## Stochastic petri nets: An elementary introduction (1989)

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Venue: | In Advances in Petri Nets |

Citations: | 54 - 0 self |

### BibTeX

@INPROCEEDINGS{Marsan89stochasticpetri,

author = {M. Ajmone Marsan},

title = {Stochastic petri nets: An elementary introduction},

booktitle = {In Advances in Petri Nets},

year = {1989},

pages = {1--29},

publisher = {Springer}

}

### Years of Citing Articles

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### Abstract

ABSTRACT- Petri nets in which random firing delays are associated with transitions whose

### Citations

731 |
Net Theory and the Modeling of Systems
- Peterson, Petri
- 1981
(Show Context)
Citation Context ...iring Times 3.5 Relations with Other Models 3.6 Structural Analysis of SPN .3.7 Current Research Activities 3.8 Open Problems 4 CONCLUSIONS 5 ACKNOWLEDGMENTS 1 INTRODUCTION CONTENTS J Petri nets (PN) =-=[1,2,3]-=-, in their various shapes and sizes, have been used for the study of the qualitative properties of systems exhibiting concurrency and synchronization characteristics. The use of PN-based techniques fo... |

577 |
Petri Nets, An Introduction
- Reisig
- 1985
(Show Context)
Citation Context ...iring Times 3.5 Relations with Other Models 3.6 Structural Analysis of SPN .3.7 Current Research Activities 3.8 Open Problems 4 CONCLUSIONS 5 ACKNOWLEDGMENTS 1 INTRODUCTION CONTENTS J Petri nets (PN) =-=[1,2,3]-=-, in their various shapes and sizes, have been used for the study of the qualitative properties of systems exhibiting concurrency and synchronization characteristics. The use of PN-based techniques fo... |

258 | A Class of Generalized Stochastic Petri Nets for the Performance Evaluation of Multiprocessor Systems”, retrieved from http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1 .90.8002 on 17/5/2013
- Marsan, Balbo, et al.
(Show Context)
Citation Context ...marking-dependent firing rates in SPN assumed that the analyst be aware of all reachable markings in order to correctly specify the marking dependency. Even more so was the initial definition of GSPN =-=[20]-=-, in which the choice of the immediate transition to be fired in a vanishing marking was based on a user-defined switching distribution, which could be correctly defined only by knowing the GSPN reach... |

243 | Introduction to Stochastic Processes - Cinlar - 1975 |

137 |
A proof for the queueing formula
- Little
- 1993
(Show Context)
Citation Context ...e set of transitions enabled in Mi, and Xj(Mi) is the firing rate of tj in Mi. . . The avemge delay of a token in traversing a subnet in steady-state conditions can be computed using Little's formula =-=[7,19]-=- E[Nl W"l = E[.I1 where E[T] is the average delay, E[N] is the average number of tokens in the process of traversing the subnet, and E[7] is the average input (or output) rate of tokens into (or out o... |

136 | On Petri Nets with Deterministic and Exponentially Distributed Firing Times. Advances in Petri Nets, vol 266 - Marsan - 1987 |

133 |
Single Server Queue
- Cohen
- 1969
(Show Context)
Citation Context ...ling tools were proposed. The main such tools are based on queuing theory.s2.3 Queues Customer Customer Arrivals Departures Service Waiting Room Figure 4: Pictorial representation of a queue. A queue =-=[7,8,9,10,11,12,13]-=- is a!system to which customer^ arrive to receive service by a service station. The service station may comprise one or more servers. When all servers are busy, customers are forced to wait in a waiti... |

118 |
Computer Performance Modeling Handbook
- Lavenberg, editor
- 1983
(Show Context)
Citation Context ...ling tools were proposed. The main such tools are based on queuing theory.s2.3 Queues Customer Customer Arrivals Departures Service Waiting Room Figure 4: Pictorial representation of a queue. A queue =-=[7,8,9,10,11,12,13]-=- is a!system to which customer^ arrive to receive service by a service station. The service station may comprise one or more servers. When all servers are busy, customers are forced to wait in a waiti... |

102 |
Performance Models of Multiprocessor Systems
- Ajmone-Marsan, Balbo, et al.
- 1986
(Show Context)
Citation Context ...ling tools were proposed. The main such tools are based on queuing theory.s2.3 Queues Customer Customer Arrivals Departures Service Waiting Room Figure 4: Pictorial representation of a queue. A queue =-=[7,8,9,10,11,12,13]-=- is a!system to which customer^ arrive to receive service by a service station. The service station may comprise one or more servers. When all servers are busy, customers are forced to wait in a waiti... |

