Abstract
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.
The full version of the paper is available at ftp://ftp.cs.unibo.it/pub/techreports/98-06.ps.gz. This research has been partially funded by Progetto Strategico CNR “Modelli e Metodi per la Matematica e l'lngegneria”.
Preview
Unable to display preview. Download preview PDF.
References
M. Ajmone Marsan, A. Bianco, L. Ciminiera, R. Sisto, A. Valenzano, “A LOTOS Extension for the Performance Analysis of Distributed Systems”, in IEEE/ACM Trans. on Networking 2:151–164, 1994
L. Aceto, M. Hennessy, “Adding Action Refinement to a Finite Process Algebra”, in Information and Computation 115:179–247, 1994
M. Bernardo, “An Algebra-Based Method to Associate Rewards with EMPA Terms”, in Proc. of the 24th Int. Coll. on Automata, Languages and Programming (ICALP '97), LNCS 1256:358–368, Bologna (Italy), 1997
M. Bernardo, L. Donatiello, R. Gorrieri, “A Formal Approach to the Integration of Performance Aspects in the Modeling and Analysis of Concurrent Systems”, to appear in Information and Computation, 1998
M. Bernardo, R. Gorrieri, “A Tutorial on EMPA: A Theory of Concurrent Processes with Nondeterminism, Priorities, Probabilities and Time”, to appear in Theoretical Computer Science, 1998
G. Boudol, I. Castellani, “Permutation of Transitions: An Event Structure Semantics for CCS and SCCS”, in Proc. of the Workshop on Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, LNCS 354:411–427, Noordwijkerhout (The Netherlands), 1988
M. Bravetti, M. Bernardo, R. Gorrieri, “Generalized Semi Markovian Process Algebra”, Technical Report UBLCS-97-9, University of Bologna (Italy), October 1997
N. Busi, R.J. van Glabbeek, R. Gorrieri, “Axiomatising ST-Bisimulation Equivalence”, in Proc. of the IFIP Working Conf. on Programming Concepts, Methods and Calculi (PROCOMET '94), S. Miniato (Italy), 1994
E. Brinksma, J.-P. Katoen, R. Langerak, D. Latella, “A Stochastic Causality-Based Process Algebra”, in Computer Journal 38:553–565, 1995
D. R. Cox, “The Analysis of non-Markovian Stochastic Processes by the Inclusion of Supplementary Variables”, in Proc. of the Cambridge Philosophical Society 51:433–440, 1955
P.R. D'Argenio, J.-P. Katoen, E. Brinksma, “A Stochastic Automata Model and its Algebraic. Approach” in Proc. of the 5th Workshop on Process Algebras and Performance Modelling (PAPM '97), pp. 1–16, Enschede (The Netherlands), 1997
R.J. van Glabbeek, F.W. Vaandrager, “Petri Net Models for Algebraic Theories of Concurrency”, in Proc. of the Conf. on Parallel Architectures and Languages Europe (PARLE '87), LNCS 259:224–242, Eindhoven (The Netherlands), 1987
N. Götz, U. Herzog, M. Rettelbach, “Multiprocessor and Distributed System Design: The Integration of Functional Specification and Performance Analysis Using Stochastic Process Algebras”, in Proc. of the 16th Int. Symp. on Computer Performance Modelling, Measurement and Evaluation (PERFORMANCE '93), LNCS 729:121–146, Rome (Italy), 1993
N. Götz, U. Herzog, M. Rettelbach, “TIPP — A Stochastic Process Algebra”, in Proc. of the 1st Workshop on Process Algebras and Performance Modelling (PAPM '93), pp. 31–36, Edinburgh (UK), 1993
W. Henderson, D. Lucic, “Aggregation and Disaggregation through Insensitivity in Stochastic Petri Nets”, in Performance Evaluation 17:91–114, 1993
H. Hermanns, M. Rettelbach, “Syntax, Semantics, Equivalences, and Axioms for MTIPP”, in Proc. of the 2nd Workshop on Process Algebras and Performance Modelling (PAPM '94), pp. 71–87, Erlangen (Germany), 1994
J. Hillston, “A Compositional Approach to Performance Modelling”, Cambridge University Press, 1996
C.A.R. Hoare, “Communicating Sequential Processes”, Prentice Hall, 1985
L. Kleinrock, “Queueing Systems”, John Wiley & Sons, 1975
K.G. Larsen, A. Skou, “Bisimulation through Probabilistic Testing”, in Information and Computation 94:1–28, 1991
K. Matthes, “Zur Theorie der Bedienungsprozesse”, in Trans. of the 3rd Prague Conf. on Information Theory, Stat. Dec. Fns. and Random Processes, pp. 513–528, 1962
M. Nielsen, P.S. Thiagarajan, “Degrees of Nondeterminism and Concurrency”, in Proc. of the 4th Conf. on Foundations of Software Technologies and Theoretical Computer Science, LNCS 181:89–117, 1984
C. Priami, “Stochastic π-Calculus with General Distributions”, in Proc. of the 4th Workshop on Process Algebras and Performance Modelling (PAPM '96), CLUT, pp. 41–57, Torino (Italy), 1996
C. Tofts, “Processes with Probabilities, Priority and Time”, in Formal Aspects of Computing 6:536–564, 1994
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bravetti, M., Bernardo, M., Gorrieri, R. (1998). Towards performance evaluation with general distributions in process algebras. In: Sangiorgi, D., de Simone, R. (eds) CONCUR'98 Concurrency Theory. CONCUR 1998. Lecture Notes in Computer Science, vol 1466. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055638
Download citation
DOI: https://doi.org/10.1007/BFb0055638
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-64896-3
Online ISBN: 978-3-540-68455-8
eBook Packages: Springer Book Archive