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Analysis of Software Rejuvenation using Markov Regenerative Stochastic Petri Net
, 1995
"... In a clientserver type system, the server software is required to run continuously for very long periods. Due to repeated and potentially faulty usage by many clients, such software "ages" with time and eventually fails. Huang et. al. proposed a technique called "software rejuvenatio ..."
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Cited by 53 (22 self)
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In a clientserver type system, the server software is required to run continuously for very long periods. Due to repeated and potentially faulty usage by many clients, such software "ages" with time and eventually fails. Huang et. al. proposed a technique called "software rejuvenation" [9] in which the software is periodically stopped and then restarted in a "robust" state after proper maintenance. This "renewal" of software prevents (or at least postpones) the crash failure. As the time lost (or the cost incurred) due to the software failure is typically more than the time lost (or the cost incurred) due to rejuvenation, the technique reduces the expected unavailability of the software. In this paper, we present a quantitative analysis of software rejuvenation. The behavior of the system is represented through a Markov Regenerative Stochastic Petri Net (MRSPN) model which is solved both for steady state as well as transient conditions. We provide a closedform analytical solution for ...
Transient Analysis of Markov Regenerative Stochastic Petri Nets: A Comparison of Approaches
 In 6th International Conference on Petri Nets and Performance Models  PNPM95
, 1995
"... In this paper we present and compare two different approaches for the transient solution of Markov regenerative stochastic Petri Nets: the method based on Markov regenerative theory and the method of supplementary variables. In both cases the equations that govern the marking process of the nonMark ..."
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Cited by 30 (12 self)
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In this paper we present and compare two different approaches for the transient solution of Markov regenerative stochastic Petri Nets: the method based on Markov regenerative theory and the method of supplementary variables. In both cases the equations that govern the marking process of the nonMarkovian stochastic Petri net are presented and then solved either in timedomain or using a LaplaceStieltjes transformation. We develop expressions for asymptotic computational costs and storage requirements. We also perform experimental studies to compare accuracy, time, and space complexity of the methods. 1 Introduction Stochastic Petri nets (SPNs) are well suited for the modelbased performance and dependability evaluation of complex systems. In the past few years, several papers were published dealing with the transient and stationary analysis of nonMarkovian SPNs in which, under certain structural restrictions, the firing times may be generally distributed. Besides the approach of ap...
Logical and stochastic modeling with SMART
, 2003
"... We describe the main features of SmArT, a software package providing a seamless environment for the logic and probabilistic analysis of complex systems. SmArT can combine dierent formalisms in the same modeling study. For the analysis of logical behavior, both explicit and symbolic statespace g ..."
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Cited by 29 (16 self)
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We describe the main features of SmArT, a software package providing a seamless environment for the logic and probabilistic analysis of complex systems. SmArT can combine dierent formalisms in the same modeling study. For the analysis of logical behavior, both explicit and symbolic statespace generation techniques, as well as symbolic CTL modelchecking algorithms, are available. For the study of stochastic and timing behavior, both sparsestorage and Kronecker numerical solution approaches are available when the underlying process is a Markov chain. In addition,
DISCRETETIME MARKOVIAN STOCHASTIC PETRI NETS
, 1995
"... We revisit and extend the original definition of discretetime stochastic Petri nets, by allowing the firing times to have a “defective discrete phase distribution”. We show that this formalism still corresponds to an underlying discretetime Markov chain. The structure of the state for this process ..."
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Cited by 27 (8 self)
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We revisit and extend the original definition of discretetime stochastic Petri nets, by allowing the firing times to have a “defective discrete phase distribution”. We show that this formalism still corresponds to an underlying discretetime Markov chain. The structure of the state for this process describes both the marking of the Petri net and the phase of the firing time for of each transition, resulting in a large state space. We then modify the wellknown power method to perform a transient analysis even when the state space is infinite, subject to the condition that only a finite number of states can be reached in a finite amount of time. Since the memory requirements might still be excessive, we suggest a bounding technique based on truncation.
New results for the analysis of deterministic and stochastic Petri nets
 In International Computer Performance and Dependability Symposium  IPDS95
, 1995
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A Modeling Framework to Implement Preemption Policies in NonMarkovian SPNs
 IEEE TRANSACTIONS ON SOFTWARE ENGINEERING
, 2000
"... ... this paper, we consider, in particular, the class of stochastic Petri nets whose marking process can be mapped into a Markov regenerative process. An adequate mathematical framework is developed to deal with the considered class of Markov Regenerative Stochastic Petri Nets (#####). An unified ..."
