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Computing response time distributions using stochastic Petri nets and matrix diagrams
, 2003
"... In this paper, we consider random variables expressed in terms of the time required for the state of a stochastic Petri net to pass from a set of starting markings to a set of stopping markings. These random variables have continuous phasetype distributions when the all transitions have exponentia ..."
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In this paper, we consider random variables expressed in terms of the time required for the state of a stochastic Petri net to pass from a set of starting markings to a set of stopping markings. These random variables have continuous phasetype distributions when the all transitions have exponentiallydistributed firing delays. We demonstrate how to numerically compute the distribution of the random variable using both explicit techniques and an implicit approach based on multiway decision diagrams and matrix diagrams. We present an efficient matrixvector multiplication algorithm for matrix diagrams that is necessary for numerical solution. We demonstrate the efficiency of our approaches using several models. The lower storage requirements of the implicit approach effectively increases the size of models that can be analyzed by about an order of magnitude.
A pattern recognition approach for speculative firing prediction in distributed saturation statespace generation
 Proc. PDMC, pp.65– 79
, 2005
"... The saturation strategy for symbolic statespace generation is particularly effective for globallyasynchronous locallysynchronous systems. A distributed version of saturation, SaturationNOW, uses the overall memory available on a network of workstations to effectively spread the memory load, but i ..."
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Cited by 8 (2 self)
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The saturation strategy for symbolic statespace generation is particularly effective for globallyasynchronous locallysynchronous systems. A distributed version of saturation, SaturationNOW, uses the overall memory available on a network of workstations to effectively spread the memory load, but its execution is essentially sequential. To achieve true parallelism, we explore a speculative firing prediction, where idle workstations work on predicted future event firing requests. A naïve approach where all possible firings may be explored a priori, given enough idle time, can result in excessive memory requirements. Thus, we introduce a historybased approach for firing prediction that recognizes firing patterns and explores only firings conforming to these patterns. Experiments show that our heuristic improves the runtime and has a small memory overhead.
A dynamic firing speculation to speedup distributed symbolic statespace generation
 In Proceedings of the International Parallel & Distributed Processing Symposium (IPDPS
, 2006
"... The saturation strategy for symbolic statespace generation is very effective for globallyasynchronous locallysynchronous discretestate systems. Its inherently sequential nature, however, makes it difficult to parallelize on a NOW. An initial attempt that utilizes idle workstations to recognize e ..."
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Cited by 8 (1 self)
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The saturation strategy for symbolic statespace generation is very effective for globallyasynchronous locallysynchronous discretestate systems. Its inherently sequential nature, however, makes it difficult to parallelize on a NOW. An initial attempt that utilizes idle workstations to recognize event firing patterns and then speculatively compute firings conforming to these patterns is at times effective but can introduce large memory overheads. We suggest an implicit method to encode the firing history of decision diagram nodes, where patterns can be shared by nodes. By preserving the actual firing history efficiently and effectively, the speculation is more informed. Experiments show that our implicit encoding method not only reduces the memory requirements but also enables dynamic speculation schemes that further improve runtime. 1.
Reachability set generation for petri nets: Can brute force be smart
 In Proceedings of Applications and Theory of Petri Nets 2004: 25th International Conference (ICATPN’04), volume 3099 of LNCS
, 2004
"... Abstract. Generating the reachability set is one of the most commonly required step when analyzing the logical or stochastic behavior of a system modeled with Petri nets. Traditional “explicit ” algorithms that explore the reachability graph of a Petri net require memory and time at least proportion ..."
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Abstract. Generating the reachability set is one of the most commonly required step when analyzing the logical or stochastic behavior of a system modeled with Petri nets. Traditional “explicit ” algorithms that explore the reachability graph of a Petri net require memory and time at least proportional to the number of reachable markings, thus they are applicable only to fairly small systems in practice. Symbolic “implicit” algorithms, typically implemented using binary decision diagrams, have been successfully employed in much larger systems, but much of the work to date is based on breadthfirst search techniques best suited for synchronous hardware verification. Here, instead, we describe recentlyintroduced data structures and algorithms particularly targeted to Petri nets and similar asynchronous models, and show why they are enormously more efficient for this application. We conclude with some directions for future research. 1
SelfLoop Aggregation Product — A New Hybrid Approach to OntheFly LTL Model Checking
"... Abstract. We present the SelfLoop Aggregation Product (SLAP), a new hybrid technique that replaces the synchronized product used in the automatatheoretic approach for LTL model checking. The proposed product is an explicit graph of aggregates (symbolic sets of states) that can be interpreted as a ..."
