Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Zero-suppressed BDDs for set manipulation in combinatorial problems
DAC '93 Proceedings of the 30th international Design Automation Conference
A decomposition approach for stochastic reward net models
Performance Evaluation
Introduction to the Special Issue on Multi-Terminal BinaryDecision Diagrams
Formal Methods in System Design
ON THE USE OF KRONECKER OPERATORS FOR THE SOLUTION OF GENERALIZED STOCHASTIC PETRI NETS
ON THE USE OF KRONECKER OPERATORS FOR THE SOLUTION OF GENERALIZED STOCHASTIC PETRI NETS
Efficient Solution of GSPNs Using Canonical Matrix Diagrams
PNPM '01 Proceedings of the 9th international Workshop on Petri Nets and Performance Models (PNPM'01)
Generating BDDs for symbolic model checking in CCS
Distributed Computing
Proceedings of the 2nd international conference on Performance evaluation methodologies and tools
An easy-to-use, efficient tool-chain to analyze the availability of telecommunication equipment
FMICS'06/PDMC'06 Proceedings of the 11th international workshop, FMICS 2006 and 5th international workshop, PDMC conference on Formal methods: Applications and technology
Symbolic partition refinement with automatic balancing of time and space
Performance Evaluation
Partially-shared zero-suppressed multi-terminal BDDs: concept, algorithms and applications
Formal Methods in System Design
A CTL model checker for stochastic automata networks
QEST'13 Proceedings of the 10th international conference on Quantitative Evaluation of Systems
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High-level stochastic description methods such as stochastic Petri nets, stochastic UML statecharts etc., together with specifications of performance variables (PVs), enable a compact description of systems and quantitative measures of interest. The underlying Markov reward models (MRMs) often exhibit a significant blow-up in size, commonly known as the state space explosion problem. In this paper we employ our recently developed type of symbolic data structure, zero-suppressed multi-terminal binary decision diagram (ZDD). In addition to earlier work [12] the following innovations are introduced: (a) new algorithms for efficiently generating ZDD-based representation of user-defined PVs, (b) a new ZDD-based variant of the approach of [17] for computing state probabilities, and (c) a new ZDD-based algorithm for computing moments of the PVs. These contributions yield a ZDD-based framework which allows the computation of complex performance and reliability measures of high-level system specifications, whose underlying MRMs consist of more than 108 states. The proposed algorithms for generating user-defined PVs and computing their moments are independent of the employed symbolic data type. Thus they are highly suited to fit into other symbolic frameworks as realized in popular performance evaluation tools. The efficiency of the presented approach, which we incorporated into the Möbius modeling framework [16], is demonstrated by analyzing several benchmark models from the literature and comparing the obtained run-time data to other techniques.