# Exploiting Quasi-reversible Structures in Markovian Process Algebra Models

@article{Harrison1995ExploitingQS, title={Exploiting Quasi-reversible Structures in Markovian Process Algebra Models}, author={Peter G. Harrison and Jane Hillston}, journal={Comput. J.}, year={1995}, volume={38}, pages={510-520} }

Efficient product form solution is one of the major attractions of queueing networks for performance modelling purposes. These models rely on a form of interaction between nodes in a network which allows them to be solved in isolation, since they behave as if independent up to normalisation. Markovian process algebras (MPA) extend classical process algebras with information about the duration of actions but retain their compositional structure: a system is modelled as an interaction of…

## 55 Citations

### A two-level decomposition scheme for Markovian process algebra models

- Mathematics, Computer Science
- 2009

This work proposes a novel approach to solve MPA models which explicitly exploits the concurrent nature of the given model, and derives a novel result on cumulative measures of absorbing joint Markov chains.

### A Syntactical Analysis of Reversible PEPA

- Mathematics
- 1998

Product form solutions have played an important role in the development of performance modelling and in particular in the popularity of queueing network models. The notions of reversibility and…

### On the relations among product-form stochastic models

- Computer Science
- 2009

Two results, the M ⇒ M property and the Reversed Compound Agent Theorem (RCAT) are used to explore the relations among several product-form model classes belonging to different formalisms: queueing networks (QN), stochastic Petri nets (SPN), generalized stochasia nets (GSPn), Markovian Process Algebra (MPA), and it is proved that previous results on product- form SPNs can be studied using RCAT.

### Lumping and reversed processes in cooperating automata

- Computer Science, MathematicsAnn. Oper. Res.
- 2012

A notion of typed lumpability is introduced, which gives sufficient conditions under which a lumping of the process can be derived, allowing the exact computation of marginal stationary probabilities of the cooperating components.

### Applying Quasi-Separability to Markovian Process Algebra

- Mathematics
- 1998

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 is studied.

### Time Scale Decomposition of Stochastic Process Algebra Models

- Mathematics, Computer Science
- 1997

This work presents a major advancement related to a preliminary version of this technique already presented at a workshop of this series, and develops a transformation technique based on a delayed choice operator and preserves equivalence.

### Product form solution for an insensitive stochastic process algebra structure

- MathematicsPerform. Evaluation
- 2002

### Product form solution for a class of PEPA models

- Computer ScienceProceedings. IEEE International Computer Performance and Dependability Symposium. IPDS'98 (Cat. No.98TB100248)
- 1998

It is shown that PEPA models that generate such processes may be readily identified and show how the product form solution may be obtained and can be easily generalised to any of the other stochastic process algebra languages.

### Stochastic Process Algebra Structure for Insensitivity

- Mathematics, Computer Science
- 1999

A construction which guarantees the insensitivity of certain concurrently enabled non-connicting stochastic process algebra activities is described, and a derived combinator is given for constructing process algebra models that do not match any of those currently known to exist for stochastically process algebra.

### Using Markovian Process Algebra to Specify Interactions in Queueing Systems

- Mathematics
- 1997

It is shown that the most common interactive behaviours found in queueing systems can be modelled simply in a Markovian process algebra, and discusses how such specifications can lead to an automated numerical solution method.

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