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36
Process Algebras for Quantitative Analysis
, 2005
"... 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 m ..."
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Cited by 49 (6 self)
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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.
MoDeST  A Modelling and Description Language for Stochastic Timed Systems
, 2001
"... This paper presents a modelling language, called MoDeST, for describingth beh viour of discrete event systems.Th language combines conventional programming constructs  such as iteration, alternatives, atomic statements, and exception hceptio with means to describe complexsystems in a ..."
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Cited by 24 (9 self)
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This paper presents a modelling language, called MoDeST, for describingth beh viour of discrete event systems.Th language combines conventional programming constructs  such as iteration, alternatives, atomic statements, and exception hceptio with means to describe complexsystems in a compositional manner. In addition, MoDeST incorporates means to describe important ph[flL8xI such as nondeterminism, probabilistic branchanc and hdx realtime as well as soft realtime (i.e., stoch8Lfl'fl aspects.Th language is influenced by popular and userfriendly specification languages such as Promela, and dealswith compositionality in aligh tweigh t processalgebra style.Th us, MoDeST (i) covers a very broad spectrum of modelling concepts, (ii) possesses a rigid, processalgebra style semantics, and (iii) yet provides modern and flexible specification constructs.
Tutte le algebre insieme: Concepts, discussions and relations of stochastic process algebras with general distributions
 In Validation of Stochastic Systems
, 2004
"... Abstract. We report on the state of the art in the formal specification and analysis of concurrent systems whose activity duration depends on general probability distributions. First of all the basic notions and results introduced in the literature are explained and, on this basis, a conceptual clas ..."
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Cited by 18 (5 self)
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Abstract. We report on the state of the art in the formal specification and analysis of concurrent systems whose activity duration depends on general probability distributions. First of all the basic notions and results introduced in the literature are explained and, on this basis, a conceptual classification of the different approaches is presented. We observe that most of the approaches agree on the fact that the specification of systems with general distributions has a three level structure: the process algebra level, the level of symbolic semantics and the level of concrete semantics. Based on such observations, a new very expressive model is introduced for representing timed systems with general distributions. We show that many of the approaches in the literature can be mapped into this model establishing therefore a formal framework to compare these approaches. 1
Revisiting interactive Markov chains
 In Proc. Models for TimeCritical Systems
, 2002
"... 1 Introduction The advantages of using process algebras for the performance modeling and evaluation of concurrent systems due to their feature of compositionality have been widely recognized (see [12,2,18,9,5,3] and the references therein). Particularly simple and successful has been the extension o ..."
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Cited by 17 (1 self)
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1 Introduction The advantages of using process algebras for the performance modeling and evaluation of concurrent systems due to their feature of compositionality have been widely recognized (see [12,2,18,9,5,3] and the references therein). Particularly simple and successful has been the extension of standard process algebras with time delays whose duration follows an exponential probability distribution, called Markovian process algebras (see e.g. [12,2,18,9]). The &quot;timed &quot; behavior of systems specified with a Markovian process algebra can represented by a continuous time Markov chain (CTMC), i.e. a simple continuous time stochastic process where in each time point the future behavior of
A compositional semantics for Dynamic Fault Trees in terms of Interactive Markov Chains
"... Abstract. Dynamic fault trees (DFTs) are a versatile and common formalism to model and analyze the reliability of computerbased systems. This paper presents a formal semantics of DFTs in terms of input/output interactive Markov chains (I/OIMCs), which extend continuoustime Markov chains with disc ..."
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Cited by 16 (9 self)
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Abstract. Dynamic fault trees (DFTs) are a versatile and common formalism to model and analyze the reliability of computerbased systems. This paper presents a formal semantics of DFTs in terms of input/output interactive Markov chains (I/OIMCs), which extend continuoustime Markov chains with discrete input, output and internal actions. This semantics provides a rigorous basis for the analysis of DFTs. Our semantics is fully compositional, that is, the semantics of a DFT is expressed in terms of the semantics of its elements (i.e. basic events and gates). This enables an efficient analysis of DFTs through compositional aggregation, which helps to alleviate the statespace explosion problem by incrementally building the DFT state space. We have implemented our methodology by developing a tool, and showed, through four case studies, the feasibility of our approach and its effectiveness in reducing the state space to be analyzed. Fault trees (FTs) [20], also called static FTs, provide a highlevel, graphical formalism
Deciding and axiomatizing weak ST bisimulation for a process algebra with recursion and action refinement
 ACM Transactions on Computational Logic
, 2002
"... 1. INTRODUCTION ST semantics, originally defined in [van Glabbeek and Vaandrager 1987] over Petri Nets, is one of the most studied noninterleaving semantics. The main reason is that ST semantics is the less informative semantics that is a congruence for ..."
