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339
Model Checking for a Probabilistic Branching Time Logic with Fairness
 Distributed Computing
, 1998
"... We consider concurrent probabilistic systems, based on probabilistic automata of Segala & Lynch [55], which allow nondeterministic choice between probability distributions. These systems can be decomposed into a collection of "computation trees" which arise by resolving the nondeterm ..."
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Cited by 131 (41 self)
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We consider concurrent probabilistic systems, based on probabilistic automata of Segala & Lynch [55], which allow nondeterministic choice between probability distributions. These systems can be decomposed into a collection of "computation trees" which arise by resolving the nondeterministic, but not probabilistic, choices. The presence of nondeterminism means that certain liveness properties cannot be established unless fairness is assumed. We introduce a probabilistic branching time logic PBTL, based on the logic TPCTL of Hansson [30] and the logic PCTL of [55], resp. pCTL of [14]. The formulas of the logic express properties such as "every request is eventually granted with probability at least p". We give three interpretations for PBTL on concurrent probabilistic processes: the first is standard, while in the remaining two interpretations the branching time quantifiers are taken to range over a certain kind of fair computation trees. We then present a model checking algorithm for...
A tutorial on EMPA: A theory of concurrent processes with nondeterminism, priorities, probabilities and time
 Theoretical Computer Science
, 1998
"... In this tutorial we give an overview of the process algebra EMPA, a calculus devised in order to model and analyze features of realworld concurrent systems such as nondeterminism, priorities, probabilities and time, with a particular emphasis on performance evaluation. The purpose of this tutorial ..."
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Cited by 117 (11 self)
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In this tutorial we give an overview of the process algebra EMPA, a calculus devised in order to model and analyze features of realworld concurrent systems such as nondeterminism, priorities, probabilities and time, with a particular emphasis on performance evaluation. The purpose of this tutorial is to explain the design choices behind the development of EMPA and how the four features above interact, and to show that a reasonable trade off between the expressive power of the calculus and the complexity of its underlying theory has been achieved.
On probabilistic model checking
, 1996
"... Abstract. This tutorial presents an overview of model checking for both discrete and continuoustime Markov chains (DTMCs and CTMCs). Model checking algorithms are given for verifying DTMCs and CTMCs against specifications written in probabilistic extensions of temporal logic, including quantitative ..."
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Cited by 107 (25 self)
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Abstract. This tutorial presents an overview of model checking for both discrete and continuoustime Markov chains (DTMCs and CTMCs). Model checking algorithms are given for verifying DTMCs and CTMCs against specifications written in probabilistic extensions of temporal logic, including quantitative properties with rewards. Example properties include the probability that a fault occurs and the expected number of faults in a given time period. We also describe the practical application of stochastic model checking with the probabilistic model checker PRISM by outlining the main features supported by PRISM and three realworld case studies: a probabilistic security protocol, dynamic power management and a biological pathway. 1
Reachability analysis of probabilistic systems by successive refinements
 Proc. 1st Joint International Workshop on Process Algebra and Probabilistic Methods, Performance Modeling and Veri (PAPM/PROBMIV'01), volume 2165 of LNCS
, 2001
"... Abstract. We report on a novel development to model check quantitative reachability properties on Markov decision processes together with its prototype implementation. The innovation of the technique is that the analysis is performed on an abstraction of the model under analysis. Such an abstraction ..."
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Cited by 73 (3 self)
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Abstract. We report on a novel development to model check quantitative reachability properties on Markov decision processes together with its prototype implementation. The innovation of the technique is that the analysis is performed on an abstraction of the model under analysis. Such an abstraction is significantly smaller than the original model and may safely refute or accept the required property. Otherwise, the abstraction is refined and the process repeated. As the numerical analysis necessary to determine the validity of the property is more costly than the refinement process, the technique profits from applying such numerical analysis on smaller state spaces.
Implementation of Symbolic Model Checking for Probabilistic Systems
, 2002
"... In this thesis, we present ecient implementation techniques for probabilistic model checking, a method which can be used to analyse probabilistic systems such as randomised distributed algorithms, faulttolerant processes and communication networks. A probabilistic model checker inputs a probabilist ..."
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Cited by 72 (21 self)
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In this thesis, we present ecient implementation techniques for probabilistic model checking, a method which can be used to analyse probabilistic systems such as randomised distributed algorithms, faulttolerant processes and communication networks. A probabilistic model checker inputs a probabilistic model and a speci cation, such as \the message will be delivered with probability 1", \the probability of shutdown occurring is at most 0.02" or \the probability of a leader being elected within 5 rounds is at least 0.98", and can automatically verify if the speci cation is true in the model.
Stochastic Hybrid Systems: Application to Communication Networks
 in Hybrid Systems: Computation and Control, ser. Lect. Notes in Comput. Science
, 2004
"... Abstract. We propose a model for Stochastic Hybrid Systems (SHSs) where transitions between discrete modes are triggered by stochastic events much like transitions between states of a continuoustime Markov chains. However, the rate at which transitions occur is allowed to depend both on the continu ..."
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Cited by 68 (14 self)
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Abstract. We propose a model for Stochastic Hybrid Systems (SHSs) where transitions between discrete modes are triggered by stochastic events much like transitions between states of a continuoustime Markov chains. However, the rate at which transitions occur is allowed to depend both on the continuous and the discrete states of the SHS. Based on results available for PiecewiseDeterministic Markov Process (PDPs), we provide a formula for the extended generator of the SHS, which can be used to compute expectations and the overall distribution of the state. As an application, we construct a stochastic model for onoff TCP flows that considers both the congestionavoidance and slowstart modes and takes directly into account the distribution of the number of bytes transmitted. Using the tools derived for SHSs, we model the dynamics of the moments of the sending rate by an infinite system of ODEs, which can be truncated to obtain an approximate finitedimensional model. This model shows that, for transfersize distributions reported in the literature, the standard deviation of the sending rate is much larger than its average. Moreover, the later seems to vary little with the probability of packet drop. This has significant implications for the design of congestion control mechanisms. 1
Discounting the future in systems theory
 In Automata, Languages, and Programming, LNCS 2719
, 2003
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Compositionality for probabilistic automata
 In Proc. 14th International Conference on Concurrency Theory (CONCUR 2003), volume 2761 of LNCS
, 2003
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How to Specify and Verify the LongRun Average Behavior of Probabilistic Systems
 In Proc. LICS'98
, 1998
"... Longrun average properties of probabilistic systems refer to the average behavior of the system, measured over a period of time whose length diverges to infinity. These properties include many relevant performance and reliability indices, such as system throughput, average response time, and mean t ..."
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Cited by 60 (3 self)
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Longrun average properties of probabilistic systems refer to the average behavior of the system, measured over a period of time whose length diverges to infinity. These properties include many relevant performance and reliability indices, such as system throughput, average response time, and mean time between failures. In this paper, we argue that current formal specification methods cannot be used to specify longrun average properties of probabilistic systems. To enable the specification of these properties, we propose an approach based on the concept of experiments. Experiments are labeled graphs that can be used to describe behavior patterns of interest, such as the request for a resource followed by either a grant or a rejection. Experiments are meant to be performed infinitely often, and it is possible to specify their longrun average outcome or duration. We propose simple extensions of temporal logics based on experiments, and we present modelchecking algorithms for the verif...