Results 1  10
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14
Model checking probabilistic timed automata with one or two clocks
 In TACAS 2007, volume 4424 of LNCS
, 2007
"... Abstract. Probabilistic timed automata are an extension of timed automata with discrete probability distributions. We consider modelchecking algorithms for the subclasses of probabilistic timed automata which have one or two clocks. Firstly, we show that PCTL probabilistic modelchecking problems ( ..."
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Cited by 27 (7 self)
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Abstract. Probabilistic timed automata are an extension of timed automata with discrete probability distributions. We consider modelchecking algorithms for the subclasses of probabilistic timed automata which have one or two clocks. Firstly, we show that PCTL probabilistic modelchecking problems (such as determining whether a set of target states can be reached with probability at least 0.99 regardless of how nondeterminism is resolved) are PTIMEcomplete for one clock probabilistic timed automata, and are EXPTIMEcomplete for probabilistic timed automata with two clocks. Secondly, we show that the modelchecking problem for the probabilistic timed temporal logic PTCTL is EXPTIMEcomplete for one clock probabilistic timed automata. However, the corresponding modelchecking problem for the subclass of PTCTL which does not permit both (1) punctual timing bounds, which require the occurrence of an event at an exact time point, and (2) comparisons with probability bounds other than 0 or 1, is PTIMEcomplete. 1
On ZoneBased Analysis of Duration Probabilistic Automata
"... We propose an extension of the zonebased algorithmics for analyzing timed automata to handle systems where timing uncertainty is considered as probabilistic rather than settheoretic. We study duration probabilistic automata (DPA), expressing multiple parallel processes admitting memoryfull continu ..."
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Cited by 9 (4 self)
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We propose an extension of the zonebased algorithmics for analyzing timed automata to handle systems where timing uncertainty is considered as probabilistic rather than settheoretic. We study duration probabilistic automata (DPA), expressing multiple parallel processes admitting memoryfull continuouslydistributed durations. For this model we develop an extension of the zonebased forward reachability algorithm whose successor operator is a density transformer, thus providing a solution to verification and performance evaluation problems concerning acyclic DPA (or the boundedhorizon behavior of cyclic DPA). 1
Symbolic Analysis for GSMP Models with One Stateful Clock ⋆
"... Abstract. We consider the problem of verifying reachability properties of stochastic realtime systems modeled as generalized semiMarkov processes (GSMPs). The standard simulationbased techniques for GSMPs are not adequate for solving verification problems, and existing symbolic techniques either ..."
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Cited by 7 (0 self)
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Abstract. We consider the problem of verifying reachability properties of stochastic realtime systems modeled as generalized semiMarkov processes (GSMPs). The standard simulationbased techniques for GSMPs are not adequate for solving verification problems, and existing symbolic techniques either require memoryless distributions for firing times, or approximate the problem using discrete time or bounded horizon. In this paper, we present a symbolic solution for the case where firing times are random variables over a rich class of distributions, but only one event is allowed to retain its firing time when a discrete change occurs. The solution allows us to compute the probability that such a GSMP satisfies a property of the form “can the system reach a target, while staying within a set of safe states”. We report on illustrative examples and their analysis using our procedure. 1
Probabilistic Model Checking of nonMarkovian Models with Concurrent Generally Distributed Timers
"... Abstract—In the analysis of stochastic concurrent timed models, probabilistic model checking combines qualitative identification of feasible behaviors with quantitative evaluation of their probability. If the stochastic process underlying the model is a Continuous Time Markov Chain (CTMC), the probl ..."
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Cited by 4 (2 self)
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Abstract—In the analysis of stochastic concurrent timed models, probabilistic model checking combines qualitative identification of feasible behaviors with quantitative evaluation of their probability. If the stochastic process underlying the model is a Continuous Time Markov Chain (CTMC), the problem can be solved by leveraging on the memoryless property of exponential distributions. However, when multiple generally distributed timers can be concurrently enabled, the underlying process may become a Generalized Semi Markov Process (GSMP) for which simulation is often advocated as the only viable approach to evaluation. The method of stochastic state classes provides a means for the analysis of models belonging to this class, that relies on the derivation of multivariate joint distributions of times to fire supported over Difference Bounds Matrix (DBM) zones. Transient stochastic state classes extend the approach with an additional age clock associating each state with the distribution of the time at which it can be reached. We show how transient stochastic state classes can be used to perform bounded probabilistic model checking also for models with underlying GSMPs, and we characterize the conditions for termination of the resulting algorithm, both in exact and approximate evaluation. We also show how the number of classes enumerated to complete the analysis can be largely reduced through a lookahead in the nondeterministic state class graph of reachable DBM zones. As notable traits, the proposed technique accepts efficient implementation based on DBM zones without requiring the split of domains in regions, and it expresses the bound in terms of a bilateral constraint on the elapsed time without requiring assumptions on the discrete number of executed transitions. Experimental results based on a preliminary implementation in the Oris tool are reported. Index Terms—Generalized SemiMarkov Process, NonMarkovian Stochastic Petri net, probabilistic model checking, stochastic state class, DBM zones. I.
