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Stochastic transition systems for continuous state spaces and nondeterminism
 In FoSSaCS’05, LNCS 3441
, 2005
"... Abstract. We study the interaction between nondeterministic and probabilistic behaviour in systems with continuous state spaces, arbitrary probability distributions and uncountable branching. Models of such systems have been proposed previously. Here, we introduce a model that extends probabilistic ..."
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Cited by 12 (3 self)
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Abstract. We study the interaction between nondeterministic and probabilistic behaviour in systems with continuous state spaces, arbitrary probability distributions and uncountable branching. Models of such systems have been proposed previously. Here, we introduce a model that extends probabilistic automata to the continuous setting. We identify the class of schedulers that ensures measurability properties on executions, and show that such measurability properties are preserved by parallel composition. Finally, we demonstrate how these results allow us to define an alternative notion of weak bisimulation in our model. 1
Probability and Nondeterminism in Operational Models of Concurrency
 In Proc. CONCUR, LNCS
, 2006
"... Abstract. We give a brief overview of operational models for concurrent systems that exhibit probabilistic behavior, focussing on the interplay between probability and nondeterminism. Our survey is carried out from the perspective of probabilistic automata, a model originally developed for the analy ..."
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Cited by 12 (1 self)
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Abstract. We give a brief overview of operational models for concurrent systems that exhibit probabilistic behavior, focussing on the interplay between probability and nondeterminism. Our survey is carried out from the perspective of probabilistic automata, a model originally developed for the analysis of randomized distributed algorithms. 1
MODEST: A compositional modeling formalism for hard and softly timed systems
 IEEE TRANSACTIONS ON SOFTWARE ENGINEERING
"... This paper presents MODEST (MOdeling and DEscription language for Stochastic Timed systems), a formalism that is aimed to support (i) the modular description of reactive system’s behaviour while covering both (ii) functional and (iii) nonfunctional system aspects such as timing and qualityofservi ..."
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Cited by 11 (5 self)
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This paper presents MODEST (MOdeling and DEscription language for Stochastic Timed systems), a formalism that is aimed to support (i) the modular description of reactive system’s behaviour while covering both (ii) functional and (iii) nonfunctional system aspects such as timing and qualityofservice constraints in a single specification. The language contains features such as simple and structured data types, structuring mechanisms like parallel composition and abstraction, means to control the granularity of assignments, exception handling, and nondeterministic and random branching and timing. MODEST can be viewed as an overarching notation for a wide spectrum of models, ranging from labeled transition systems, to timed automata (and probabilistic variants thereof) as well as prominent stochastic processes such as (generalized semi)Markov chains and decision processes. The paper describes the design rationales and details of the syntax and semantics.
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.
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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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.
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.
Semantics, bisimulation and congruence results for a general stochastic process operator
"... f We introduce a general stochastic process operator p(d) which behaves as the process p(d) where d:D the value d is chosen from a data domain D with a probability density determined by f. We require that f is a measurable function from D to R ≥0 such that R f(d)dµD = 1. For finite or countable D th ..."
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f We introduce a general stochastic process operator p(d) which behaves as the process p(d) where d:D the value d is chosen from a data domain D with a probability density determined by f. We require that f is a measurable function from D to R ≥0 such that R f(d)dµD = 1. For finite or countable D the d∈D function f represents the probability distribution directly. For bigger domains f represents the density function. We provide a natural operational semantics for a basic process algebra with this operator and define strong stochastic timed bisimulation and general stochastic bisimulation, which due to the potential uncountable nature of D had to be generalised compared to existing notions. We introduce the notion bisimulation resilience, which restricts the use of the language, such that the bisimulation closure of measurable sets is again measurable, and argue that without such a notion stochastic process expressions make little sense. We prove that the bisimulation equivalences are congruences provided the language is bisimulation resilient. 1