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EnglishWe consider a particular class of Stochastic Petri Nets whose stationary probabilities at arbitrary instants exhibit a product form. We study these nets at specific instants in the steady state that occur directly after the firing of a transition. We focus our attention on the instant after tokens are removed from the places specified by a transition's input bag and just before tokens are entered into the places specified by the same transition's output bag. We show that the stationary probabilities at “arrival instants” are related to corresponding stationary probabilities at arbitrary instants in net(s) with lower load. We then show how one of the “arrival” theorems can be applied to the derivation of a formula for the mean sojourn time of a token in a place at steady state. This is the basis for the development of a Mean Value Analysis algorithm for the computation of performance indices for Product-Form Stochastic Petri Nets.
| Titolo: | Arrival theorems for product-form stochastic Petri nets | |
| Autori Riconosciuti: | ||
| Autori: | G. BALBO; S. C. BRUELL; M. SERENO | |
| Data di pubblicazione: | 1994 | |
| Abstract: | We consider a particular class of Stochastic Petri Nets whose stationary probabilities at arbitrary instants exhibit a product form. We study these nets at specific instants in the steady state that occur directly after the firing of a transition. We focus our attention on the instant after tokens are removed from the places specified by a transition's input bag and just before tokens are entered into the places specified by the same transition's output bag. We show that the stationary probabilities at “arrival instants” are related to corresponding stationary probabilities at arbitrary instants in net(s) with lower load. We then show how one of the “arrival” theorems can be applied to the derivation of a formula for the mean sojourn time of a token in a place at steady state. This is the basis for the development of a Mean Value Analysis algorithm for the computation of performance indices for Product-Form Stochastic Petri Nets. | |
| Volume: | Volume 22 , Issue 1 (May 1994) | |
| Pagina iniziale: | 87 | |
| Pagina finale: | 97 | |
| Nome del convegno: | Conference on Measurement and modeling of computer systems (ACM SIGMETRICS) | |
| Luogo del convegno: | Nashville, Tennessee, United States | |
| Anno del convegno: | 16-20 Maggio 1994 | |
| Digital Object Identifier (DOI): | 10.1145/183018.183028 | |
| Parole Chiave: | Stochastic Petri Nets; Product form; Arrival theorem; Computational algorithms; Mean Value Analysis | |
| Rivista: | PERFORMANCE EVALUATION REVIEW | |
| Appare nelle tipologie: | 04B-Conference paper in rivista |
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