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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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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
P.R.: General distributions in process algebra. In: Lectures on formal methods and performance analysis: first EEF/Euro summer school on trends in computer science
, 2002
"... Abstract. 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 exponenti ..."
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Cited by 10 (1 self)
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Abstract. 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. 1
Performance Evaluation of Distributed Systems Based on a Discrete Real and StochasticTime Process Algebra
, 2009
"... We present a processalgebraic framework for performance evaluation of discretetime discreteevent systems. The modeling of the system builds on a process algebra with conditionallydistributed discretetime delays and generallydistributed stochastic delays. In the general case, the performance a ..."
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Cited by 2 (1 self)
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We present a processalgebraic framework for performance evaluation of discretetime discreteevent systems. The modeling of the system builds on a process algebra with conditionallydistributed discretetime delays and generallydistributed stochastic delays. In the general case, the performance analysis is done with the toolset of the modeling language χ by means of discreteevent simulation. The processalgebraic setting allows for expansion laws for the parallel composition and the maximal progress operator, so one can directly manipulate the process terms and transform the specification in a required form. This approach is illustrated by specifying and solving the recursive specification of the G/G/1/ ∞ queue, as well as by specifying a variant of the concurrent alternating bit protocol with generallydistributed unreliable channels. In a specific situation when all delays are assumed deterministic, we turn to performance analysis of probabilistic timed systems. This work employs discretetime probabilistic reward graphs, which comprise deterministic delays and immediate probabilistic choices. Here, we extend previous investigations on the topic, which only touched longrun analysis, to tackle transient analysis as well. The theoretical results obtained allow us to extend the χtoolset. For illustrative purposes, we analyze the concurrent alternating bit protocol in the extended environment of the χtoolset using discreteevent simulation for generallydistributed channels, the developed analytical method for deterministic channels, and Markovian analysis for exponentiallydistributed delays.
RealTime in Stochastic Process Algebra: . . .
 PROC. EPEW
, 2006
"... A stochastic time process algebra that deals with generally distributed delays in the style of realtime process theories is presented. Two types of race condition are distinguished to enable a compositional modeling as well as a nontrivial expansion law. The interplay of realtime and stochastic ..."
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Cited by 2 (2 self)
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A stochastic time process algebra that deals with generally distributed delays in the style of realtime process theories is presented. Two types of race condition are distinguished to enable a compositional modeling as well as a nontrivial expansion law. The interplay of realtime and stochastic time is analyzed for the standard bisimulation definitions and for the race condition. Finally, a new notion of contextsensitive interpolation is proposed that captures timeadditivity as induced by the race condition.
RealTime in Stochastic Process Algebra: Keeping Track of . . .
 PROC. EPEW 2006
"... A stochastic time process algebra that deals with generally distributed delays in the style of realtime process theories is presented. Two types of race condition are distinguished to enable a compositional modeling as well as a nontrivial expansion law. The interplay of realtime and stochastic t ..."
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Cited by 1 (1 self)
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A stochastic time process algebra that deals with generally distributed delays in the style of realtime process theories is presented. Two types of race condition are distinguished to enable a compositional modeling as well as a nontrivial expansion law. The interplay of realtime and stochastic time is analyzed for the standard bisimulation definitions and for the race condition. Finally, a new notion of contextsensitive interpolation is proposed that captures timeadditivity as induced by the race condition.
Embedding Realtime in . . .
 PROC. EPEW 2006
, 2006
"... We present a stochastic process algebra including immediate actions, deadlock and termination, and explicit stochastic delays, in the setting of weak choice between immediate actions and passage of time. The operational semantics is a spent time semantics, avoiding explicit clocks. We discuss the e ..."
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We present a stochastic process algebra including immediate actions, deadlock and termination, and explicit stochastic delays, in the setting of weak choice between immediate actions and passage of time. The operational semantics is a spent time semantics, avoiding explicit clocks. We discuss the embedding of weakchoice realtime process theories and analyze the behavior of parallel composition in the weak choice framework.
Formal Methods Group, Technische Universiteit Eindhoven
"... A realtime process algebra is presented that features stochastic delays governed by general distributions. In a setting of weak choice, dependent and independent alternative and parallel composition are distinguished. This enables an expansion law for the parallel operator, as well as modular proce ..."
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A realtime process algebra is presented that features stochastic delays governed by general distributions. In a setting of weak choice, dependent and independent alternative and parallel composition are distinguished. This enables an expansion law for the parallel operator, as well as modular process definitions. The interplay of realtime, stochastic delays and immediate actions is illustrated by a modeling of the G/G/1/ ∞ queue. 1.
Discrete RealTime and StochasticTime Process Algebra for Performance Analysis of Distributed Systems
"... We present a process algebra with conditionally distributed discretetime delays and generallydistributed stochastic delays. The treatment allows for expansion laws for the parallel composition and the maximal progress operator. The approach is illustrated by a specification of the concurrent alter ..."
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We present a process algebra with conditionally distributed discretetime delays and generallydistributed stochastic delays. The treatment allows for expansion laws for the parallel composition and the maximal progress operator. The approach is illustrated by a specification of the concurrent alternating bit protocol with generallydistributed unreliable channels in the language χ. We compare performance analysis using timed probabilistic reward graphs and discreteevent simulation. 1.
Under consideration for publication in Formal Aspects of Computing Reconciling Real and Stochastic Time: the Need for Probabilistic Refinement
"... Abstract. We conservatively extend an ACPstyle discretetime process theory with discrete stochastic delays. The semantics of the timed delays relies on time additivity and time determinism, which are properties that enable us to merge subsequent timed delays and to impose their synchronous expirat ..."
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Abstract. We conservatively extend an ACPstyle discretetime process theory with discrete stochastic delays. The semantics of the timed delays relies on time additivity and time determinism, which are properties that enable us to merge subsequent timed delays and to impose their synchronous expiration. Stochastic delays, however, interact with respect to a socalled race condition that determines the set of delays that expire first, which is guided by an (implicit) probabilistic choice. The race condition precludes the property of time additivity as the merger of stochastic delays alters this probabilistic behavior. To this end, we resolve the race condition using conditionallydistributed unit delays. We give a sound and groundcomplete axiomatization of the process theory comprising the standard set of ACPstyle operators. In this generalized setting, the alternative composition is no longer associative, so we have to resort to special normal forms that explicitly resolve the underlying race condition. Our treatment succeeds in the initial challenge to conservatively extend standard time with stochastic time. However, the ‘dissection ’ of the stochastic delays to conditionallydistributed unit delays comes at a price, as we can no longer relate the resolved race condition to the original stochastic delays. We seek a solution in the field of probabilistic refinements that enable the interchange of probabilistic and nondeterministic choices. 1.