RECAL—a new efficient algorithm for the exact analysis of multiple-chain closed queuing networks
Journal of the ACM (JACM)
An Approximate Minimum Degree Ordering Algorithm
SIAM Journal on Matrix Analysis and Applications
On the worst-case complexity of integer Gaussian elimination
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Mean-Value Analysis of Closed Multichain Queuing Networks
Journal of the ACM (JACM)
Linearizer: a heuristic algorithm for queueing network models of computing systems
Communications of the ACM
Computational algorithms for product form queueing networks
Communications of the ACM
Computational algorithms for closed queueing networks with exponential servers
Communications of the ACM
A Survey of Numerical Mathematics
A Survey of Numerical Mathematics
Introduction to Algorithms
Primality Testing with Gaussian Periods
FST TCS '02 Proceedings of the 22nd Conference Kanpur on Foundations of Software Technology and Theoretical Computer Science
Product Form Queueing Networks
Performance Evaluation: Origins and Directions
Reducing the bandwidth of sparse symmetric matrices
ACM '69 Proceedings of the 1969 24th national conference
SIGMETRICS '06/Performance '06 Proceedings of the joint international conference on Measurement and modeling of computer systems
Java Modelling Tools: an Open Source Suite for Queueing Network Modelling andWorkload Analysis
QEST '06 Proceedings of the 3rd international conference on the Quantitative Evaluation of Systems
A Simple Derivation of the MVA and LBANC Algorithms from the Convolution Algorithm
IEEE Transactions on Computers
CoMoM: Efficient Class-Oriented Evaluation of Multiclass Performance Models
IEEE Transactions on Software Engineering
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The solution of service performance models based on closed queueing networks often relies on the Mean Value Analysis (MVA) algorithm, which is unable to solve exactly large models with multiple service classes and hundreds or thousands of users. The Method of Moments (MoM) algorithm has been introduced and addressed this problem, by relying on the exact solution of large linear systems with rational coefficients. In this paper, we focus on the design, analysis and implementation of a parallel solver for MoM linear systems. Parallelization is introduced using residue number systems and recombining the results by the Chinese Remainder Theorem. A comprehensive test set representative of modern applications is used for experimental evaluation. The overall result proves the enhanced performance of both the MoM algorithm over established ones, namely Convolution and RECAL, and of the parallel solver over the serial one.