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Cited by 7 (4 self)
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Abstract. We present the SelfLoop Aggregation Product (SLAP), a new hybrid technique that replaces the synchronized product used in the automatatheoretic approach for LTL model checking. The proposed product is an explicit graph of aggregates (symbolic sets of states) that can be interpreted as a Büchi automaton. The criterion used by SLAP to aggregate states from the Kripke structure is based on the analysis of selfloops that occur in the Büchi automaton expressing the property to verify. Our hybrid approach allows on the one hand to use classical emptinesscheck algorithms and build the graph onthefly, and on the other hand, to have a compact encoding of the state space thanks to the symbolic representation of the aggregates. Our experiments show that this technique often outperforms other existing (hybrid or fully symbolic) approaches. 1
Faster Discreteevent Simulation Through Structural Caching
 IN PROC. PMCCS
, 2003
"... We develop a structural caching strategy to improve the performance of simulation for a wide class of models expressed in highlevel formalisms. By imposing a Kronecker consistent partition of a model into submodels, we compute once, and cache for future use, the effect of each event on each submod ..."
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Cited by 7 (3 self)
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We develop a structural caching strategy to improve the performance of simulation for a wide class of models expressed in highlevel formalisms. By imposing a Kronecker consistent partition of a model into submodels, we compute once, and cache for future use, the effect of each event on each submodel. This greatly reduces the cost of processing events, updating the current state, and collecting statistics.
Implicit GSPN reachability set generation using decision diagrams
 PERF. EVAL
, 2004
"... Implicit techniques for representing and generating the reachability set of a highlevel model have become quite efficient. However, such techniques are usually restricted to models whose events have equal priority. Models containing events with differing classes of priority or complex priority stru ..."
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Cited by 6 (2 self)
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Implicit techniques for representing and generating the reachability set of a highlevel model have become quite efficient. However, such techniques are usually restricted to models whose events have equal priority. Models containing events with differing classes of priority or complex priority structure, in particular models with immediate events, have thus been required to use lessefficient explicit reachability set generation techniques. In this paper, we present an efficient implicit technique, based on multivalued decision diagram representations for sets of states and matrix diagram representations for nextstate functions, that can handle models with complex priority structure. We adapt an efficient Kroneckerbased reachability set generation algorithm to work with matrix diagrams. If the model contains immediate events, the vanishing states can be eliminated either during generation, by manipulating the matrix diagram, or after generation, by manipulating the multivalued decision diagram. We apply both techniques to several models and give detailed experimental results.
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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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
New metrics for static variable ordering in decision diagrams
 In TACAS, LNCS 3920:90–104
, 2006
"... Abstract. We investigate a new class of metrics to find good variable orders for decision diagrams in symbolic statespace generation. Most of the previous work on static ordering is centered around the concept of minimum variable span, which can also be found in the literature under several other n ..."
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Abstract. We investigate a new class of metrics to find good variable orders for decision diagrams in symbolic statespace generation. Most of the previous work on static ordering is centered around the concept of minimum variable span, which can also be found in the literature under several other names. We use a similar concept, but applied to event span, and generalize it to a family of metrics parameterized by a moment, where the metric of moment 0 is the combined event span. Finding a good variable order is then reduced to optimizing one of these metrics, and we design extensive experiments to evaluate them. First, we investigate how the actual optimal order performs in statespace generation, when it can be computed by evaluating all possible permutations. Then, we study the performance of these metrics on selected models and compare their impact on two different statespace generation algorithms: classic breadthfirst and our own saturation strategy. We conclude that the new metric of moment 1 is the best choice. In particular, the saturation algorithm seems to benefit the most from using it, as it achieves the better performance in nearly 80 % of the cases. 1
Symbolic CTL Model Checking of Asynchronous Systems Using Constrained Saturation ⋆
"... Abstract. The saturation statespace generation algorithm has demonstrated clear improvements over stateoftheart symbolic methods for asynchronous systems. This work is motivated by efficiently applying saturation to CTL model checking. First, we introduce a new “constrained saturation ” algorith ..."
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Abstract. The saturation statespace generation algorithm has demonstrated clear improvements over stateoftheart symbolic methods for asynchronous systems. This work is motivated by efficiently applying saturation to CTL model checking. First, we introduce a new “constrained saturation ” algorithm which constrains state exploration to a set of states satisfying given properties. This algorithm avoids the expensive afterthefact intersection operations and retains the advantages of saturation, namely, exploiting event locality and benefiting from recursive local fixpoint computations. Then, we employ constrained saturation to build the set of states satisfying EU and EG properties for asynchronous systems. The new algorithm can achieve ordersofmagnitude reduction in runtime and memory consumption with respect to methods based on breathfirst search, and even with a previouslyproposed hybrid approach that alternates between “safe ” saturation and “unsafe ” breadthfirst searches. Furthermore, the new approch is fully general, as it does not require the nextstate function to be expressable in Kronecker form. We conclude this paper with a discussion of some possible future work, such as building the set of states belonging to strongly connected components. 1