A Simple Time Scale Decomposition Technique for Stochastic Process Algebras

@article{Hillston1995AST,
  title={A Simple Time Scale Decomposition Technique for Stochastic Process Algebras},
  author={Jane Hillston and Vassilis Mertsiotakis},
  journal={Comput. J.},
  year={1995},
  volume={38},
  pages={566-577}
}
Many modern computer and communication systems result in large, complex performance models. The compositional approach offered by stochastic process algebra constructs a model from submodels which are smaller and more easily understood. This gives the model a clear component-based structure. In this paper we present cases when this structure may be used to inform the solution of the model, leading to an efficient solution based on a decomposition of the underlying Markov process. The… 
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References

SHOWING 1-10 OF 27 REFERENCES
Compositional Markovian Modelling Using a Process Algebra
We introduce a stochastic process algebra, PEPA, as a high-level modelling paradigm for continuous time Markov chains (CTMC). Process algebras are mathematical theories which model concurrent systems
Towards a Product Form Solution for Stochastic Process Algebras
TLDR
Although the product form criterion derived in this paper is developed in the context of Performance Evaluation Process Algebra, the results can be easily generalised to any of the other stochastic process algebras.
Time Scale Decomposition of a Class of Generalized Stochastic Petri Net Models
A time-scale decomposition (TSD) algorithm of a class of generalized stochastic Petri net (GSPN) models of systems comprising activities whose duration differ by orders of magnitude is presented. The
A comparison of performance evaluation process algebra and generalized stochastic Petri nets
TLDR
A comparison of the two formalisms in terms of the facilities that they provide to the modeller is presented; considering both the definition and the analysis of the performance model.
Multiprocessor and Distributed System Design: The Integration of Functional Specification and Performance Analysis Using Stochastic Process Algebras
We introduce Stochastic Process Algebras as a novel approach for the structured design and analysis of both the functional behaviour and performance characteristics of parallel and distributed
Performability modeling with UltraSAN
TLDR
UltraSAN incorporates three innovations: a class of SAN-level performability variables common to both analytical and simulation solution methods, methods that use the performability-variable choice and the SAN structure to greatly reduce the size of the stochastic process required for an analytical solution.
Closed Queuing Systems with Exponential Servers
TLDR
It is found that the distribution of customers in the closed queuing system is regulated by the stage or stages with the slowest effective service rate, which means that closed systems are shown to be stochastically equivalent to open systems in which the number of customers cannot exceed N.
A compositional approach to performance modelling
TLDR
Modelling study: multi-server multi-queue systems shows strong equivalence between strong and weak isomorphism and strong bisimilarity.
Aggregation of Variables in Dynamic Systems
TLDR
In many problems of economic theory, the general Walrasian system and its more modern dynamic extensions are relatively barren of results for macroeconomics and economic policy.
Communication and concurrency
  • R. Milner
  • Computer Science
    PHI Series in computer science
  • 1989
TLDR
This chapter discusses Bisimulation and Observation Equivalence as a Modelling Communication, a Programming Language, and its application to Equational laws.
...
...