Asymptotic expansions for closed Markovian networks with state-dependent service rates
Journal of the ACM (JACM)
RECAL—a new efficient algorithm for the exact analysis of multiple-chain closed queuing networks
Journal of the ACM (JACM)
Solving sparse linear equations over finite fields
IEEE Transactions on Information Theory
Mean Value Analysis by Chain of Product form Queueing Networks
IEEE Transactions on Computers
Implementation of Monte Carlo integration for the analysis of product-form queueing networks
Performance Evaluation
Queueing networks and Markov chains: modeling and performance evaluation with computer science applications
Open, Closed, and Mixed Networks of Queues with Different Classes of Customers
Journal of the ACM (JACM)
Mean-Value Analysis of Closed Multichain Queuing Networks
Journal of the ACM (JACM)
The Distribution of Queuing Network States at Input and Output Instants
Journal of the ACM (JACM)
Dynamic Scaling and Growth Behavior of Queuing Network Normalization Constants
Journal of the ACM (JACM)
The Operational Analysis of Queueing Network Models
ACM Computing Surveys (CSUR)
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
On the asymptotic behaviour of closed multiclass queueing networks
Performance Evaluation
A Unifying Framework for the Approximate Solution of Closed Multiclass Queuing Networks
IEEE Transactions on Computers
Solving Large Sparse Linear Systems over Finite Fields
CRYPTO '90 Proceedings of the 10th Annual International Cryptology Conference on Advances in Cryptology
SIGMETRICS '06/Performance '06 Proceedings of the joint international conference on Measurement and modeling of computer 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
Queuing networks with multiple closed chains: theory and computational algorithms
IBM Journal of Research and Development
Exact analysis of performance models by the Method of Moments
Performance Evaluation
Closed Queueing Networks Under Congestion: Nonbottleneck Independence and Bottleneck Convergence
Mathematics of Operations Research
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We introduce a new solution technique for closed product-form queueing networks that generalizes the Method of Moments (MoM), a recently proposed exact algorithm that is several orders of magnitude faster and memory efficient than the established Mean Value Analysis (MVA) algorithm. Compared to MVA, MoM recursively computes higher-order moments of queue lengths instead of mean values, an approach that remarkably reduces the computational costs of exact solutions, especially on models with large numbers of jobs. In this paper, we show that the MoM recursion can be generalized to include multiple recursive branches that evaluate models with different numbers of queues, a solution approach inspired by the Convolution algorithm. Combining the approaches of MoM and Convolution simplifies the evaluation of normalizing constants and leads to large computational savings with respect to the recursive structure originally proposed for MoM.