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Cited by 22 (4 self)
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... this paper, we consider, in particular, the class of stochastic Petri nets whose marking process can be mapped into a Markov regenerative process. An adequate mathematical framework is developed to deal with the considered class of Markov Regenerative Stochastic Petri Nets (#####). An unified approach for the solution of #####s where different preemption policies can be defined in the same model is presented. The solution is provided both in steadystate and in transient condition. An example concludes the paper.
E.: StateDensity Functions over DBM Domains in the Analysis of NonMarkovian Models
 IEEE Trans. on SW Eng
, 2009
"... Abstract—Quantitative evaluation of models with generally distributed transitions requires the analysis of nonMarkovian processes that may be not isomorphic to their underlying untimed models and may include any number of concurrent nonexponential timers. The analysis of stochastic Time Petri Nets ..."
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Cited by 22 (17 self)
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Abstract—Quantitative evaluation of models with generally distributed transitions requires the analysis of nonMarkovian processes that may be not isomorphic to their underlying untimed models and may include any number of concurrent nonexponential timers. The analysis of stochastic Time Petri Nets (sTPNs) copes with the problem by covering the state space with stochastic classes, which extend the theory of Difference Bounds Matrix (DBM) with a state probability density function. As a core step, the analysis process requires symbolic manipulation of density functions supported over DBM domains. We characterize and engineer the critical steps of this derivation. We first show that the statedensity function accepts a continuous piecewise representation over a partition in DBMshaped subdomains. We then develop a closedform symbolic calculus of statedensity functions under the assumption that transitions in the sTPN model have expolynomial distributions over possibly bounded intervals. The calculus shows that within each subdomain, the statedensity function is a multivariate expolynomial function, and it makes explicit the way in which this form evolves and grows in complexity as the state accumulates memory through subsequent transitions. This enables an efficient implementation of the analysis process and provides the formal basis that supports the introduction of an imprecise analysis based on the approximation of statedensity functions through Bernstein Polynomials. The approximation attacks practical and theoretical limits in the applicability of stochastic state classes and devises a new approach to the analysis of nonMarkovian models, relying on approximations in the state space rather than in the structure of the model. Index Terms—Correctness verification, performance and dependability, quantitative evaluation, stochastic Time Petri nets, densetime statespace analysis, Difference Bounds Matrix, Markov Renewal Theory, approximate statespace representation, density function approximation, Bernstein polynomials. Ç 1
Recent Developments in NonMarkovian Stochastic Petri Nets
, 1998
"... Analytical modeling plays a crucial role in the analysis and design of computer systems. Stochastic Petri Nets represent a powerful paradigm, widely used for such modeling in the context of dependability, performance and performability. Many structural and stochastic extensions have been proposed in ..."
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Cited by 22 (4 self)
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Analytical modeling plays a crucial role in the analysis and design of computer systems. Stochastic Petri Nets represent a powerful paradigm, widely used for such modeling in the context of dependability, performance and performability. Many structural and stochastic extensions have been proposed in recent years to increase their modeling power, or their capability to handle large systems. This paper reviews recent developments by providing the theoretical background and the possible areas of application. Markovian Petri nets are first considered together with very well established extensions known as Generalized Stochastic Petri nets and Stochastic Reward Nets. Key ideas for coping with large state spaces are then discussed. The challenging area of nonMarkovian Petri nets is considered, and the related analysis techniques are surveyed together with the detailed elaboration of an example. Finally new models based on Continuous or Fluid Stochastic Petri Nets are briefly discussed.
Preemptive Repeat Identical Transitions in Markov Regenerative Stochastic Petri Nets
 In 6th International Conference on Petri Nets and Performance Models  PNPM95
, 1995
"... The recent literature on Markov Regenerative Stochastic Petri Nets (MRSPN) assumes that the random firing time associated to each transition is resampled each time the transition fires or is disabled by the firing of a competitive transition. This modeling assumption does not cover the case of preem ..."
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Cited by 22 (14 self)
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The recent literature on Markov Regenerative Stochastic Petri Nets (MRSPN) assumes that the random firing time associated to each transition is resampled each time the transition fires or is disabled by the firing of a competitive transition. This modeling assumption does not cover the case of preemption mechanisms of repeat identical nature (pri). In this policy, an interrupted job must be repeated with an identical requirement so that its associated random variable must not be resampled. The paper investigates the implication of a pri policy into a MRSPN and describes an analytical procedure for the derivation of expressions for the transient probabilities. Key words: Stochastic Petri Nets, SemiMarkov Reward Models, Markov regenerative processes, preemptive repeat identical policy. 1 Introduction The analysis of stochastic systems with nonexponential timing is of increasing interest in the literature and requires the development of suitable modeling tools. Choi et al. have shown ...