Efficient descriptor-vector multiplications in stochastic automata networks
Journal of the ACM (JACM)
Parallel programming: techniques and applications using networked workstations and parallel computers
An efficient disk-based tool for solving large Markov models
Performance Evaluation - Special issue on tools for performance evaluation
Using MPI (2nd ed.): portable parallel programming with the message-passing interface
Using MPI (2nd ed.): portable parallel programming with the message-passing interface
Generalized Stochastic Petri Nets: A Definition at the Net Level and its Implications
IEEE Transactions on Software Engineering
Parallel multiplication of a vector by a kronecker product of matrices
Parallel numerical linear algebra
Solving Eigenvalue Problems on Networks of Processors
VECPAR '98 Selected Papers and Invited Talks from the Third International Conference on Vector and Parallel Processing
Parallel Randomization for Large Structured Markov Chains
DSN '02 Proceedings of the 2002 International Conference on Dependable Systems and Networks
Performance comparison of MPI and three openMP programming styles on shared memory multiprocessors
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Journal of Parallel and Distributed Computing
On the benefits of using functional transitions and Kronecker algebra
Performance Evaluation
Load balancing and OpenMP implementation of nested parallelism
Parallel Computing - OpenMp
Distributed disk-based algorithms for model checking very large Markov chains
Formal Methods in System Design
Parallel Programming in C with MPI and OpenMP
Parallel Programming in C with MPI and OpenMP
Scientific Programming - OpenMP
Split: a flexible and efficient algorithm to vector-descriptor product
Proceedings of the 2nd international conference on Performance evaluation methodologies and tools
Data and thread affinity in openmp programs
Proceedings of the 2008 workshop on Memory access on future processors: a solved problem?
Using OpenMP: Portable Shared Memory Parallel Programming (Scientific and Engineering Computation)
Using OpenMP: Portable Shared Memory Parallel Programming (Scientific and Engineering Computation)
Distributed Markovian Bisimulation Reduction aimed at CSL Model Checking
Electronic Notes in Theoretical Computer Science (ENTCS)
Performance Evaluation of MPI, UPC and OpenMP on Multicore Architectures
Proceedings of the 16th European PVM/MPI Users' Group Meeting on Recent Advances in Parallel Virtual Machine and Message Passing Interface
GTAexpress: A Software Package to Handle Kronecker Descriptors
QEST '09 Proceedings of the 2009 Sixth International Conference on the Quantitative Evaluation of Systems
Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling
Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling
Performance Models For Master/Slave Parallel Programs
Electronic Notes in Theoretical Computer Science (ENTCS)
Kronecker descriptor partitioning for parallel algorithms
SpringSim '10 Proceedings of the 2010 Spring Simulation Multiconference
Experiences with the OpenMP parallelization of DROPS, a Navier-Stokes solver written in C++
IWOMP'05/IWOMP'06 Proceedings of the 2005 and 2006 international conference on OpenMP shared memory parallel programming
Kronecker products and shuffle algebra
IEEE Transactions on Computers
Performance Evaluation of Software Development Teams: a Practical Case Study
Electronic Notes in Theoretical Computer Science (ENTCS)
Efficient vector-descriptor product exploiting time-memory trade-offs
ACM SIGMETRICS Performance Evaluation Review
A Structured Stochastic Model for Prediction of Geological Stratal Stacking Patterns
Electronic Notes in Theoretical Computer Science (ENTCS)
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Numerical analysis of Markovian models is relevant for performance evaluation and probabilistic analysis of systems' behavior from several fields in science and engineering. These models can be represented in a compact fashion using Kronecker algebra. The Vector-Descriptor Product (VDP) is the key operation to obtain stationary and transient solutions of models represented by Kronecker-based descriptors. VDP algorithms are usually CPU intensive, requiring alternatives such as data partitioning to produce results in less time. This paper introduces a set of parallel implementations of a hybrid algorithm for handling descriptors and a detailed performance analysis on four real Markovian models. The implementations are based on different scheduling strategies using OpenMP and existing techniques of static and dynamic load balancing, along with data partitioning presented in the literature. The performance evaluation study contains analysis of speed-up, synchronization and scheduling overheads, task mapping policies, and memory affinity. The results presented here provide insights into different implementation choices for an application on shared-memory systems and how this application benefited from this architecture.