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Cited by 14 (6 self)
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1. INTRODUCTION ST semantics, originally defined in [van Glabbeek and Vaandrager 1987] over Petri Nets, is one of the most studied noninterleaving semantics. The main reason is that ST semantics is the less informative semantics that is a congruence for
General distributions in process algebra
 IN: LECTURES ON FORMAL METHODS AND PERFORMANCE ANALYSIS: FIRST EEF/EURO SUMMER SCHOOL ON TRENDS IN COMPUTER SCIENCE
, 2001
"... This paper is an informal tutorial on stochastic process algebras, i.e., process calculi where action occurrences may be subject to a delay that is governed by a (mostly continuous) random variable. Whereas most stochastic process algebras consider delays determined by negative exponential distr ..."
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Cited by 11 (1 self)
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This paper is an informal tutorial on stochastic process algebras, i.e., process calculi where action occurrences may be subject to a delay that is governed by a (mostly continuous) random variable. Whereas most stochastic process algebras consider delays determined by negative exponential distributions, this tutorial is concerned with the integration of general, nonexponential distributions into a process algebraic setting. We discuss the issue of incorporating such distributions in an interleaving semantics, and present some existing solutions to this problem. In particular, we present a process algebra for the specification of stochastic discreteevent systems modeled as generalized semiMarkov chains (GSMCs). Using this language stochastic discreteevent systems can be described in an abstract and modular way. The operational semantics of this process algebra is given in terms of stochastic automata, a novel mixture of timed automata and GSMCs. We show that GSMCs are a proper subset of stochastic automata, discuss various notions of equivalence, present congruence results, treat equational reasoning, and argue how an expansion law in the process algebra can be obtained. As a case study, we specify the root contention phase within the standardized IEEE 1394 serial bus protocol and study the delay until root contention resolution. An overview of related work on general distributions in process algebra and a discussion of trends and future work complete this tutorial.
Pamr: A Process Algebra For The Management Of Resources In Concurrent Systems
, 2001
"... In this paper we present a process algebra for the management of resources in concurrent systems. Our aim is to define a formal framework that can help in the task of specifying systems that depend, for their execution, on a set of resources that they use. Usually, systems consist in a set of proces ..."
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Cited by 9 (1 self)
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In this paper we present a process algebra for the management of resources in concurrent systems. Our aim is to define a formal framework that can help in the task of specifying systems that depend, for their execution, on a set of resources that they use. Usually, systems consist in a set of processes. In order to improve their performance, these processes will be able to exchange resources among them. In our language, processes will consist in a behavior (formalized as a LOTOS process) and in information about the resources that they own. Systems will be defined as the parallel composition of a set of processes. We will study some examples applying the features of PAMR. These examples will try to show the usefulness of our language for specifying and analyzing concurrent systems where resources play an important role.
Product Form Solution for an Insensitive Stochastic Process Algebra Structure
, 2002
"... Recent research has investigated ways in which generally distributed random variables may be incorporated into stochastic process algebra. These proposals allow the arbitrary use of such variables, improving expressibility, but in general this makes performance evaluation di#cult. Typically, simulat ..."
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Cited by 9 (5 self)
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Recent research has investigated ways in which generally distributed random variables may be incorporated into stochastic process algebra. These proposals allow the arbitrary use of such variables, improving expressibility, but in general this makes performance evaluation di#cult. Typically, simulation techniques must be employed. We attack the goal of generally distributed random variables from the opposite direction, using the stochastic property of insensitivity. In this paper we describe a construction which guarantees the insensitivity of certain concurrently enabled nonconflicting stochastic process algebra activities. We give a derived combinator for constructing process algebra models. Use of this combinator guarantees that the stochastic process underlying the model is insensitive to a particular set of activities. Therefore, the user need not assume these activities are exponentially distributed, yet may still use familiar Markovian techniques to solve the model. We find that the model structure we identify has a product form solution and the criteria we list do not match any of those currently proposed for stochastic process algebra. We highlight our technique with an example drawn from the field of transaction processing systems. Our analysis uses the stochastic process algebra PEPA, and its associated conventions. 1
Axiomatizing ST Bisimulation for a Process Algebra with Recursion and Action Refinement (Extended Abstract)
, 1999
"... ) 1 Mario Bravetti, Roberto Gorrieri Dipartimento di Scienze dell'Informazione Universit`a di Bologna Mura Anteo Zamboni 7, 40127 Bologna, Italy Email: fbravetti, gorrierig@cs.unibo.it Abstract Due to the complex nature of bisimulation equivalences which express some form of history de ..."
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Cited by 7 (5 self)
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) 1 Mario Bravetti, Roberto Gorrieri Dipartimento di Scienze dell'Informazione Universit`a di Bologna Mura Anteo Zamboni 7, 40127 Bologna, Italy Email: fbravetti, gorrierig@cs.unibo.it Abstract Due to the complex nature of bisimulation equivalences which express some form of history dependence, it turned out to be problematic to axiomatize them for non trivial classes of systems. Here we introduce the idea of "compositional levelwise renaming" which gives rise to the new possibility of axiomatizing the class of history dependent bisimulations with slight modifications to the machinery for standard bisimulation. We propose two techniques, which are based on this idea, in the special case of the ST semantics, defined for terms of a process algebra with recursion. The first technique, which is more intuitive, is based on dynamic names, allowing weak ST bisimulation to be decided and axiomatized for all processes that possess a finite state interleaving semantics. The second techn...