A Numerical Algorithm for the Solution of Product-Form Models with Infinite State Spaces
Markovian models play a pivotal role in system performance evaluation field. Several high level formalisms are capable to model systems consisting of some interacting sub-models, but often the resulting underlying process has a number of states that makes the computation of the solution unfeasible. Product-form models consist of a set of interacting sub-models and have the property that their steady-state solution is the product of the sub-model solutions considered in isolation and opportunely parametrised. The computation of the steady-state solution of a composition of arbitrary and possibly different types of models in product-form is still an open problem. It consists of two parts: a) deciding whether the model is in product-form and b) in this case, compute the stationary distribution efficiently. In this paper we propose an algorithm to solve these problems that extends that proposed in  by allowing the sub-models to have infinite state spaces. This is done without a-priori knowledge of the structure of the stochastic processes underlying the model components. As a consequence, open models consisting of non homogeneous components having infinite state space (e.g., a composition of G-queues, G-queues with catastrophes, Stochastic Petri Nets with product-forms) may be modelled and efficiently studied.
KeywordsState Space Reversed Rate Strong Connected Component First Come First Serve Jackson Network
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