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18
Saturation-based symbolic reachability analysis using conjunctive and disjunctive partitioning
- Proc. CHARME, LNCS 3725
, 2005
"... Abstract. We propose a new saturation-based symbolic state-space generation algorithm for finite discrete-state systems. Based on the structure of the high-level model specification, we first disjunctively partition the transition relation of the system, then conjunctively partition each disjunct. O ..."
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Cited by 24 (13 self)
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Abstract. We propose a new saturation-based symbolic state-space generation algorithm for finite discrete-state systems. Based on the structure of the high-level model specification, we first disjunctively partition the transition relation of the system, then conjunctively partition each disjunct. Our new encoding recognizes identity transformations of state variables and exploits event locality, enabling us to apply a recursive fixed-point image computation strategy completely different from the standard breadth-first approach employing a global fix-point image computation. Compared to breadth-first symbolic methods, saturation has already been empirically shown to be several orders more efficient in terms of runtime and peak memory requirements for asynchronous concurrent systems. With the new partitioning, the saturation algorithm can now be applied to completely general asynchronous systems, while requiring similar or better run-times and peak memory than previous saturation algorithms. 1
A Structured Path-Based Approach for Computing Transient Rewards of Large CTMCs
"... Structured (a.k.a. symbolic) representation techniques of Markov models have, to a large extent, been used effectively for representing very large transition matrices and their associated state spaces. However, their success means that the largest space requirement encountered when analyzing these m ..."
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Cited by 16 (7 self)
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Structured (a.k.a. symbolic) representation techniques of Markov models have, to a large extent, been used effectively for representing very large transition matrices and their associated state spaces. However, their success means that the largest space requirement encountered when analyzing these models is often the representation of their iteration and solution vectors. In this paper, we present a new approach for computing bounds on solutions of transient measures in large continuous-time Markov chains (CTMCs). The approach extends existing path- and uniformizationbased methods by identifying sets of paths that are equivalent with respect to a reward measure and related to one another via a simple structural relationship. This relationship allows us to explore multiple paths at the same time, thus significantly increasing the number of paths that can be explored in a given amount of time. Furthermore, the use of a structured representation for the state space and the direct computation of the desired reward measure (without ever storing the solution vector) allow us to analyze very large models using a very small amount of storage. In addition to presenting the method itself, we illustrate its use to compute the reliability and the availability of a large distributed information service system in which faults may propagate across subsystems.
Symbolic Performance and Dependability Evaluation with the Tool CASPA
- In FORTE Workshops, volume 3236 of LNCS
, 2004
"... This paper describes the tool CASPA,anewperformance evaluation tool which is based on a Markovian stochastic process algebra. ..."
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Cited by 8 (2 self)
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This paper describes the tool CASPA,anewperformance evaluation tool which is based on a Markovian stochastic process algebra.
Lumping matrix diagram representations of markov models
- In Proc. of the 2005 Int. Conf. on Dependable Systems and Networks
, 2005
"... Continuous-time Markov chains (CTMCs) have been used successfully to model the dependability and performability of many systems. Matrix diagrams (MDs) are known to be a space-efficient, symbolic representation of large CTMCs. In this paper, we identify local conditions for exact and ordinary lumping ..."
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Cited by 6 (2 self)
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Continuous-time Markov chains (CTMCs) have been used successfully to model the dependability and performability of many systems. Matrix diagrams (MDs) are known to be a space-efficient, symbolic representation of large CTMCs. In this paper, we identify local conditions for exact and ordinary lumpings that allow us to lump MD representations of Markov models in a compositional manner. We propose a lumping algorithm for CTMCs that are represented as MDs that is based on partition refinement, is applied to each level of an MD directly, and results in an MD representation of the lumped CTMC. Our compositional lumping approach is complementary to other known model-level lumping approaches for matrix diagrams. The approach has been implemented, and we demonstrate its efficiency and benefits by evaluating an example model of a tandem multi-processor system with load balancing and failure and repair operations. 1
Möbius 2.3: An Extensible Tool for Dependability, Security, and Performance Evaluation of Large and Complex System Models
"... Möbius 2.3 is an extensible dependability, security, and performance modeling environment for large-scale discrete-event systems. It provides multiple model formalisms and solution techniques, facilitating the representation of each part of a system in the formalism that is most appropriate for it, ..."
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Cited by 6 (0 self)
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Möbius 2.3 is an extensible dependability, security, and performance modeling environment for large-scale discrete-event systems. It provides multiple model formalisms and solution techniques, facilitating the representation of each part of a system in the formalism that is most appropriate for it, and the application of the solution method or methods best-suited to estimating the system’s behavior. Since its initial release in 2001, many advances have been made in Möbius’ design and implementation that have strengthened its place in the modeling and analysis community. With almost a decade of widespread academic and industrial use, Möbius has proven itself to be useful in a wide variety of modeling situations. This paper documents the current feature set of Möbius 2.3, emphasizing recent significant enhancements.
The Möbius Modeling Environment: Recent Developments
- in Proc. of the 1st Int. Conference on Quantitative Evaluation of Systems (QEST 2004), IEEE-CS
, 2004
"... The Möbius modeling tool 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 in such a way that they can interact with those already implemented without requiring additional changes to the pr ..."