Performance evaluation of schedulers in a probabilistic setting
 In FORMATS
, 2011
"... Abstract. We show how to evaluate the performance of solutions to finitehorizon scheduling problems where task durations are specified by bounded uniform distributions. Our computational technique, based on computing the volumes of zones, constitutes a contribution to the computational study of sc ..."
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Abstract. We show how to evaluate the performance of solutions to finitehorizon scheduling problems where task durations are specified by bounded uniform distributions. Our computational technique, based on computing the volumes of zones, constitutes a contribution to the computational study of scheduling under uncertainty and stochastic systems in general. 1
Fixeddelay Events in Generalized SemiMarkov Processes Revisited?
"... Abstract. We study long run average behavior of generalized semiMarkov processes with both fixeddelay events as well as variabledelay events. We show that allowing two fixeddelay events and one variabledelay event may cause an unstable behavior of a GSMP. In particular, we show that a frequen ..."
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Cited by 2 (0 self)
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Abstract. We study long run average behavior of generalized semiMarkov processes with both fixeddelay events as well as variabledelay events. We show that allowing two fixeddelay events and one variabledelay event may cause an unstable behavior of a GSMP. In particular, we show that a frequency of a given state may not be defined for almost all runs (or more generally, an invariant measure may not exist). We use this observation to disprove several results from literature. Next we study GSMP with at most one fixeddelay event combined with an arbitrary number of variabledelay events. We prove that such a GSMP always possesses an invariant measure which means that the frequencies of states are always well defined and we provide algorithms for approximation of these frequencies. Additionally, we show that the positive results remain valid even if we allow an arbitrary number of reasonably restricted fixeddelay events. 1
As Soon as Probable: Optimal Scheduling under Stochastic Uncertainty
"... Abstract. In this paper we continue our investigation of stochastic (and hence dynamic) variants of classical scheduling problems. Such problems can be modeled as duration probabilistic automata (DPA), a wellstructured class of acyclic timed automata where temporal uncertainty is interpreted as a b ..."
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Cited by 1 (0 self)
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Abstract. In this paper we continue our investigation of stochastic (and hence dynamic) variants of classical scheduling problems. Such problems can be modeled as duration probabilistic automata (DPA), a wellstructured class of acyclic timed automata where temporal uncertainty is interpreted as a bounded uniform distribution of task durations [18]. In [12] we have developed a framework for computing the expected performance of a given scheduling policy. In the present paper we move from analysis to controller synthesis and develop a dynamicprogramming style procedure for automatically synthesizing (or approximating) expected time optimal schedulers, using an iterative computation of a stochastic timetogo function over the state and clock space of the automaton. 1
Transient Analysis of Networks of Stochastic Timed Automata Using Stochastic State Classes
"... Abstract. Stochastic Timed Automata (STA) associate logical locations with continuous, generally distributed sojourn times. In this paper, we introduce Networks of Stochastic Timed Automata (NSTA), where the components interact with each other by message broadcasts. This results in an underlying st ..."
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Abstract. Stochastic Timed Automata (STA) associate logical locations with continuous, generally distributed sojourn times. In this paper, we introduce Networks of Stochastic Timed Automata (NSTA), where the components interact with each other by message broadcasts. This results in an underlying stochastic process whose state is made of the vector of logical locations, the remaining sojourn times, and the value of clocks. We characterize this general state space Markov process through transient stochastic state classes that sample the state and the absolute age after each event. This provides an algorithmic approach to transient analysis of NSTAmodels, with fairly general termination conditions which we characterize with respect to structural properties of individual components that can be checked through straightforward algorithms. 1
Symbolic Analysis for GSMP Models with One
"... We consider the problem of verifying reachability properties of stochastic realtime systems modeled as generalized semiMarkov processes (GSMPs). The standard simulationbased techniques for GSMPs are not adequate for solving verification problems, and existing symbolic techniques either require me ..."
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We consider the problem of verifying reachability properties of stochastic realtime systems modeled as generalized semiMarkov processes (GSMPs). The standard simulationbased techniques for GSMPs are not adequate for solving verification problems, and existing symbolic techniques either require memoryless distributions for firing times, or approximate the problem using discrete time or bounded horizon. In this paper, we present a symbolic solution for the case where firing times are random variables over a rich class of distributions, but only one event is allowed to retain its firing time when a discrete change occurs. The solution allows us to compute the probability that such a GSMP satisfies a property of the form “can the system reach a target, while staying within a set of safe states”. We report on illustrative examples and their analysis using our procedure.