Process algebras for quantitative analysis

In the 1980s process algebras became widely accepted formalisms for describing and analysing concurrency. Extensions of the formalisms, incorporating some aspects of systems which had previously been abstracted, were developed for a number of different purposes. In the area of performance analysis models must quantify both timing and probability. Addressing this domain led to the formulation of stochastic process algebras. In this paper we give a brief overview of stochastic process algebras and the problems which motivated them, before focussing on their relationship with the underlying mathematical stochastic process. This is presented in the context of the PEPA formalism.

[1]  K. Mani Chandy,et al.  Open, Closed, and Mixed Networks of Queues with Different Classes of Customers , 1975, JACM.

[2]  Leonard Kleinrock,et al.  Queueing Systems: Volume I-Theory , 1975 .

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

[4]  Iso. Lotos,et al.  A Formal Description Technique Based on the Temporal Ordering of Observational Behaviour , 1985 .

[5]  C. Ryff.  Happiness is everything, or is it? Explorations on the meaning of psychological well-being. , 1989 .

[6]  Ulrich Herzog,et al.  Formal Description, Time and Performance Analysis. A Framework , 1990, Entwurf und Betrieb verteilter Systeme.

[7]  E. Gelenbe.  Product-form queueing networks with negative and positive customers , 1991 .

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

[9]  Erol Gelenbe,et al.  G-Networks with multiple class negative and positive customers , 1994, Proceedings of International Workshop on Modeling, Analysis and Simulation of Computer and Telecommunication Systems.

[10]  J. Hillston.  The nature of synchronisation , 1994 .

[11]  Richard J. Boucherie.  A Characterization of Independence for Competing Markov Chains with Applications to Stochastic Petri Nets , 1994, IEEE Trans. Software Eng..

[12]  R. Boucherie,et al.  A Characterisation of Independence for Competing Markov Chains with Applications to Stochastic Petri Nets a Characterisation of Independence for Competing Markov Chains with Applications to Stochastic Petri Nets , 1994 .

[13]  C. Keyes,et al.  The structure of psychological well-being revisited , 1995 .

[14]  Peter G. Harrison,et al.  Exploiting Quasi-reversible Structures in Markovian Process Algebra Models , 1995, Comput. J..

[15]  Corrado Priami,et al.  Stochastic pi-Calculus , 1995, Comput. J..

[16]  J. Hillston.  Compositional Markovian Modelling Using a Process Algebra , 1995 .

[17]  C. Ryff.  Psychological Well-Being in Adult Life , 1995 .

[18]  Robert Holton,et al.  A PEPA Specification of an Industrial Production Cell , 1995, Comput. J..

[19]  Peter G. Harrison,et al.  Detecting reversibility in Markovian Process Algebras , 1996 .

[20]  Robert K. Brayton,et al.  Verifying Continuous Time Markov Chains , 1996, CAV.

[21]  Marta Kwiatkowska,et al.  Analysing Performance of Lift Systems in PEPA , 1996 .

[22]  J. Hillston.  Exploiting Structure in Solution: Decomposing Composed Models , 1998 .

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

[24]  A Syntactical Analysis of Reversible PEPA , 1998 .

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

[26]  William H. Sanders,et al.  An Efficient Disk-Based Tool for Solving Large Markov Models , 1998, Perform. Evaluation.

[27]  M. Siegle,et al.  Multi Terminal Binary Decision Diagrams to Represent and Analyse Continuous Time Markov Chains , 1999 .

[28]  Jane Hillston,et al.  Product Form Solution for a Class of PEPA Models , 1999, Perform. Evaluation.

[29]  Pedro R. D'Argenio,et al.  Algebras and Automata for Timed and Stochastic Systems , 1999 .

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

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

[32]  Peter G. Harrison,et al.  SPADES - a process algebra for discrete event simulation , 2000, J. Log. Comput..

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

[34]  Jane Hillston,et al.  An Efficient Kronecker Representation for PEPA Models , 2001, PAPM-PROBMIV.

[35]  Joost-Pieter Katoen,et al.  MoDeST - A Modelling and Description Language for Stochastic Timed Systems , 2001, PAPM-PROBMIV.

[36]  Mario Bravetti,et al.  The theory of interactive generalized semi-Markov processes , 2002, Theor. Comput. Sci..

[37]  Marta Z. Kwiatkowska,et al.  PRISM: Probabilistic Symbolic Model Checker , 2002, Computer Performance Evaluation / TOOLS.

[38]  C. Keyes,et al.  Optimizing Well-Being: The Empirical Encounter of Two Traditions , 2002 .

[39]  Holger Hermanns,et al.  Interactive Markov Chains , 2002, Lecture Notes in Computer Science.

[40]  Jane Hillston,et al.  Product form solution for an insensitive stochastic process algebra structure , 2002, Perform. Evaluation.

[41]  Christel Baier,et al.  Model checking performability properties , 2002, Proceedings International Conference on Dependable Systems and Networks.

[42]  Stephen Gilmore,et al.  Performance modelling with UML and stochastic process algebras , 2002 .

[43]  C. Keyes,et al.  The measurement and utility of adult subjective well-being. , 2003 .

[44]  C. R. Snyder,et al.  Positive Psychological Assessment: A Handbook of Models and Measures , 2003 .

[45]  Stephen Gilmore,et al.  Performance modelling with the Unified Modelling Language and stochastic process algebras , 2003 .

[46]  Marta Z. Kwiatkowska,et al.  Model checking for probability and time: from theory to practice , 2003, 18th Annual IEEE Symposium of Logic in Computer Science, 2003. Proceedings..

[47]  Peter G. Harrison,et al.  Turning back time in Markovian process algebra , 2003, Theor. Comput. Sci..

[48]  J. Hillston,et al.  Analysing Web Service Composition with PEPA , 2004 .

[49]  Jeremy T. Bradley,et al.  Expressing performance requirements using regular expressions to specify stochastic probes over process algebra models , 2004, WOSP '04.

[50]  James R. Jackson,et al.  Jobshop-Like Queueing Systems , 2004, Manag. Sci..

[51]  Flemming Nielson,et al.  A calculus for control flow analysis of security protocols , 2004, International Journal of Information Security.

[52]  B. Nordstrom.  FINITE MARKOV CHAINS , 2005 .

[53]  I. McDowell,et al.  Psychological Well-being , 2006 .

[54]  M. Bravetti,et al.  From EMPA to GSMPA : Allowing for General DistributionsMario Bravetti , 2007 .

[55]  U. Herzog,et al.  Stochastic Process Algebras Applied to Failure Modelling , 2007 .