3): 292. doi:10.1109/TSE.2012.42. S2CID 8064028.
^Amparore, E. G. (2014). "A New GreatSPN GUI for GSPN Editing and CSLTA Model Checking". Quantitative Evaluation of Systems. Lecture Notes in Computer Science. Vol. 8657. pp. 170–173. doi:10.1007/978-3-319-10696-0_13. ISBN978-3-319-10695-3.
External linksedit
Stochastic Petri Nets: an Introduction
Stochastic Petri Nets
January 01, 1970
stochastic, petri, this, article, needs, additional, citations, verification, please, help, improve, this, article, adding, citations, reliable, sources, unsourced, material, challenged, removed, find, sources, news, newspapers, books, scholar, jstor, january,. This article needs additional citations for verification Please help improve this article by adding citations to reliable sources Unsourced material may be challenged and removed Find sources Stochastic Petri net news newspapers books scholar JSTOR January 2014 Learn how and when to remove this message Stochastic Petri nets are a form of Petri net where the transitions fire after a probabilistic delay determined by a random variable Contents 1 Definition 2 Correspondence to Markov process 3 Software tools 4 References 5 External linksDefinition editA stochastic Petri net is a five tuple SPN P T F M0 L where P is a set of states called places T is a set of transitions F where F P T T P is a set of flow relations called arcs between places and transitions and between transitions and places M0 is the initial marking L is the array of firing rates l associated with the transitions The firing rate a random variable can also be a function l M of the current marking Correspondence to Markov process editThe reachability graph of stochastic Petri nets can be mapped directly to a Markov process It satisfies the Markov property since its states depend only on the current marking Each state in the reachability graph is mapped to a state in the Markov process and the firing of a transition with firing rate l corresponds to a Markov state transition with probability l Software tools editPlatform Independent Petri net Editor 1 ORIS Tool 2 GreatSPN 3 References edit Dingle N J Knottenbelt W J Suto T 2009 PIPE2 ACM SIGMETRICS Performance Evaluation Review 36 4 34 doi 10 1145 1530873 1530881 S2CID 3265173 Carnevali L Ridi L Vicario E 2013 A Quantitative Approach to Input Generation in Real Time Testing of Stochastic Systems IEEE Transactions on Software Engineering 39 3 292 doi 10 1109 TSE 2012 42 S2CID 8064028 Amparore E G 2014 A New GreatSPN GUI for GSPN Editing and CSLTA Model Checking Quantitative Evaluation of Systems Lecture Notes in Computer Science Vol 8657 pp 170 173 doi 10 1007 978 3 319 10696 0 13 ISBN 978 3 319 10695 3 External links editStochastic Petri Nets an Introduction Stochastic Petri Nets Retrieved from https en wikipedia org w index php title Stochastic Petri net amp oldid 1147264383, wikipedia, wiki, book, books, library,
