## Stochastic Petri Net Semantics for Stochastic Process Algebras (1995)

Venue: | In Proc. 6th International Workshop on Petri Nets and Performance Models |

Citations: | 21 - 1 self |

### BibTeX

@INPROCEEDINGS{Ribaudo95stochasticpetri,

author = {Marina Ribaudo},

title = {Stochastic Petri Net Semantics for Stochastic Process Algebras},

booktitle = {In Proc. 6th International Workshop on Petri Nets and Performance Models},

year = {1995},

pages = {148--157}

}

### Years of Citing Articles

### OpenURL

### Abstract

In this paper we define a Stochastic Petri Net (SPN) semantics for Stochastic Process Algebras (SPAs), a recently introduced formalism that offers a novel approach for performance modeling. The proposed semantics is evaluated in terms of three criteria: Concurrency and Retrievability, as defined by Olderog for untimed net semantics, and Markov Equivalence for the stochastic aspects. 1 Introduction SPNs and SPAs have had somewhat of a common development. In both cases the original definitions (standard Petri nets and pure Process Algebra) did not include any temporal information, so that they were used only for the qualitative analysis of concurrent systems. The timing extensions of the basic formalisms also allowed one to study the quantitative properties of systems. In particular, in both SPNs and SPAs, negative exponentially distributed delays have been associated with the elementary events (transitions and actions), and it has been proved that both formalisms can be viewed as high...

### Citations

3609 | Communicating Sequential Processes
- Hoare
- 1985
(Show Context)
Citation Context ...d using the language constructors to obtain a model that reflects the structure of the system itself. The Calculus of Communicating Systems (CCS) [13] and the Communicating Sequential Processes (CSP) =-=[10]-=- can be considered as the starting point in this field. CCS and CSP cannot express time delays between events: action executions take zero time and only relative ordering is represented via the traces... |

3389 |
Communication and Concurrency
- Milner
- 1989
(Show Context)
Citation Context ...em is modeled in isolation. Submodels are then composed using the language constructors to obtain a model that reflects the structure of the system itself. The Calculus of Communicating Systems (CCS) =-=[13]-=- and the Communicating Sequential Processes (CSP) [10] can be considered as the starting point in this field. CCS and CSP cannot express time delays between events: action executions take zero time an... |

1616 |
Petri nets: Properties, analysis and applications
- Murata
- 1989
(Show Context)
Citation Context ...f this paper is as follows. In Section 2 we define the basic concepts concerning SPAs. Being a well known formalism SPNs are not described in detail; information on SPNs may be found, for example, in =-=[14, 15]-=-. The SPN semantics for SPAs is defined in Section 3 and some properties that the semantics must satisfy are described in Section 4. Section 5 provides a brief comparison among the different SPA langu... |

838 |
Finite Markov Chains, D
- Snell
- 1960
(Show Context)
Citation Context ... A Markov process is lumpable if it is possible to find a partition of its states such that for any two states within a partition their aggregated transition rates to any other partition are the same =-=[11]-=-. Two Markov processes are lumpable equivalent if there exists a one-to-one correspondence between the lumpable partitions of their states that preserves the aggregated transition rates. In [8] it has... |

693 |
Concurrency and automata on infinite sequences
- Park
- 1981
(Show Context)
Citation Context ...ts RG. We say that the interleaving semantics is retrievable from the SPN semantics when the DG of any PEPA model and the Reachability Graph (RG) of the corresponding SPN model are strongly bisimilar =-=[19]-=-. The strong bisimulation relation between the DG of a PEPA term and the RG of the corresponding SPN model is derived from the strong bisimulation relation over process terms [13] and is defined as fo... |

