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A framework to design and solve Markov Decision Wellformed Net models
"... The Markov Decision Process (MDP) [7] formalism is widely used for modeling systems which exhibit both non deterministic and probabilistic behaviors (e.g. distributed systems, resource management systems,...). ..."
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The Markov Decision Process (MDP) [7] formalism is widely used for modeling systems which exhibit both non deterministic and probabilistic behaviors (e.g. distributed systems, resource management systems,...).
Non deterministic Repairable Fault Trees for computing optimal repair strategy
"... In this paper, the Non deterministic Repairable Fault Tree (NdRFT) formalism is proposed: it allows to model failure modes of complex systems as well as their repair processes. The originality of this formalism with respect to other Fault Tree extensions is that it allows to face repair strategies o ..."
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In this paper, the Non deterministic Repairable Fault Tree (NdRFT) formalism is proposed: it allows to model failure modes of complex systems as well as their repair processes. The originality of this formalism with respect to other Fault Tree extensions is that it allows to face repair strategies optimization problems: in an NdRFT model, the decision on whether to start or not a given repair action is non deterministic, so that all the possibilities are left open. The formalism is rather powerful allowing to specify which failure events are observable, whether local repair or global repair can be applied, and the resources needed to start a repair action. The optimal repair strategy can then be computed by solving an optimization problem on a Markov Decision Process (MDP) derived from the NdRFT. A software framework is proposed in order to perform in automatic way the derivation of an MDP from a NdRFT model, and to deal with the solution of the MDP.
Partial Stochastic Characterization of Timed Runs over DBM
 Domains,” Proc. Ninth Int’l Workshop Performability Modeling of Computer and Comm. Systems
, 2009
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Parametric NdRFT for the derivation of optimal repair strategies
"... Non deterministic Repairable Fault Trees (NdRFT) are a recently proposed modeling formalism for the study of optimal repair strategies: they are based on the widely adopted Fault Tree formalism, but in addition to the failure modes, NdRFTs allow to define possible repair actions. In a previous paper ..."
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Cited by 4 (3 self)
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Non deterministic Repairable Fault Trees (NdRFT) are a recently proposed modeling formalism for the study of optimal repair strategies: they are based on the widely adopted Fault Tree formalism, but in addition to the failure modes, NdRFTs allow to define possible repair actions. In a previous paper the formalism has been introduced together with an analysis method and a tool allowing to automatically derive the best repair strategy to be applied in each state. The analysis technique is based on the generation and solution of a Markov Decision Process. In this paper we present an extension, ParNdRFT, that allows to exploit the presence of redundancy to reduce the complexity of the model and of the analysis. It is based on the translation of the ParNdRFT into a Markov Decision WellFormed Net, i.e. a model specified by means of an High Level Petri Net formalism. The translated model can be efficiently solved thanks to existing algorithms that generate a reduced state space automatically exploiting the model symmetries.
Multiple abstraction levels in performance analysis of WSN monitoring systems
 In Proc. of the WSNperf (Satellite Workshop of VALUETOOLS09
, 2009
"... In this paper we illustrate the use of different methods to support the design of a Wireless Sensor Network (WSN), by using as a case study a monitoring system that must track a moving object within a given area. The goal of the study is to find a good trade off between the power consumption and the ..."
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In this paper we illustrate the use of different methods to support the design of a Wireless Sensor Network (WSN), by using as a case study a monitoring system that must track a moving object within a given area. The goal of the study is to find a good trade off between the power consumption and the object tracking reliability. Power saving can be achieved by periodically powering off some of the nodes for a given time interval. Of course nodes can detect the moving object only when they are on, so that the power management strategy can affect the ability to accurately track the object movements. We propose two models and the corresponding analysis and simulation tools, that can be used in a synergistic way: the first model is based on the Markov Decision Wellformed Net (MDWN) formalism while the second one is based on the Stochastic Activity Network (SAN) formalism. The MDWN model is more abstract and is used to compute an optimal power management strategy by solving a Markov Decision Process (MDP); the SAN model is more detailed and is used to perform extensive simulation (using the Möbius tool) in order to analyze different performance indices, both when applying the power management policy derived from the first model and when using different policies.
Computing optimal repair strategies by means of NdRFT modeling and analysis, The Computer Journal Available online
"... In this paper, the Nondeterministic Repairable Fault Tree (NdRFT) formalism is proposed: it allows the modeling of failures of complex systems in addition to their repair processes. Its originality with respect to other Fault Tree extensions allows us to address repair strategy optimization problem ..."
