Results 1  10
of
18
Partial order reduction for probabilistic systems
 In Proc. 1st QEST
, 2004
"... In the past, several model checking algorithms have been proposed to verify probabilistic reactive systems. The techniques to combat the stateexplosion problem have mainly concentrated on symbolic methods with variants of decision diagrams or abstraction methods. In this paper, we show how partial ..."
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Cited by 30 (3 self)
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In the past, several model checking algorithms have been proposed to verify probabilistic reactive systems. The techniques to combat the stateexplosion problem have mainly concentrated on symbolic methods with variants of decision diagrams or abstraction methods. In this paper, we show how partial order reduction with a variant of Peled’s ample set method can be applied in the context of LTL model checking for probabilistic systems modelled by Markov decision processes. 1
Advances and Challenges of Probabilistic Model Checking
 48TH ANNUAL ALLERTON CONFERENCE ON COMMUNICATION, CONTROL AND COMPUTING (2010) 16911698
, 2010
"... Probabilistic model checking is a powerful technique for formally verifying quantitative properties of systems that exhibit stochastic behaviour. Such systems are found in many domains: probabilistic behaviour may arise, for example, due to failures of unreliable components, communication across los ..."
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Cited by 7 (0 self)
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Probabilistic model checking is a powerful technique for formally verifying quantitative properties of systems that exhibit stochastic behaviour. Such systems are found in many domains: probabilistic behaviour may arise, for example, due to failures of unreliable components, communication across lossy media, or through the use of randomisation in distributed protocols. In this paper, we give a short overview of probabilistic model checking and of PRISM (www.prismmodelchecker.org), currently the leading software tool in this area. We then mention some of the limitations of these techniques, describe some of the advances that are being made to overcome them, and outline key challenges that remain in this research area.
Lumping matrix diagram representations of markov models
 In Proc. of the 2005 Int. Conf. on Dependable Systems and Networks
, 2005
"... Continuoustime Markov chains (CTMCs) have been used successfully to model the dependability and performability of many systems. Matrix diagrams (MDs) are known to be a spaceefficient, 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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Continuoustime Markov chains (CTMCs) have been used successfully to model the dependability and performability of many systems. Matrix diagrams (MDs) are known to be a spaceefficient, 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 modellevel 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 multiprocessor system with load balancing and failure and repair operations. 1
Dualprocessor parallelisation of symbolic probabilistic model checking
 In Proc. 12th International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems (MASCOTS’04
, 2004
"... In this paper, we describe the dualprocessor parallelisation of a symbolic (BDDbased) implementation of probabilistic model checking. We use multiterminal BDDs, which allow a compact representation of large, structured Markov chains. We show that they also provide a convenient block decomposition ..."
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Cited by 6 (5 self)
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In this paper, we describe the dualprocessor parallelisation of a symbolic (BDDbased) implementation of probabilistic model checking. We use multiterminal BDDs, which allow a compact representation of large, structured Markov chains. We show that they also provide a convenient block decomposition of the Markov chain which we use to implement a parallelised version of the GaussSeidel iterative method. We provide experimental results on a range of case studies to illustrate the effectiveness of the technique, observing an average speedup of 1.8 with two processors. Furthermore, we present an optimisation for our method based on preconditioning. 1
Combining Response Surface Methodology with Numerical Models for Optimization of Class Based Queueing Systems
 Proc. Int. Conf. on Dependable Systems and Networks (DSN
, 2005
"... In general, decision support is one of the main purposes of modelbased analysis of systems. Response surface methodology (RSM) is an optimization technique that has been applied frequently in practice, but few automated variants are currently available. In this paper, we propose the combination of ..."
