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135
A Decomposition Approach for Stochastic Reward Net Models
 Perf. Eval
, 1993
"... We present a decomposition approach for the solution of large stochastic reward nets (SRNs) based on the concept of nearindependence. The overall model consists of a set of submodels whose interactions are described by an import graph. Each node of the graph corresponds to a parametric SRN submodel ..."
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Cited by 126 (29 self)
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We present a decomposition approach for the solution of large stochastic reward nets (SRNs) based on the concept of nearindependence. The overall model consists of a set of submodels whose interactions are described by an import graph. Each node of the graph corresponds to a parametric SRN submodel and an arc from submodel A to submodel B corresponds to a parameter value that B must receive from A. The quantities exchanged between submodels are based on only three primitives. The import graph normally contains cycles, so the solution method is based on fixed point iteration. Any SRN containing one or more of the nearlyindependent structures we present, commonly encountered in practice, can be analyzed using our approach. No other restriction on the SRN is required. We apply our technique to the analysis of a flexible manufacturing system.
Efficient DescriptorVector Multiplications in Stochastic Automata Networks
, 1996
"... This paper examines numerical issues in computing solutions to networks of stochastic automata. It is wellknown that when the matrices that represent the automata contain only constant values, the cost of performing the operation basic to all iterative solution methods, that of matrixvector multi ..."
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Cited by 119 (20 self)
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This paper examines numerical issues in computing solutions to networks of stochastic automata. It is wellknown that when the matrices that represent the automata contain only constant values, the cost of performing the operation basic to all iterative solution methods, that of matrixvector multiply, is given by ae N = N Y i=1 n i \Theta N X i=1 n i ; where n i is the number of states in the i th automaton and N is the number of automata in the network. We introduce the concept of a generalized tensor product and prove a number of lemmas concerning this product. The result of these lemmas allows us to show that this relatively small number of operations is sufficient in many practical cases of interest in which the automata contain functional and not simply constant transitions. Furthermore, we show how the automata should be ordered to achieve this.
Exact and Ordinary Lumpability in Finite Markov Chains
, 1994
"... Exact and ordinary lumpability in finite Markov chains is considered. Both concepts naturally define an aggregation of the Markov chain yielding an aggregated chain that allows the exact determination of several stationary and transient results for the original chain. We show which quantities can be ..."
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Cited by 116 (8 self)
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Exact and ordinary lumpability in finite Markov chains is considered. Both concepts naturally define an aggregation of the Markov chain yielding an aggregated chain that allows the exact determination of several stationary and transient results for the original chain. We show which quantities can be determined without an error from the aggregated process and describe methods to calculate bounds on the remaining results. Furthermore, the concept of lumpability is extended to nearly lumpability yielding approximative aggregation. AGGREGATION, STATIONARY AND TRANSIENT ANALYSIS, PERFORMANCE AND RELIABILITY MODELLING yy 1 Introduction The concept of lumpability and weak lumpability of partitions on state spaces of finite Markov chains (Markov chains) has been known for a long time [8, 9, 11, 12]. In those papers lumpability is defined by the fact that the process resulting from the observation of the Markov chain by masking out transitions and states inside a partition group is also a Mar...
The Möbius Framework and Its Implementation
"... The Möbius framework is an environment for supporting multiple modeling formalisms and solution techniques. Models expressed in formalisms that are compatible with the framework are translated into equivalent models using Mobius framework components. This translation preserves the structure of the m ..."
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Cited by 113 (21 self)
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The Möbius framework is an environment for supporting multiple modeling formalisms and solution techniques. Models expressed in formalisms that are compatible with the framework are translated into equivalent models using Mobius framework components. This translation preserves the structure of the models, allowing e#cient solutions. The framework is implemented in the tool by a welldefined abstract functional interface. Models and solution techniques interact with one another through the use of the standard interface, allowing them to interact with Mobius framework components, not formalism components. This permits novel combinations of modeling techniques, and will be a catalyst for new research in modeling techniques. This paper describes our approach, focusing on the "atomic model." We describe the formal description of the Mobius components as well as their implementations in our software tool.
Modelbased evaluation: From dependability to security
 IEEE TRANSACTIONS ON DEPENDABLE AND SECURE COMPUTING
, 2004
"... The development of techniques for quantitative, modelbased evaluation of computer system dependability has a long and rich history. A wide array of modelbased evaluation techniques are now available, ranging from combinatorial methods, which are useful for quick, roughcut analyses, to statebased ..."
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Cited by 99 (5 self)
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The development of techniques for quantitative, modelbased evaluation of computer system dependability has a long and rich history. A wide array of modelbased evaluation techniques are now available, ranging from combinatorial methods, which are useful for quick, roughcut analyses, to statebased methods, such as Markov reward models, and detailed, discreteevent simulation. The use of quantitative techniques for security evaluation is much less common, and has typically taken the form of formal analysis of small parts of an overall design, or experimental red teambased approaches. Alone, neither of these approaches is fully satisfactory, and we argue that there is much to be gained through the development of a sound modelbased methodology for quantifying the security one can expect from a particular design. In this work, we survey existing modelbased techniques for evaluating system dependability, and summarize how they are now being extended to evaluate system security. We find that many techniques from dependability evaluation can be applied in the security domain, but that significant challenges remain, largely due to fundamental differences between the accidental nature of the faults commonly assumed in dependability evaluation, and the intentional, human nature of cyber attacks.