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Cited by 5 (0 self)
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The Möbius modeling tool 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 in such a way that they can interact with those already implemented without requiring additional changes to the previously implemented ones. We have continued to add features to the Möbius tool in order to enhance the extensibility of the tool and to allow increased interaction between new and different formalisms and solvers. In this paper, we discuss some recent additions to Möbius, including expanded state variable types, a fixed-point mechanism called “connection, ” and improvements to CTMC solution that includes a new state level abstract functional interface. 1 Möbius Tool Möbius is a system-level performance and dependability modeling tool that was motivated by the observations that no one formalism is best for building and solving models, that no single solution method is appropriate for solving all models, and that new formalisms and solution techniques are often hindered by the need to build a complete tool to handle them. We dealt with these three issues by defining a broad framework (a formal, mathematical specification of model construction and execution [1]) in which new modeling formalisms and model solution methods can be easily integrated. In implementing the framework we defined an abstract functional interface (AFI) [2], which is realized as a set of functions that facilitates inter-model communication as well as communication between models and solvers. The Möbius tool architecture is separated into two different logical layers: model specification and model execution. Model specification in the tool is done through graphical user interfaces in Java, while all model execution is done exclusively in C++ to attain efficiency and high performance. This material is based upon work supported by the National Science
Activity-local symbolic state graph generation for high-level stochastic models
- In Proceedings of the 13th GI/ITG Conference on Measurement, Modeling, and Evaluation of Computer and Communication Systems (MMB
, 2006
"... Abstract. This paper introduces a new, efficient method for deriving compact symbolic representations of very large (labelled) Markov chains resulting from high-level model specifications such as stochastic Petri nets, stochastic process algebras, etc.. This so called “activity-local” scheme is comb ..."
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Cited by 4 (2 self)
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Abstract. This paper introduces a new, efficient method for deriving compact symbolic representations of very large (labelled) Markov chains resulting from high-level model specifications such as stochastic Petri nets, stochastic process algebras, etc.. This so called “activity-local” scheme is combined with a new data structure, called zero-suppressed multi-terminal binary decision diagram, and a new efficient “activityoriented” scheme for symbolic reachability analysis. Several standard benchmark models from the literature are analyzed in order to show the superiority of our approach. 1
Symbolic partition refinement with automatic balancing of time and space
- Perform. Eval
"... State space lumping is one of the classical means to fight the state space explosion problem in state-based performance evaluation and verification. Particularly when numerical algorithms are applied to analyze a Markov model, one often observes that those algorithms do not scale beyond systems of m ..."
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Cited by 3 (2 self)
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State space lumping is one of the classical means to fight the state space explosion problem in state-based performance evaluation and verification. Particularly when numerical algorithms are applied to analyze a Markov model, one often observes that those algorithms do not scale beyond systems of moderate size. To alleviate this problem, symbolic lumping algorithms have been devised to effectively reduce very large – but symbolically represented – Markov models to moderate size explicit representations. This lumping step partitions the Markov model in such a way that any numerical analysis carried out on the lumped model is guaranteed to produce exact results for the original system. But even this lumping preprocessing may fail due to time or memory limitations. This paper discusses the two main approaches to symbolic lumping, and combines them to improve on their respective limitations. The algorithm automatically converts between known symbolic partition representations in order to provide a trade-off between memory consumption and runtime. We show how to apply this algorithm for the lumping of Markov chains, but the same techniques can be adapted in a straightforward way to other models like Markov reward models, labeled transition systems, or interactive Markov chains. Key words: state space lumping, symbolic methods, Markov chains 1.
Dependability Analysis with Markov Chains: How Symmetries Improve Symbolic Computations
"... We propose a novel approach that combines two general and complementary methods for dependability analysis based on the steady state or transient analysis of Markov chains. The first method allows us to automatically detect all symmetries in a compositional Markovian model with state-sharing composi ..."
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Cited by 2 (0 self)
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We propose a novel approach that combines two general and complementary methods for dependability analysis based on the steady state or transient analysis of Markov chains. The first method allows us to automatically detect all symmetries in a compositional Markovian model with state-sharing composition. Symmetries are detected with the help of an automorphism group of the model composition graph, which yields a reduction of the associated Markov chain due to lumpability. The second method allows us to represent and numerically solve the lumped Markov chain, even in the case of very large state spaces, with the help of symbolic data structures, in particular matrix diagrams. The overall approach has been implemented and is able to compute stationary and transient measures for large Markovian models of dependable systems.
An Extension to Pi-Calculus for Performance Evaluation
"... Pi-Calculus is a formal method for describing and analyzing the behavior of large distributed and concurrent systems. Pi-calculus offers a conceptual framework for describing and analyzing the concurrent systems whose configuration may change during the computation. With all the advantages that pi-c ..."
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Cited by 1 (1 self)
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Pi-Calculus is a formal method for describing and analyzing the behavior of large distributed and concurrent systems. Pi-calculus offers a conceptual framework for describing and analyzing the concurrent systems whose configuration may change during the computation. With all the advantages that pi-calculus offers, it does not provide any methods for performance evaluation of the systems described by it; nevertheless performance is a crucial factor that needs to be considered in designing of a multi-process system. Currently, the available tools for pi-calculus are high level language tools that provide facilities for describing and analyzing systems but there is no practical tool on hand for pi-calculus based performance evaluation. In this paper, the performance evaluation is incorporated with pi-calculus by adding performance primitives and associating performance parameters with each action that takes place internally in a system. By using such parameters, the designers can benchmark multi-process systems and compare the performance of different architectures against one another. Keywords: Pi-calculus, Performance Evaluation, Multi-Agent Systems, System Modeling 1.
