Exploiting Modal Logic to Express Performance Measures

Stochastic process algebras such as PEPA provide ample support for the component-based construction of models. Tools compute the numerical solution of these models; however, the stochastic process algebra methodology has lacked support for the specification and calculation of complex performance measures. In this paper we present a stochastic modal logic which can aid the construction of a reward structure over the model. We discuss its relationship to the underlying theory of PEPA. We also present a performance specification language which supports high level reasoning about PEPA models, and allows queries about their equilibrium behaviour. The meaning of the specification language has its foundations in the stochastic modal logic. We describe the implementation of the logic within the PEPA Workbench and a case study is presented to illustrate the approach.

[1]  Stephen Gilmore,et al.  An Efficient Algorithm for Aggregating PEPA Models , 2001, IEEE Trans. Software Eng..

[2]  Peter G. Harrison,et al.  Performance modelling of communication networks and computer architectures , 1992, International computer science series.

[3]  Jane Hillston,et al.  A compositional approach to performance modelling , 1996 .

[4]  Kim G. Larsen,et al.  Bisimulation through Probabilistic Testing , 1991, Inf. Comput..

[5]  Howard Bowman,et al.  Analysis of a Multimedia Stream using Stochastic Process Algebra , 2001, Comput. J..

[6]  S Gilmore,et al.  An Eecient Algorithm for Aggregating Pepa Models , 1997 .

[7]  Stephen Gilmore,et al.  Specifying Performance Measures for PEPA , 1999, ARTS.

[8]  Marco Bernardo,et al.  An Algebra-Based Method to Associate Rewards with EMPA Terms , 1997, ICALP.

[9]  Norbert Götz,et al.  Multiprocessor and Distributed System Design: The Integration of Functional Specification and Performance Analysis Using Stochastic Process Algebras , 1993, Performance/SIGMETRICS Tutorials.

[10]  Robin Milner,et al.  Algebraic laws for nondeterminism and concurrency , 1985, JACM.

[11]  Stephen Gilmore,et al.  Feature interaction in PEPA , 1998 .

[12]  Luca de Alfaro,et al.  How to Specify and Verify the Long-Run Average Behavior of Probabilistic Systems , 1998, LICS.

[13]  Christel Baier,et al.  Approximate Symbolic Model Checking of Continuous-Time Markov Chains , 1999, CONCUR.

[14]  Stephen Gilmore,et al.  The PEPA Workbench: A Tool to Support a Process Algebra-based Approach to Performance Modelling , 1994, Computer Performance Evaluation.

[15]  Stephen Gilmore,et al.  Experiences with the PEPA performance modelling , 1999, IEE Proc. Softw..

[16]  Sérgio Vale Aguiar Campos,et al.  ProbVerus: Probabilistic Symbolic Model Checking , 1999, ARTS.

[17]  William H. Sanders,et al.  Stochastic Activity Networks: Structure, Behavior, and Application , 1985, PNPM.

[18]  Marco Ajmone Marsan,et al.  Modelling with Generalized Stochastic Petri Nets , 1995, PERV.

[19]  Graham Clark,et al.  Techniques for the construction and analysis of algebraic performance models , 2000 .

[20]  Philippe Jacquet,et al.  Analytical Depoissonization and its Applications , 1998, Theor. Comput. Sci..

[21]  Roberto Gorrieri,et al.  A Tutorial on EMPA: A Theory of Concurrent Processes with Nondeterminism, Priorities, Probabilities and Time , 1998, Theor. Comput. Sci..

[22]  Ronald A. Howard,et al.  Dynamic Probabilistic Systems , 1971 .

[23]  Vasiliki Hartonas-Garmhausen.  Probabilistic symbolic model checking with engineering models and applications , 1998 .

[24]  Michael Huth,et al.  Quantitative analysis and model checking , 1997, Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science.