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In this paper, the Nondeterministic Repairable Fault Tree (NdRFT) formalism is proposed: it allows the modeling of failures of complex systems in addition to their repair processes. Its originality with respect to other Fault Tree extensions allows us to address repair strategy optimization problems: in an NdRFT model, the decision as to whether to start or not a given repair action is nondeterministic, so that all the possibilities are left open. The formalism is rather powerful, it allows: the specification of selfrevealing events, the representation of components degradation, the choice among local repair, global repair, preventive maintenance, and the specification of the resources needed to start a repair action. The optimal repair strategy with respect to some relevant system state function, e.g. system unavailability, can then be computed by solving an optimization problem on a Markov Decision Process derived from the NdRFT. Such derivation is obtained by converting the NdRFT model into an intermediate formalism called Markov Decision Petri Net (MDPN). In the paper, the NdRFT syntax and semantics are formally described, together with the conversion rules to derive from the NdRFT the corresponding MDPN model. The application of NdRFT is illustrated through examples.
MDWNsolver: A Framework to Design and Solve Markov Decision Petri Nets
, 2011
"... MDWNsolver is a framework for system modeling and optimization of performability measures based on Markov Decision Petri Net (MDPN) and Markov Decision Wellformed Net (MDWN) formalisms, two Petri Net extensions for high level specification of Markov Decision Processes (MDP). It is integrated in th ..."
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MDWNsolver is a framework for system modeling and optimization of performability measures based on Markov Decision Petri Net (MDPN) and Markov Decision Wellformed Net (MDWN) formalisms, two Petri Net extensions for high level specification of Markov Decision Processes (MDP). It is integrated in the GreatSPN suite which provides a GUI to design MDPN/MDWN models. From the analysis point of view, MDWNsolver uses efficient algorithms that take advantage of system symmetries, thus reducing the analysis complexity. In this paper the MDWNsolver framework features and architecture are presented, and some application examples are discussed.
Markov Decision Petri Nets with Uncertainty
"... Abstract. Markov Decision Processes (MDPs) are a well known mathematical formalism that combines probabilities with decisions and allows one to compute optimal sequences of decisions, denoted as policies, for fairly large models in many situations. However, the practical application of MDPs is oft ..."
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Abstract. Markov Decision Processes (MDPs) are a well known mathematical formalism that combines probabilities with decisions and allows one to compute optimal sequences of decisions, denoted as policies, for fairly large models in many situations. However, the practical application of MDPs is often faced with two problems: the specification of large models in an efficient and understandable way, which has to be combined with algorithms to generate the underlying MDP, and the inherent uncertainty on transition probabilities and rewards, of the resulting MDP. This paper introduces a new graphical formalism, called Markov Decision Petri Net with Uncertainty (MDPNU), that extends the Markov Decision Petri Net (MDPN) formalism, which has been introduced to define MDPs. MDPNUs allow one to specify MDPs where transition probabilities and rewards are defined by intervals rather than constant values. The resulting process is a Bounded Parameter MDP (BMDP). The paper shows how BMDPs are generated from MDPNUs, how analysis methods can be applied and which results can be derived from the models.
CHAPTER 1 MODELING AND VERIFICATION OF DISTRIBUTED SYSTEMS USING MARKOV DECISION PROCESSES
"... The Markov Decision Process (MDP) formalism is a wellknown mathematical formalism to study systems with unknown scheduling mechanisms or with transitions whose nextstate probability distribution is not known with precision. Analysis methods for MDPs are based generally on the identification of t ..."
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The Markov Decision Process (MDP) formalism is a wellknown mathematical formalism to study systems with unknown scheduling mechanisms or with transitions whose nextstate probability distribution is not known with precision. Analysis methods for MDPs are based generally on the identification of the strategies that maximize (or minimize) a target function based on the MDP’s rewards (or costs). Alternatively, formal languages can be defined to express quantitative properties that we want to be ensured by an MDP, including those which extend classical temporal logics with probabilistic operators.
Performance Optimization for a Class of Generalized Stochastic Petri Nets
"... Abstract — This paper considers the problem of optimizing the (longterm) performance of operations that are modeled by Generalized Stochastic Petri nets. The proposed methodology employs the representational power of the GSPN framework in order to articulate an explicit tradeoff between the comput ..."
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Abstract — This paper considers the problem of optimizing the (longterm) performance of operations that are modeled by Generalized Stochastic Petri nets. The proposed methodology employs the representational power of the GSPN framework in order to articulate an explicit tradeoff between the computational tractability of the formulated problem and the operational efficiency of the derived solutions. On the other hand, the solution of the considered formulations is based on recent results regarding the sensitivity analysis of Markov reward processes. A more expansive treatment of the presented results, together with a case study that highlights the relevance of the considered problem and the efficacy of the proposed methodology, can be found in a companion document that is accessible from the website of the second author. I.