Stochastic Activity Networks: Formal Definitions and Concepts
, 2001
"... Stochastic activity networks have been used since the mid1980s for performance, dependability, and performability evaluation. They have ..."
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Cited by 93 (2 self)
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Stochastic activity networks have been used since the mid1980s for performance, dependability, and performability evaluation. They have
A Unified Approach for Specifying Measures of Performance, Dependability, and Performability
, 1991
"... Methods for evaluating system performance, dependability, and performability are becoming increasingly more important, particularly in the case of critical applications. Central to the evaluation process is the definition of specific measures of system behavior that are of interest to a user. This p ..."
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Cited by 76 (8 self)
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Methods for evaluating system performance, dependability, and performability are becoming increasingly more important, particularly in the case of critical applications. Central to the evaluation process is the definition of specific measures of system behavior that are of interest to a user. This paper presents a unified approach to the specification of measures of performance, dependability, and performability. The unification is achieved by 1) using a model class well suited for representation of all three aspects of system behavior, and 2) system behavior. The resulting approach permits the specification of many nontraditional as well as traditional measures of system performance, dependability, and performability in a unified manner. Example instantiations of variables within this class are given and their relationships to variables used in traditional performance and dependability evaluations are illustrated.
The Möbius Modeling Tool
 IN PROCEEDINGS OF THE 9TH INTERNATIONAL WORKSHOP ON PETRI NETS AND PERFORMANCE MODELS
"... Despite the development of many modeling formalisms and model solution methods, most tool implementations support only a single formalism. Furthermore, models expressed in the chosen formalism cannot be combined with models expressed in other formalisms. This monolithic approach both limits the usef ..."
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Cited by 74 (12 self)
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Despite the development of many modeling formalisms and model solution methods, most tool implementations support only a single formalism. Furthermore, models expressed in the chosen formalism cannot be combined with models expressed in other formalisms. This monolithic approach both limits the usefulness of such tools to practitioners, and hampers new and existing formalisms and solvers. This paper describes the method that a new modeling tool, cal led Mobius, uses to eliminate these limitations. Mobius provides an infrastructure to support multiple interacting formalisms and solvers, and is extensible in that new formalisms and solvers can be added to the tool without changing those already implemented. Mobius provides this capability through the use of an abstract functional interface, which provides a formalismindependent interface to models. This allows models expressed in multiple formalisms to interact with each other, and with multiple solvers.
The UltraSAN Modeling Environment
, 1995
"... Modelbased evaluation of computer systems and networks is an increasingly important activity. For modeling to be used effectively, software environments are needed that ease model specification, construction, and solution. Easy to use, graphical methods for model specification that support solution ..."
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Cited by 69 (15 self)
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Modelbased evaluation of computer systems and networks is an increasingly important activity. For modeling to be used effectively, software environments are needed that ease model specification, construction, and solution. Easy to use, graphical methods for model specification that support solution of families of models with differing parameter values, are also needed. Since no model solution technique is ideal for all situations, multiple analysis and simulationbased solution techniques should be supported. This paper describes UltraSAN, one such software environment. The design of UltraSAN reflects its two main purposes: to facilitate the evaluation of realistic computer systems and networks, and to provide a testbed for investigating new modeling techniques. In UltraSAN models are specified using stochastic activity networks, a stochastic variant of Petri nets, using a graphical XWindow based interface that supports largescale model specification, construction, and solution. Models may be parameterized to reduce the effort required to solve families of models, and a variety of analysis and simulationbased solution techniques are supported. The package has a modular organization that makes it easy to add new construction and solution techniques as they become available. In addition to describing the features, capabilities, and organization of UltraSAN, the paper illustrates the use of the package in the solution for the unreliability of a faulttolerant multiprocessor using two solution techniques.
Compositional Markovian modelling using a process algebra
 Numerical Solution of Markov Chains
, 1995
"... We introduce a stochastic process algebra, PEPA, as a highlevel modelling paradigm for continuous time Markov chains (CTMC). Process algebras are mathematical theories which model concurrent systems by their algebra and provide apparatus for reasoning about the structure and behaviour of the model ..."
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Cited by 58 (16 self)
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We introduce a stochastic process algebra, PEPA, as a highlevel modelling paradigm for continuous time Markov chains (CTMC). Process algebras are mathematical theories which model concurrent systems by their algebra and provide apparatus for reasoning about the structure and behaviour of the model. Recent extensions of these algebras, associating random variables with actions, make the models also amenable to Markovian analysis. A compositional structure is inherent in the PEPA language. As well as the clear advantages that this offers for model construction, we demonstrate how this compositionality may be exploited to reduce the state space of the CTMC. This leads to an exact aggregation based on lumpability. Moreover this technique, taking advantage of symmetries within the system, may be formally defined in terms of the PEPA description of the model. An equivalence relation, strong equivalence, developed as a process algebra bisimulation relation, is used to partition the derivation graph. 1