An analysis of an approximation algorithm for queueing networks
Performance Evaluation
Quantitative system performance: computer system analysis using queueing network models
Quantitative system performance: computer system analysis using queueing network models
Metamodeling: a study of approximations in queueing models
Metamodeling: a study of approximations in queueing models
Bound hierarchies for multiple-class queuing networks
Journal of the ACM (JACM) - The MIT Press scientific computation series
The algebraic eigenvalue problem
The algebraic eigenvalue problem
Mean-Value Analysis of Closed Multichain Queuing Networks
Journal of the ACM (JACM)
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
Performance bound hierarchies for queueing networks
ACM Transactions on Computer Systems (TOCS)
Linearizer: a heuristic algorithm for queueing network models of computing systems
Communications of the ACM
Balanced job bound analysis of queueing networks
Communications of the ACM
Computer Performance Modeling Handbook
Computer Performance Modeling Handbook
A Perspective on Iterative Methods for the Approximate Analysis of Closed Queueing Networks
Proceedings of the International Workshop on Computer Performance and Reliability
Some Extensions to Multiclass Queueing Network Analysis
Proceedings of the Third International Symposium on Modelling and Performance Evaluation of Computer Systems: Performance of Computer Systems
Improved lineariser methods for queueing networks with queue dependent centres
SIGMETRICS '84 Proceedings of the 1984 ACM SIGMETRICS conference on Measurement and modeling of computer systems
Approximate analysis of large and general queueing networks
Approximate analysis of large and general queueing networks
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This paper presents new formulations of the approximate mean value analysis (MVA) algorithms for the performance evaluation of closed product-form queueing networks. The key to the development of the algorithms is the derivation of vector nonlinear equations for the approximate network throughput. We solve this set of throughput equations using a nonlinear Gauss-Seidel type distributed algorithms, coupled with a quadratically convergent Newton's method for scalar nonlinear equations. The throughput equations have enabled us to: (a) derive bounds on the approximate throughput; (b) prove the existence, uniqueness, and convergence of the Schweitzer-Bard (S-B) approximation algorithm for a wide class of monotone, single class networks, (c) establish the existence of the S-B solution for multi-class, monotone networks, and (d) prove the asymptotic (i.e., as the number of customers of each class tends to ∞) uniqueness of the S-B throughput solution, and the asymptotic convergence of the various versions of the distributed algorithms in multi-class networks with single server and infinite server nodes. The asymptotic convergence is established using results from convex programming and convex duality theory. Extension of our algorithms to mixed networks is straighfoward. Only multi-class results are presented in this paper.