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CoMoM: class-oriented evaluation of multiclass models

We introduce the Class-Oriented Method-of-Moments (CoMoM), a new exact algorithm for computing normalizing constants, mean performance indexes and marginal queue-length probabilities in closed multiclass queueing networks [1]. Closed models are important for performance evaluation of multi-tier systems, but when the number of service classes is large they are too expensive to solve exactly using Mean Value Analysis (MVA) (see [2] and references therein). CoMoM addresses this limitation with a recursion that is computationally efficient also on models with several 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 expressed in terms of normalizing constants. This approach makes CoMoM the most efficient algorithm for models with several classes. Further, CoMoM generalizes to the efficient computation of marginal queue-length probabilities, which may find application in the evaluation of state-dependent indexes such as energy consumption or quality-of-service metrics. The next sections are organized as follows. After giving required background in Section 1.1, we introduce CoMoM in Section 2 using an illustrative example. The general structure of the algorithm is outlined in Section 3, where we also discuss the computation of marginal queue-length probabilities. Section 4 gives concluding remarks.