A decomposition approach for stochastic reward net models
Performance Evaluation
Hierarchical Markovian models: symmetries and reduction
Performance Evaluation - Special issue: 6th international conference on modelling techniques and tools for computer performance evaluation
Numerical Analysis of Superposed GSPNs
IEEE Transactions on Software Engineering - Special issue: best papers of the sixth international workshop on Petri nets and performance models (PNPM'95)
Efficient descriptor-vector multiplications in stochastic automata networks
Journal of the ACM (JACM)
Theoretical Computer Science
"On-the-Fly" Solution Techniques for Stochastic Petri Nets and Extensions
IEEE Transactions on Software Engineering
Structured analysis approaches for large Markov chains
Applied Numerical Mathematics
STL tutorial and reference guide, second edition: C++ programming with the standard template library
STL tutorial and reference guide, second edition: C++ programming with the standard template library
An Efficient Algorithm for Aggregating PEPA Models
IEEE Transactions on Software Engineering
Stochastic Well-Formed Colored Nets and Symmetric Modeling Applications
IEEE Transactions on Computers
Faster and Symbolic CTMC Model Checking
PAPM-PROBMIV '01 Proceedings of the Joint International Workshop on Process Algebra and Probabilistic Methods, Performance Modeling and Verification
Approximate Symbolic Model Checking of Continuous-Time Markov Chains
CONCUR '99 Proceedings of the 10th International Conference on Concurrency Theory
On the Representation of Probabilities over Structured Domains
CAV '99 Proceedings of the 11th International Conference on Computer Aided Verification
CADP - A Protocol Validation and Verification Toolbox
CAV '96 Proceedings of the 8th International Conference on Computer Aided Verification
An Efficient Disk-Based Tool for Solving Very Large Markov Models
Proceedings of the 9th International Conference on Computer Performance Evaluation: Modelling Techniques and Tools
Exploiting Symmetries in Stochastic Process Algebras
Proceedings of the 12th European Simulation Multiconference on Simulation - Past, Present and Future
INFORMS Journal on Computing
A structure based decomposition approach for GSPN
PNPM '95 Proceedings of the Sixth International Workshop on Petri Nets and Performance Models
A Data Structure for the Efficient Kronecker Solution of GSPNs
PNPM '99 Proceedings of the The 8th International Workshop on Petri Nets and Performance Models
Integrated Frameworks for Multi-Level and Multi-Formalism Modeling
PNPM '99 Proceedings of the The 8th International Workshop on Petri Nets and Performance Models
PNPM '01 Proceedings of the 9th international Workshop on Petri Nets and Performance Models (PNPM'01)
Möbius: Framework and Atomic Models
PNPM '01 Proceedings of the 9th international Workshop on Petri Nets and Performance Models (PNPM'01)
PNPM '01 Proceedings of the 9th international Workshop on Petri Nets and Performance Models (PNPM'01)
Compact Representations of Probability Distributions in the Analysis of Superposed GSPNs
PNPM '01 Proceedings of the 9th international Workshop on Petri Nets and Performance Models (PNPM'01)
The Möbius state-level abstract functional interface
Performance Evaluation - Modelling techniques and tools for computer performance evaluation
Proceedings of the 2nd international conference on Performance evaluation methodologies and tools
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A key advantage of the M枚bius modeling environment is the ease with which one can incorporate new modeling formalisms, model composition and connection methods, and model solution methods. In this paper, we describe a new state-level abstract functional interface (AFI) for M枚bius that allows numerical solution methods to communicate with M枚bius state-level models via the abstraction of a labeled transition system. This abstraction, and its corresponding implementation as a set of containers and iterators, yields an important separation of concerns: It is possible to treat separately the problem of representing large labeled transition systems, like generator matrices of continuous-time Markov chains, and the problem of analyzing these systems. For example, any numerical solver (e.g., Jacobi, SOR, or uniformization) that accesses a model through the M枚bius state-level AFI can operate on a variety of state-space representations, including "on-the-fly," disk-based, sparse-matrix, Kronecker, and matrix-diagram representations, without requiring that the implementation be changed to match the state-space representation. This abstraction thus avoids redundant implementations of solvers and state-generation techniques, eases research cooperation, and simplifies comparison of approaches as well as benchmarking. In addition to providing a formal definition of the M枚bius state-level AFI, we illustrate its use on two state-space representations (a sparse matrix and a Kronecker representation) and two numerical solvers (Jacobi and SOR). With the help of this implementation and two example models, we demonstrate that the AFI provides the benefits of transparency while introducing only minor slowdowns in solution speed.