Towards Performance Evaluation with General Distributions in Process Algebras

We present a process algebra for the performance modeling and evaluation of concurrent systems whose activity durations are expressed through general probability distributions. We first determine the class of generalized semi-Markov processes (GSMPs) as being the class of stochastic processes on which we must rely for performance evaluation to be possible. Then we argue that in this context the right semantics for algebraic terms is a variant of the ST semantics which accounts for both functional and performance aspects. The GSMP based process algebra we propose is introduced together with its formal semantics, an example of performance evaluation, and a notion of probabilistic bisimulation based equivalence accounting for action durations which is shown to be a congruence.

[1]  Luca Aceto,et al.  Adding Action Refinement to a Finite Process Algebra , 1994, Inf. Comput..

[2]  Rob J. van Glabbeek,et al.  Petri Net Models for Algebraic Theories of Concurrency , 1987, PARLE.

[3]  C. A. R. Hoare,et al.  Communicating sequential processes , 1978, CACM.

[4]  Joost-Pieter Katoen,et al.  A Stochastic Automata Model and its Algebraic Approach , 1997 .

[5]  Diego Latella,et al.  A Stochastic Causality-Based Process Algebra , 1995, Comput. J..

[6]  S. Wittevrongel,et al.  Queueing Systems , 2019, Introduction to Stochastic Processes and Simulation.

[7]  Marco Ajmone Marsan,et al.  A LOTOS extension for the performance analysis of distributed systems , 1994, TNET.

[8]  Roberto Gorrieri,et al.  A Formal Approach to the Integration of Performance Aspects in the Modeling and Analysis of Concurrent Systems , 1998, Inf. Comput..

[9]  C. Priami Stochastic -calculus with General Distributions , 1996 .

[10]  D. Cox The analysis of non-Markovian stochastic processes by the inclusion of supplementary variables , 1955, Mathematical Proceedings of the Cambridge Philosophical Society.

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

[12]  Ilaria Castellani,et al.  Permutation of transitions: An event structure semantics for CCS and SCCS , 1988, REX Workshop.

[13]  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.

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

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

[16]  William Henderson,et al.  Aggregation and Disaggregation Through Insensitivity in Stochastic Petri Nets , 1993, Perform. Evaluation.

[17]  Roberto Gorrieri,et al.  Axiomatising ST-Bisimulation Equivalence , 1994, PROCOMET.

[18]  H. Hermanns,et al.  Syntax , Semantics , Equivalences , and Axioms for MTIPP y , 1994 .

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