RECAL—a new efficient algorithm for the exact analysis of multiple-chain closed queuing networks
Journal of the ACM (JACM)
Systems in stochastic equilibrium
Systems in stochastic equilibrium
Decomposition and aggregation by class in closed queueing networks
IEEE Transactions on Software Engineering
Calculating joint queue-length distributions in product-form queuing networks
Journal of the ACM (JACM)
Mean Value Analysis by Chain of Product form Queueing Networks
IEEE Transactions on Computers
Queueing networks—exact computational algorithms: a unified theory based on decomposition and aggregation
The evaluation of normalizing constants in closed queueing networks
Operations Research
Asymptotic Expansions for Large Closed Queueing Networks with Multiple Job Classes
IEEE Transactions on Computers
The Fourier-series method for inverting transforms of probability distributions
Queueing Systems: Theory and Applications - Numerical computations in queues
Mean-Value Analysis of Closed Multichain Queuing Networks
Journal of the ACM (JACM)
Dynamic Scaling and Growth Behavior of Queuing Network Normalization Constants
Journal of the ACM (JACM)
A tree convolution algorithm for the solution of queueing networks
Communications of the ACM
Computational algorithms for closed queueing networks with exponential servers
Communications of the ACM
Computer Performance Modeling Handbook
Computer Performance Modeling Handbook
Asymptotic analysis of closed queueing networks with bottlenecks
Proceedings of the IFIP WG 7.3 International Conference on Performance of Distributed Systems and Integrated Communication Networks
Towards a polynomial-time randomized algorithm for closed product-form networks
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Simple bounds for closed queueing networks
Queueing Systems: Theory and Applications
SIGMETRICS '06/Performance '06 Proceedings of the joint international conference on Measurement and modeling of computer systems
A Unified Framework for Numerically Inverting Laplace Transforms
INFORMS Journal on Computing
A generalized method of moments for closed queueing networks
Performance Evaluation
Exact analysis of performance models by the Method of Moments
Performance Evaluation
Mathematical and Computer Modelling: An International Journal
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A new algorithm is developed for calculating normalization constants (partition functions) and moments of product-form steady-state distributions of closed queuing networks and related models. The essential idea is to numerically invert the generating function of the normalization constant and related generating functions appearing in expressions for the moments. It is known that the generating function of the normalization constant often has a remarkably simple form, but numerical inversion evidently has not been considered before. For p-dimensional transforms, as occur with queuing networks having p closed chains, the algorithm recursively performs p one-dimensional inversions. The required computation grows exponentially in the dimension, but the dimension can often be reduced by exploiting conditional decomposition based on special structure. For large populations, the inversion algorithm is made more efficient by computing large sums using Euler summation. The inversion algorithm also has a very low storage requirement. A key ingredient in the inversion algorithm is scaling. An effective static scaling is developed for multichain closed queuing networks with only single-server and (optionally) infinite-server queues. An important feature of the inversion algorithm is a self-contained accuracy check, which allows the results to be verified in the absence of alternative algorithms.