## Applying Quasi-Separability to Markovian Process Algebra (1998)

Venue: | University of Verona |

Citations: | 8 - 4 self |

### BibTeX

@INPROCEEDINGS{Thomas98applyingquasi-separability,

author = {Nigel Thomas and Stephen Gilmore},

title = {Applying Quasi-Separability to Markovian Process Algebra},

booktitle = {University of Verona},

year = {1998}

}

### Years of Citing Articles

### OpenURL

### Abstract

Stochastic process algebras have become an accepted part of performance modelling over recent years. Because of the advantages of compositionality and flexibility they are increasingly being used to model larger and more complex systems. Therefore tools which support the evaluation of models expressed using stochastic process algebra must be able to utilise the full range of decomposition and solution techniques available. In this paper we study a class of models which do not give rise to a product form solution but can nevertheless be decomposed into their components without loss of generality. We also exemplify the use of the Markovian process algebra PEPA with the spectral expansion technique which enables a class of PEPA models with infinite state space to be solved numerically. 1 Introduction The advantages of using a stochastic process algebra to specify performance models are well documented (see Hillston [9] for example). In brief, a process algebra allows models to be compare...

### Citations

644 | A Compositional Approach to Performance Modelling
- Hillston
- 1996
(Show Context)
Citation Context ... of PEPA models with infinite state space to be solved numerically. 1 Introduction The advantages of using a stochastic process algebra to specify performance models are well documented (see Hillston =-=[9]-=- for example). In brief, a process algebra allows models to be compared e.g. for equivalence; to be analysed e.g. to reveal deadlocks or reducible structures; to be constructed at a higher level of ab... |

161 | The PEPA workbench: a tool to support a process algebra-based approach to performance modelling
- Gilmore, Hillston
- 1994
(Show Context)
Citation Context ...uses some of the routines which were developed for the PEPA Workbench together with static analysis routines taken from the PEPA-to-Ada translator. Descriptions of those tools are available elsewhere =-=[3, 4]-=-. The static analysis routines are used in the inference of the interfaces which model components present to the rest of the system and also in determining the smallest cooperation sets for each pair ... |

49 |
Spectral expansion solution for a class of Markov models: application and comparison with the matrix-geometric method. Performance Evaluation
- Mitrani, Chakka
- 1995
(Show Context)
Citation Context ...lution by Spectral Expansion There are several methods by which a model such as the one described here can be solved. One such method is spectral expansion [2] and some evidence has been suggested in =-=[14]-=- which favours its use in this case. In addition spectral expansion has previously been used with the stochastic process algebra TIPP [15]. The results derived for TIPP and spectral expansion are read... |

43 | The nature of synchronisation
- Hillston
- 1994
(Show Context)
Citation Context ...oth components (shared activities). These activities are only enabled in P \Delta L Q when they are enabled in both P and Q. The published MPAs differ on how the rate of shared activities are defined =-=[8]-=-. In PEPA the shared activity occurs at the rate of the slowest participant. If an activity has an unspecified rate in a component, the component is passive with respect to that action type. This mean... |

31 | TIPP | a language for timed processes and performance evaluation - Gotz, Herzog, et al. - 1992 |

30 |
Towards a Product Form Solution for Stochastic Process Algebras
- Sereno
- 1995
(Show Context)
Citation Context ... be specified, but also how complex systems can be simplified and solved automatically. One part of this research has been the study of process algebra models that give rise to product form solutions =-=[6, 10, 17]-=-. However, the class of performance models exhibiting product form is limited. In addition it is not always necessary to derive a full product form decomposition. Some stochastic process algebra work ... |

22 | Product Form Solution for a Class of PEPA Models
- Hillston, Thomas
- 1999
(Show Context)
Citation Context ... be specified, but also how complex systems can be simplified and solved automatically. One part of this research has been the study of process algebra models that give rise to product form solutions =-=[6, 10, 17]-=-. However, the class of performance models exhibiting product form is limited. In addition it is not always necessary to derive a full product form decomposition. Some stochastic process algebra work ... |

13 |
Routing Among Different Nodes Where Servers Break Down Without Losing Jobs
- Thomas, Mitrani
- 1995
(Show Context)
Citation Context ...echnique has been used in the study of systems which suffer breakdowns. Very little work has been done involving breakdowns affecting more than one queue. Notable exceptions to this are Mitrani et al =-=[16, 20]-=- and Mikou et al [12, 13], none of which give rise to product form solutions. However, in [16] and [20] the models were shown to be quasi-separable. Because of that property, one can determine exactly... |

10 |
A numerical solution method for multiprocessor systems with general breakdowns and repairs
- Chakka, Mitrani
- 1992
(Show Context)
Citation Context ...e spectral expansion solution method. 4.3 Solution by Spectral Expansion There are several methods by which a model such as the one described here can be solved. One such method is spectral expansion =-=[2]-=- and some evidence has been suggested in [14] which favours its use in this case. In addition spectral expansion has previously been used with the stochastic process algebra TIPP [15]. The results der... |

