An application of exact linear algebra to capacity planning models
ACM Communications in Computer Algebra
A generalized method of moments for closed queueing networks
Performance Evaluation
Exact analysis of performance models by the Method of Moments
Performance Evaluation
Efficient parallelization of the Method of Moments for queueing networks using multi-modular algebra
Proceedings of the 5th International ICST Conference on Performance Evaluation Methodologies and Tools
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We introduce the Class-oriented Method of Moments (CoMoM), a new exact algorithm to efficiently compute normalizing constants and marginal queue-length probabilities in closed multiclass queueing networks. Closed models are important for performance evaluation of multi-tier applications, but when the number of service classes is large they become too expensive to solve with existing methods, such as Mean Value Analysis (MVA). CoMoM addresses this limitation by a new recursion that scales efficiently with the number of classes. Compared to the MVA algorithm, which recursively computes mean queue-lengths, CoMoM carries on in the recursion also information on higher-order moments of queue-lengths. We show that this additional information minimizes the number of recursive steps needed to solve the model and makes CoMoM the best-available algorithm for networks with several classes. For example, we show a model of a real J2EE application where CoMoM is several orders of magnitude faster and more memory-efficient than MVA. We conclude the paper by generalizing CoMoM to the efficient computation of marginal queue-length probabilities, which finds application in the evaluation of state-dependent indexes such as energy consumption or quality-of-service metrics.