639 | A compositional approach to performance modelling
- Hillston
- 1996
(Show Context)
Citation Context ...ormance evaluation, starting from the first steps of the design. The languages that follow the stochastic approach are usually known as Stochastic Process Algebras (SPA) or Markovian Process Algebras =-=[8, 7, 3, 2]-=-. They all start from an untimed PA, extend the basic actions with exponential delays, and generate the underlying Markov process to compute performance measures on the modeled system. In the remainin... |

267 |
Event structures
- Winskel
- 1986
(Show Context)
Citation Context ...in favor of the true concurrency approach think that the interleaving model is unrealistic and they present alternative semantic models based on Petri nets [4, 24, 17, 6, 5, 18, 23], event structures =-=[25]-=-, or traces [10, 12]. We are interested in the work on the definition of a (untimed) Petri nets semantics for PA in which it is possible to associate a Petri net representation (N [[P ]]) with each pr... |

206 |
Performance analysis using stochastic petri nets
- Molloy
- 1982
(Show Context)
Citation Context ...f this paper is as follows. In Section 2 we define the basic concepts concerning SPAs. Being a well known formalism SPNs are not described in detail; information on SPNs may be found, for example, in =-=[14, 15]-=-. The SPN semantics for SPAs is defined in Section 3 and some properties that the semantics must satisfy are described in Section 4. Section 5 provides a brief comparison among the different SPA langu... |

147 | An Overview and Synthesis on Timed Process Algebras
- Nicollin, Sifakis
- 1991
(Show Context)
Citation Context ...stochastic. In the deterministic approach the possibility of finding a calculus for real time systems in the style of CCS has been investigated (for an overview, see the paper by Nicollin and Sifakis =-=[16]-=-). The main purpose of the stochastic approach is that of combining system specification and performance evaluation, starting from the first steps of the design. The languages that follow the stochast... |

127 |
Trace theory
- Mazurkiewicz
- 1986
(Show Context)
Citation Context ...true concurrency approach think that the interleaving model is unrealistic and they present alternative semantic models based on Petri nets [4, 24, 17, 6, 5, 18, 23], event structures [25], or traces =-=[10, 12]-=-. We are interested in the work on the definition of a (untimed) Petri nets semantics for PA in which it is possible to associate a Petri net representation (N [[P ]]) with each process term P . Sever... |

119 | Multiprocessor and Distributed System Design: The Integration of Functional Specification and Performance Analysis using Stochastic Process Algebras
- Götz, Herzog, et al.
- 1993
(Show Context)
Citation Context ...ormance evaluation, starting from the first steps of the design. The languages that follow the stochastic approach are usually known as Stochastic Process Algebras (SPA) or Markovian Process Algebras =-=[8, 7, 3, 2]-=-. They all start from an untimed PA, extend the basic actions with exponential delays, and generate the underlying Markov process to compute performance measures on the modeled system. In the remainin... |

53 |
An operational semantics for CSP
- Plotkin
- 1983
(Show Context)
Citation Context ...by defining an equation such as A def = P that gives the constant A the behavior of P . The formal semantics for the operators is given following the structural operational semantics style of Plotkin =-=[20]-=-. Applying the semantic rules, a transition diagram, called Derivation Graph (DG), may be associated with each PEPA term. The DG can be viewed as an alternative way for describing the behavior of the ... |

41 | Finite Representations of CCS and TCSP Programs by Automata and Petri Nets - Taubner - 1989 |

37 |
On a Markovian Process Algebra
- Buchholz
- 1994
(Show Context)
Citation Context ...ormance evaluation, starting from the first steps of the design. The languages that follow the stochastic approach are usually known as Stochastic Process Algebras (SPA) or Markovian Process Algebras =-=[8, 7, 3, 2]-=-. They all start from an untimed PA, extend the basic actions with exponential delays, and generate the underlying Markov process to compute performance measures on the modeled system. In the remainin... |