10 | From SPA models to programs
- Gilmore, Hillston, et al.
- 1996
(Show Context)
Citation Context ...uses some of the routines which were developed for the PEPA Workbench together with static analysis routines taken from the PEPA-to-Ada translator. Descriptions of those tools are available elsewhere =-=[3, 4]-=-. The static analysis routines are used in the inference of the interfaces which model components present to the rest of the system and also in determining the smallest cooperation sets for each pair ... |

9 | TIPP and the spectral expansion method
- Mitrani, Ost, et al.
- 1995
(Show Context)
Citation Context ... this is that it is very easy to informally specify queueing problems using a common understanding amongst queueing theorists. However, stochastic process algebras provide and "easy to use" =-=interface [15]-=- as well as a formal basis for the analysis and solution of complex stochastic systems. Many examples appear in the literature of queues specified using stochastic process algebras. For the most part ... |

7 |
Exploiting Quasi-reversible Structures to find Product Form Solutions in MPA Models
- Harrison, Hillston
(Show Context)
Citation Context ... be specified, but also how complex systems can be simplified and solved automatically. One part of this research has been the study of process algebra models that give rise to product form solutions =-=[6, 10, 17]-=-. However, the class of performance models exhibiting product form is limited. In addition it is not always necessary to derive a full product form decomposition. Some stochastic process algebra work ... |

6 | Describing queueing systems with MPA
- Bernardo, Donatiello, et al.
- 1994
(Show Context)
Citation Context ...erties of the process algebra. However, a few papers do exist that use stochastic process algebra to study more complex queueing systems, amongst these are Herzog and Mertsiotakis [7], Bernardo et al =-=[1]-=- and Thomas and Hillston [18, 19]. In the following sections we will give a brief overview of the Markovian process algebra PEPA, introduce the concept of quasi-separability, define the model we wish ... |

6 | Stochastic process algebras applied to failure modelling
- Herzog, Mertsiotakis
- 1994
(Show Context)
Citation Context ...illustrate some properties of the process algebra. However, a few papers do exist that use stochastic process algebra to study more complex queueing systems, amongst these are Herzog and Mertsiotakis =-=[7]-=-, Bernardo et al [1] and Thomas and Hillston [18, 19]. In the following sections we will give a brief overview of the Markovian process algebra PEPA, introduce the concept of quasi-separability, defin... |

6 | Using Markovian process algebra to specify interactions in queueing systems
- Thomas, Hillston
- 1997
(Show Context)
Citation Context ...a. However, a few papers do exist that use stochastic process algebra to study more complex queueing systems, amongst these are Herzog and Mertsiotakis [7], Bernardo et al [1] and Thomas and Hillston =-=[18, 19]-=-. In the following sections we will give a brief overview of the Markovian process algebra PEPA, introduce the concept of quasi-separability, define the model we wish to study using PEPA and show how ... |

5 |
A two-node Jacksonâ€™s network subject to breakdowns
- Mikou
- 1988
(Show Context)
Citation Context ... the study of systems which suffer breakdowns. Very little work has been done involving breakdowns affecting more than one queue. Notable exceptions to this are Mitrani et al [16, 20] and Mikou et al =-=[12, 13]-=-, none of which give rise to product form solutions. However, in [16] and [20] the models were shown to be quasi-separable. Because of that property, one can determine exactly the performance measures... |

4 |
Two Processors Only Interacting During Breakdown: The Case Where the Load is Not Lost", submitted for publication
- Idrissi-Kacemi, Mikou, et al.
(Show Context)
Citation Context ... the study of systems which suffer breakdowns. Very little work has been done involving breakdowns affecting more than one queue. Notable exceptions to this are Mitrani et al [16, 20] and Mikou et al =-=[12, 13]-=-, none of which give rise to product form solutions. However, in [16] and [20] the models were shown to be quasi-separable. Because of that property, one can determine exactly the performance measures... |

2 |
A Syntactic Analysis of Reversible PEPA
- Hillston, Thomas
- 1998
(Show Context)
Citation Context ...ys necessary to derive a full product form decomposition. Some stochastic process algebra work on product form has been based on widely known cases of product form solution in queueing network models =-=[6, 11]-=-. In this paper we consider an alternative method of model decomposition which can be found in the queueing network literature, quasi-separability. This technique has been used in the study of systems... |

2 |
Markovian Queueing Systems modelled with PEPA
- Thomas, Hillston
- 1998
(Show Context)
Citation Context ...a. However, a few papers do exist that use stochastic process algebra to study more complex queueing systems, amongst these are Herzog and Mertsiotakis [7], Bernardo et al [1] and Thomas and Hillston =-=[18, 19]-=-. In the following sections we will give a brief overview of the Markovian process algebra PEPA, introduce the concept of quasi-separability, define the model we wish to study using PEPA and show how ... |