Journal of the ACM (JACM) - The MIT Press scientific computation series
Matrix analysis
Some aspects of the parallel and distributed iterative algorithms—a survey
Automatica (Journal of IFAC)
The Fourier-series method for inverting transforms of probability distributions
Queueing Systems: Theory and Applications - Numerical computations in queues
A decomposition approach for stochastic reward net models
Performance Evaluation
Asynchronous two-stage iterative methods
Numerische Mathematik
Iterative solution methods
A multilevel algorithm for partitioning graphs
Supercomputing '95 Proceedings of the 1995 ACM/IEEE conference on Supercomputing
Multilevel k-way partitioning scheme for irregular graphs
Journal of Parallel and Distributed Computing
Queueing networks and Markov chains: modeling and performance evaluation with computer science applications
Implicit-Explicit Parallel Asynchronous Solver of Parabolic PDEs
SIAM Journal on Scientific Computing
Hypergraph-Partitioning-Based Decomposition for Parallel Sparse-Matrix Vector Multiplication
IEEE Transactions on Parallel and Distributed Systems
Convergence rate and termination of asynchronous iterative algorithms
ICS '89 Proceedings of the 3rd international conference on Supercomputing
Asynchronous Iterative Methods for Multiprocessors
Journal of the ACM (JACM)
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. III: linear algebra
Numerical Performance of an Asynchronous Jacobi Iteration
CONPAR '92/ VAPP V Proceedings of the Second Joint International Conference on Vector and Parallel Processing: Parallel Processing
Distributed Numerical Markov Chain Analysis
Proceedings of the 8th European PVM/MPI Users' Group Meeting on Recent Advances in Parallel Virtual Machine and Message Passing Interface
Asynchronous iterations with flexible communication: contracting operators
Journal of Computational and Applied Mathematics
Iterative convergence of passage-time densities in semi-Markov performance models
Performance Evaluation - Performance modelling and evaluation of high-performance parallel and distributed systems
Future Generation Computer Systems - Systems performance analysis and evaluation
Performance analysis of asynchronous Jacobi's method implemented in MPI, SHMEM and OpenMP
International Journal of High Performance Computing Applications
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Solutions of large sparse linear fixed-point problems lie at the heart of many important performance analysis calculations. These calculations include steady-state, transient and passage-time computations in discrete-time Markov chains, continuous-time Markov chains and semi-Markov chains. In recent years, much work has been done to extend the application of asynchronous iterative solution methods to different contexts. This work has been motivated by the potential for faster solution, more efficient use of the communication channel and access to memory, and simplification of task management and programming. In this paper, we show how the key performance metrics mentioned above can be transformed into problems which can be solved using asynchronous iterative methods with guaranteed convergence-using the full breadth of Chazan and Miranker's classes of asynchronous iterations. We introduce the application of asynchronous iterative solution methods within this context by applying several algorithm variants to the steady-state analysis of a GSPN model of a flexible manufacturing system. We show that for varying numbers of processors and different problem sizes one of these algorithm variants offers consistently better wall time until convergence, a consistently better communication profile, and often requires fewer update iterations than a standard parallel Jacobi algorithm, seemingly benefiting from a form of Gauss-Seidel effect.