36 |
A distributed operational semantics for CCS based on condition/event systems
- Degano, Nicola, et al.
- 1988
(Show Context)
Citation Context ... in which this option is not present. Those in favor of the true concurrency approach think that the interleaving model is unrealistic and they present alternative semantic models based on Petri nets =-=[4, 24, 17, 6, 5, 18, 23]-=-, event structures [25], or traces [10, 12]. We are interested in the work on the definition of a (untimed) Petri nets semantics for PA in which it is possible to associate a Petri net representation ... |

22 |
Operational Petri Nets Semantics for CCSP
- Olderog
- 1987
(Show Context)
Citation Context ... in which this option is not present. Those in favor of the true concurrency approach think that the interleaving model is unrealistic and they present alternative semantic models based on Petri nets =-=[4, 24, 17, 6, 5, 18, 23]-=-, event structures [25], or traces [10, 12]. We are interested in the work on the definition of a (untimed) Petri nets semantics for PA in which it is possible to associate a Petri net representation ... |

20 | L.: MPA: A Stochastic Process Algebra
- Bernardo, Gorrieri, et al.
- 1994
(Show Context)
Citation Context |

18 |
On Representing CCS Programs by Finite Petri Nets
- Goltz
- 1988
(Show Context)
Citation Context ... in which this option is not present. Those in favor of the true concurrency approach think that the interleaving model is unrealistic and they present alternative semantic models based on Petri nets =-=[4, 24, 17, 6, 5, 18, 23]-=-, event structures [25], or traces [10, 12]. We are interested in the work on the definition of a (untimed) Petri nets semantics for PA in which it is possible to associate a Petri net representation ... |

18 |
On the relationship of CCS and Petri nets
- Goltz, Mycroft
(Show Context)
Citation Context |

15 |
The nature of the synchronization
- Hillston
- 1994
(Show Context)
Citation Context ...the model can be completely different depending on the chosen language. An interesting discussion about the implications due to the choice of a particular kind of synchronization rate can be found in =-=[9]-=-. If we consider, for instance, the example P def = (ff; r):P \Delta fffg (ff; r):P already discussed (see Fig. 8) we can compute the following rates for successive recursive steps. PEPA MTIPP 1) R mi... |

8 |
On the Relationship between Stochastic Petri Nets and Stochastic Process Algebras
- Ribaudo
- 1995
(Show Context)
Citation Context ... general translation for the CCS recursion introducing places labeled with variables. Such a translation cannot be directly applied to PEPA terms because of the lack of an explicit recursive operator =-=[22]-=-. Definition 6 Recursion The net modeling the term P def = (ff 1 ; r 1 ) : : : (ff n ; r n ):P is obtained starting from the net N 1 = (P 1 ; T 1 ; F 1 ;s1 ; M 0;1 ; l 1 ) modeling (ff 1 ; r 1 ) : : :... |

6 | Describing queueing systems with MPA
- Bernardo, Donatiello, et al.
- 1994
(Show Context)
Citation Context ...ovides an abstract framework for the comparison of the different languages [22]. The mapping of SPA models into SPNs offers a way to derive different representations (global versus distributed models =-=[1]-=-) of the same system. The problem of the apparent rate computation we encountered during the translation of the PEPA cooperation points out the differences that exist between the global state, typical... |

6 |
Nets, Terms and Formulas, volume 23 of Cambridge Tracts
- Olderog
- 1991
(Show Context)
Citation Context |

6 | Understanding Stochastic Process Algebras via their Stochastic Petri Net Semantics
- Ribaudo
- 1994
(Show Context)
Citation Context ...them may constitute a starting point for investigating the existing relationship. In this paper we thus show how to map the basic operators of SPAs into SPN models. This work extends a previous paper =-=[21]-=- in which the semantics was given by means of small examples. The balance of this paper is as follows. In Section 2 we define the basic concepts concerning SPAs. Being a well known formalism SPNs are ... |

2 |
Glabbeek and Frits Vaandrager. Petri nets models for algebraic theory of concurrency
- van
- 1987
(Show Context)
Citation Context |