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## Modeling A Scalable High-Speed Interconnect with Stochastic Petri Nets (1995)

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Venue: | In Sixth International Workshop on Petri Nets and Performance Models (PNPM’95), Duham |

Citations: | 3 - 0 self |

### Citations

947 |
Petri Net Theory and the Modeling of Systems.
- Peterson
- 1981
(Show Context)
Citation Context ...rief introduction to the basic terminology is given in the Section 2. For a complete treatment of the class of SPNs used in this paper, see [5]. 4 2 Basic SPN Notions and Denotations A Petri net (PN) =-=[12, 13]-=- is a directed bipartite graph with two sets of nodes, places and transitions. Input arcs connect a place to a transition, output arcs connect a transition to a place. A multiplicity (positive integer... |

494 |
Queueing Systems, Volume I: Theory.
- Kleinrock
- 1975
(Show Context)
Citation Context ...n underlying stochastic process, reducible to a continuous-time Markov chain (CTMC) by eliminating the vanishing markings [1, 3, 5]. The GSPN model can be extended by allowing phase-type distribution =-=[10]-=- instead of just simple exponential distributions. The underlying process is still a CTMC, but its states now describe both the marking of the PN and the phase for thesring times of the transitions, h... |

490 |
Kommunikation mit Automaten,
- Petri
- 1962
(Show Context)
Citation Context ...rief introduction to the basic terminology is given in the Section 2. For a complete treatment of the class of SPNs used in this paper, see [5]. 4 2 Basic SPN Notions and Denotations A Petri net (PN) =-=[12, 13]-=- is a directed bipartite graph with two sets of nodes, places and transitions. Input arcs connect a place to a transition, output arcs connect a transition to a place. A multiplicity (positive integer... |

305 | A class of generalized stochastic Petri nets for the performance evaluation of multiprocessor systems
- Marsan, Balbo, et al.
- 1984
(Show Context)
Citation Context ...the enabling rules changes. A transition t is disbaled if there is an inhibitor arc with multiplicity k from place p to t, and p contains k or more tokens. A \generalized stochastic Petri net" (GSPN) =-=[1]-=- is a PN where each transition has an associatedsring time, which can be zero (immediate transition) or exponentially distributed with a parameter dependent on the marking (timed transition). If sever... |

266 |
Coloured Petri nets
- Jensen
- 1993
(Show Context)
Citation Context ...nalyzed two net models of the interconnect. We used SPNP [6], based on Stochastic Petri Nets (SPNs), to build an approximate model for a quick numerical analysis of performance. We used Design/CPN TM =-=[7]-=- based on Hierarchical Colored Petri Nets to develop a detailed simulation model to help refine the design and identify performance bottlenecks. This model was also used to verify the accuracy and cor... |

196 | SPNP: stochastic Petri net package
- Ciardo, Muppala, et al.
- 1989
(Show Context)
Citation Context ...ewlettPackard Labs. network size (which can scale up to hundreds of nodes) and the number of internal buffers on each node. We have built and analyzed two net models of the interconnect. We used SPNP =-=[6]-=-, based on Stochastic Petri Nets (SPNs), to build an approximate model for a quick numerical analysis of performance. We used Design/CPN TM [7] based on Hierarchical Colored Petri Nets to develop a de... |

154 | On Petri nets with deterministic and exponentially distributed firing times - Marsan, Chiola - 1987 |

124 | A decomposition approach for stochastic reward net models
- Ciardo, Trivedi
- 1993
(Show Context)
Citation Context ... for an exact numerical solution, even for the E 2 interconnect having only 7 nodes. In this section, we describe an approximate model based on the idea of SPN decomposition and fixed-point iteration =-=[5]-=-. This approximate model exploits the large amount of symmetry possessed by the interconnect and essentially describes the behavior of one node under a workload that is generated by the whole intercon... |

101 |
Automated generation and analysis of Markov reward models using Stochastic Reward Nets
- Ciardo, Blakemore, et al.
- 1993
(Show Context)
Citation Context ... improve the applicability of such a tool. We assume that the reader is familiar with the basic definitions and behavior of SPNs. For a complete treatment of the class of SPNs used in this paper, see =-=[3]-=-. 2 System The interconnect topology is a continuous hexagonal mesh which permits each node to communicate with its six immediate neighbors. We refer to a mesh having n nodes on each edge as an En mes... |

94 | A characterization of the stochastic process underlying a stochastic Petri net - Ciardo, German, et al. - 1993 |

28 |
Discrete time stochastic Petri nets
- Molloy
- 1985
(Show Context)
Citation Context ...n. However, as we have seen, this can lead to a sharp increase in the size of the state space. To solve this problem, we are investigating the use of SPN having underlying discrete-time Markov chains =-=[8, 2]-=-. We are currently working on the design of a software package that will allow us to solve SPNs with continuous-time phase-type distributions, as those used in this paper, their discrete equivalent (w... |

27 | Discrete-time Markovian stochastic Petri nets. In: Computations with Markov Chains
- Ciardo
- 1995
(Show Context)
Citation Context ...n. However, as we have seen, this can lead to a sharp increase in the size of the state space. To solve this problem, we are investigating the use of SPN having underlying discrete-time Markov chains =-=[8, 2]-=-. We are currently working on the design of a software package that will allow us to solve SPNs with continuous-time phase-type distributions, as those used in this paper, their discrete equivalent (w... |

6 |
GreatSPN Users’ Manual. Technical report, Dipartimento di Informatica, Università degli Studi di
- Chiola
- 1987
(Show Context)
Citation Context ...obability ofsnding the GSPN in a vanishing marking is zero. A GSPN describes an underlying stochastic process, reducible to a continuous-time Markov chain (CTMC) by eliminating the vanishing markings =-=[1, 3, 5]-=-. The GSPN model can be extended by allowing phase-type distribution [10] instead of just simple exponential distributions. The underlying process is still a CTMC, but its states now describe both the... |

3 |
Validation of a VLSI Chip Using Hierarchical Colored Petri Nets
- Shapiro
- 1991
(Show Context)
Citation Context ...t and analyzed two net models of the interconnect. We used SPNP [8], based on Stochastic Petri Nets, to build an approximate model for a quick numerical analysis of performance. We used Design/CPN TM =-=[9, 14]-=- based on Hierarchical Colored Petri Nets to develop a detailed simulation model to help rene the design and identify performance bottlenecks. This model was also used to verify the accuracy and corr... |