54 |
Extended stochastic Petri nets: Applications and analysis
- Dugan, Trivedi, et al.
- 1984
(Show Context)
Citation Context ...rts were devoted to attempts to increase the modeling power of SPN and GSPN by allowing firing delays to be random variables with arbitrary pdf. This resulted in the definition of extended SPN (ESPN) =-=[24]-=-, deterministic and stochastic PN (DSPN) (25,261, and SPN with phase-distributed firing delays [27,28]. It is important to note that the existence in these models of random firing delays with pdf othe... |

33 |
G.: Generalized stochastic Petri nets revisited: Random switches and priorities
- Marsan, Balbo, et al.
- 1987
(Show Context)
Citation Context ...ion to be fired in a vanishing marking was based on a user-defined switching distribution, which could be correctly defined only by knowing the GSPN reachability set. With the revised GSPN definition =-=[21]-=-, an effort was made to integrate the structural and the stochastic characteristics of the model, so that the model definition be possible at the net level, without requiring the generation of the rea... |

14 |
On the efficient construction of the tangible reachability graph of generalized stochastic Petri nets
- Balbo, Chiola, et al.
- 1987
(Show Context)
Citation Context .... The equivalence of this behaviour with the one resulting from the simultaneous firing of some immediate transitions in the model can be exploited to reduce the complexity of the solution algorithms =-=[22]-=-. The presence of inhibitor arcs and priorities reduces the number of reachable markings with respect to the basic underlying PN. The GSPN reachability set is equal to the one of the underlying PN whi... |

11 |
Les réseaux de Petri stochastiques et leur application a l’evaluation des systemes informatiques
- Natkin
- 1980
(Show Context)
Citation Context ...endent of the marking history. To this purpose, sbjourn times in markings must be random variables with negative exponential pdf. This idea formed the basis of the doctoral dissertations of S. Natkin =-=[14]-=- at the Conservatoire National des Arts et MCtiers in Paris, France, and of M. K. Molloy [15] at the University of California at Los Angeles in the United States. These works were performed independen... |

9 |
Queues
- Cox, Smith
- 1961
(Show Context)
Citation Context |

8 |
Introduction to numerical Petri nets, a general graphical model of concurrent processing systems
- Symons
- 1980
(Show Context)
Citation Context ...he idea of associating an exponentially distributed random delay with the PN transitions was already present in the doctoral dissertation of F. J. Symons within the definition of Numerical Petri nets =-=[16,17]-=-. f 3.1 The Basic Model An SPN is a six-tuple .. . . 8 '. SPN = (P, T, I, 0, M,, A)swhere (P, T, I, 0, Mo) is the marked untimed PN underlying the SPN, which as usual comprises a set of places P = (p1... |

4 |
Analysis and Synthesis of Computer Systems
- Mitrani, Gelenbe
- 1980
(Show Context)
Citation Context |

3 |
The description and definition of Queueing Systems by numerical Petri nets
- Symons
- 1980
(Show Context)
Citation Context ...he idea of associating an exponentially distributed random delay with the PN transitions was already present in the doctoral dissertation of F. J. Symons within the definition of Numerical Petri nets =-=[16,17]-=-. f 3.1 The Basic Model An SPN is a six-tuple .. . . 8 '. SPN = (P, T, I, 0, M,, A)swhere (P, T, I, 0, Mo) is the marked untimed PN underlying the SPN, which as usual comprises a set of places P = (p1... |

3 |
Performance analysis of degradable multiprocessor systems using generalized stochastic Petri nets
- Marsan, Bobbio, et al.
- 1984
(Show Context)
Citation Context ...rarrival times whose rate is proportional to the number of customers out of the queue. As a third example of a GSPN model, we analyze the performance of the two-processor system depicted in Figure 11 =-=[18]-=-. Two processing units comprising a processor (PI and P2) and a private memory (PMl and PM2) connected by a local bus (LBl and LB2), access two common memory modules (CMl and CM2) through a global bus... |

1 | UCommunication with Automatan - Petri - 1966 |

1 | An Introduction to Probability Theory and Ita Applications - Feller - 1966 |

1 | Dynamic Probabilistic Systems - 'oward - 1971 |

1 | Introduction to Queueing Theory, Mac MiUan - Cooper - 1972 |

1 |
Analysis of the Generalized Stochastic Petri Nets by State Aggregationn
- Ammar, Liu
- 1985
(Show Context)
Citation Context ...raph labeled with the rates or weights of the transitions causing the change of marking. A different approach to the analysis of GSPN models, which also implies a different semantics, is presented in =-=[23]-=-. As a first example of a GSPN model, in Figure 9 we show the GSPN representation of the M/M/1 queue described in Section 2.3. The possibility of using an immediate transition allows the explicit repr... |