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In general, decision support is one of the main purposes of modelbased analysis of systems. Response surface methodology (RSM) is an optimization technique that has been applied frequently in practice, but few automated variants are currently available. In this paper, we propose the combination of RSM with numerical analysis methods to solve continuous time Markov chain models of classbased queueing systems (CBQ). We consider first and secondorder models in RSM to identify an optimal parameter configuration for CBQ as part of the differentiated service architecture. Among the many known numerical solution methods for large Markov chains, we consider a GaussSeidel solver with relaxation that relies on a hierarchical Kronecker representation as implemented in the APNN Toolbox. To effectively apply the proposed optimization methodology we determine a suitable configuration of RSM and compare the results with previous results for optimizing CBQ. 1.
Solution of Large Markov Models using Lumping Techniques and Symbolic Data Structures
, 2005
"... Continuous time Markov chains (CTMCs) are among the most fundamental mathematical structures used for performance and dependability modeling of communication and computer systems. They are often constructed from models described in one of the various highlevel formalisms. Since the size of a CTMC u ..."
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Continuous time Markov chains (CTMCs) are among the most fundamental mathematical structures used for performance and dependability modeling of communication and computer systems. They are often constructed from models described in one of the various highlevel formalisms. Since the size of a CTMC usually grows exponentially with the size of the corresponding highlevel model, one often encounters the infamous statespace explosion problem, which often makes solution of the CTMCs intractable and sometimes makes it impossible. In statebased numerical analysis, which is the solution technique we have chosen to use to solve for measures defined on a CTMC, the statespace explosion problem is manifested in two ways: 1) large state transition rate matrices, and 2) large iteration vectors. The goal of this dissertation is to extend, improve, and combine existing solutions of the statespace explosion problem in order to make possible the construction and solution of very large CTMCs generated from highlevel models. Our new techniques follow largeness avoidance and largeness tolerance approaches. In the former approach, we reduce the size of the CTMC that needs to be solved in order to compute the measures of interest. That
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 statesharing composi ..."
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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 statesharing 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.
Reaction Cycles in Membrane Systems and Molecular Dynamics
"... Summary. We are considering molecular dynamics and (sequential) membrane systems from the viewpoint of Markov chain theory. The first step is to understand the structure of the configuration space, with respect to communicating classes. Instead of a reachability analysis by traditional methods, we u ..."
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Summary. We are considering molecular dynamics and (sequential) membrane systems from the viewpoint of Markov chain theory. The first step is to understand the structure of the configuration space, with respect to communicating classes. Instead of a reachability analysis by traditional methods, we use the explicit monoidal structure of this space with respect to rule applications. This leads to the notion of precycle, which is an element of the integer kernel of the stoichiometric matrix. The generators of the set of precycles can be effectively computed by an incremental algorithm due to Contejean and Devie. To arrive at a characterization of cycles, we introduce the notion of defect, which is a set of geometric constraints on a configuration to allow a precycle to be enabled, that is, be a cycle. An important open problem is the efficient calculation of the defects. We also discuss aspects of asymptotic behavior and connectivity, as well as give a biological example, showing the usefulness of the method for model checking. Corresponding author186 M. Muskulus et al.
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"... Continuous time Markov chains (CTMCs) are a common mathematical model for studying the dependability of many complex processes and have been especially successful in modeling large computer systems. CTMCs are typically generated from more natural modeling formalisms that often better represent the s ..."
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Continuous time Markov chains (CTMCs) are a common mathematical model for studying the dependability of many complex processes and have been especially successful in modeling large computer systems. CTMCs are typically generated from more natural modeling formalisms that often better represent the system they model. This results in the famous statespace explosion problem, in which the number of states in the CTMC depends exponentially on the number of models in the higherlevel formalism. The problem affects numerical analysis in two ways: the space needed to represent the transition rate matrix, and the space needed to represent the iteration vectors. The goal of this thesis is to develop new techniques to extend the size of models that can be studied using CTMCs generated from higherlevel formalisms. To combat the statespace explosion problem, we present a combination of a largenessavoidance and a largenesstolerance technique to address the size of the transition rate matrix. In the first technique, we present a representation of the model called the model composition graph, which separates