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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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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...
New results for the analysis of deterministic and stochastic Petri nets
 In International Computer Performance and Dependability Symposium  IPDS95
, 1995
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Transient Analysis of Deterministic and Stochastic Petri Nets with TimeNET
 Lecture Notes in Computer Science Vol. 977: Quantitative Evaluation of Computing and Communication Systems
, 1995
"... . This paper descibes the transient analysis component for deterministic and stochastic Petri nets which has recently been added to the software package TimeNET. The technique is based on the derivation of state equations by the method of supplementary variables. The system of equations consists of ..."
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. This paper descibes the transient analysis component for deterministic and stochastic Petri nets which has recently been added to the software package TimeNET. The technique is based on the derivation of state equations by the method of supplementary variables. The system of equations consists of partial and ordinary differential equations which are combined with initial and boundary conditions. Algorithms for the numerical analysis of the equations are presented. Emphasis is put on implementation aspects. Different cases are identified for which different variants of the algorithms can be used. The computational complexity is investigated by asymptotical expressions and by measurements. Several examples are used in order to illustrate the modeling process and transient analysis with TimeNET. 1 Introduction Stochastic Petri nets (SPNs) are well suited for the modelbased performance and dependability evaluation. Most commonly, the firing times of the transitions are exponentially di...
Stochastic dependability analysis of system architecture based on uml models
 Architecting Dependable Systems, LNCS–2667
, 2003
"... Abstract. The work in this paper 1 is devoted to the definition of a dependability modeling and model based evaluation approach based on UML models. It is to be used in the early phases of the system design to capture system dependability attributes like reliability and availability, thus providing ..."
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Cited by 24 (4 self)
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Abstract. The work in this paper 1 is devoted to the definition of a dependability modeling and model based evaluation approach based on UML models. It is to be used in the early phases of the system design to capture system dependability attributes like reliability and availability, thus providing guidelines for the choice among different architectural and design solutions. We show how structural UML diagrams can be processed to filter out the dependability related information and how a systemwide dependability model is constructed. Due to the modular construction, this model can be refined later as more detailed information becomes available. We discuss the model refinement based on the General Resource Model, an extension of UML. We show that the dependability model can be constructed automatically by using graph transformation techniques. 1
Model Checking Timed and Stochastic Properties with CSL^TA
, 2008
"... Markov chains are a wellknown stochastic process that provide a balance between being able to adequately model the system’s behavior and being able to afford the cost of the model solution. Systems can be modelled directly as Markov chains, or with a higherlevel formalism for which Markov chains r ..."
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Cited by 23 (6 self)
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Markov chains are a wellknown stochastic process that provide a balance between being able to adequately model the system’s behavior and being able to afford the cost of the model solution. Systems can be modelled directly as Markov chains, or with a higherlevel formalism for which Markov chains represent the underlying semantics. Markov chains are widely used to study the performance of computer and telecommunication systems. The definition of stochastic temporal logics like Continuous Stochastic Logic (CSL) and its variant asCSL, and of their modelchecking algorithms, allows a unified approach to the verification of systems, allowing the mix of performance evaluation and probabilistic verification. In this paper we present the stochastic logic CSL TA, which is more expressive than CSL and asCSL, and in which properties can be specified using automata (more precisely, timed automata with a single clock). The extension with respect to expressiveness allows the specification of properties referring to the probability of a finite sequence of timed events. A typical example is the responsiveness property “with probability at least 0.75, a message sent at time 0 by a system A will be received before time 5 by system B and the acknowledgment will be back at A before time 7”, a property that cannot be expressed in either CSL or asCSL. Furthermore, the choice of using automata rather than the classical temporal operators Next and Until should help in enlarging the accessibility of model checking to a larger public. We also present a modelchecking algorithm for CSL TA. 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.
Techniques for the Construction and Analysis of Algebraic Performance Models
 Department of Computer Science, University of Edinburgh, Edinburgh
, 2000
"... The performance modeller may attempt to quantitatively analyse the behaviour of computer systems by building performance models. Such models may become unwieldy, and so highlevel structured modelling techniques have been developed. A stochastic process algebra (SPA) provides such a technique, a com ..."
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The performance modeller may attempt to quantitatively analyse the behaviour of computer systems by building performance models. Such models may become unwieldy, and so highlevel structured modelling techniques have been developed. A stochastic process algebra (SPA) provides such a technique, a compositional modelling calculus. Hillston's PEPA is an SPA, a classical process algebra enhanced to represent the performance of systems. This thesis uses PEPA as a foundation, and examines di#erent ways to assist the SPA performance modeller. A weak stage in the SPA methodology is the calculation of concrete performance measures, since much research does not focus beyond a steadystate probability vector. A framework is developed for specifying steadystate performance measures for PEPA models. The technique is used at the highlevel of the process algebra, and not applied directly to states, or the stochastic process. It employs an enhanced modal logic to allow the modeller to identify inte...
Dependability Modeling and Evaluation of Phased Mission Systems: a DSPN Approach
 in IEEE DCCA7  7th IFIP Int. Conference on Dependable Computing for Critical Applications
, 1999
"... Personal use of the material in this paper is permitted. However, permission to reprint or republish this material for advertising or promotional purposes or for creating new works for resale or redistribution, or to reuse any copyrighted component of this work in other works must be obtained from t ..."
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Cited by 20 (12 self)
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Personal use of the material in this paper is permitted. However, permission to reprint or republish this material for advertising or promotional purposes or for creating new works for resale or redistribution, or to reuse any copyrighted component of this work in other works must be obtained from the authors of this paper.
Steady State Analysis of Markov Regenerative SPN with Age Memory Policy
, 1995
"... . NonMarkovian Stochastic Petri Nets (SPN) have been developed as a tool to deal with systems characterized by non exponentially distributed timed events. Recently, some eort has been devoted to the study of SPN with generally distributed ring times, whose underlying marking process belongs to the ..."
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Cited by 20 (15 self)
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. NonMarkovian Stochastic Petri Nets (SPN) have been developed as a tool to deal with systems characterized by non exponentially distributed timed events. Recently, some eort has been devoted to the study of SPN with generally distributed ring times, whose underlying marking process belongs to the class of Markov Regenerative Processes (MRGP). We refer to this class of models as Markov Regenerative SPN (MRSPN). In this paper, we describe a computationally eective algorithm for the steady state solution of MRSPN with age memory policy and subordinated Continuous Time Markov Chain (CTMC). Key words: Stochastic Petri Nets, Generally distributed transitions, Markov regenerative processes, Preemptive resume policies. 1 Introduction In the last decade several classes of SPN's have been developed to deal with nonexponentially distributed events [7, 3]. The main reason for this is the observation that it is possible to identify a wide number of real situations in which deterministic or g...
Welldefined stochastic Petri nets, in
 Proceedings of the 4th International Workshop on Modeling, Analysis, and Simulation of Computer and Telecommunications Systems, MASCOTS ’96, IEEE Computer Society
, 1996
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