In the last few years several new results about product-form solutions of stochastic models have been formulated. In particular, the Reversed Compound Agent Theorem (RCAT) and its extensions play a pivotal role in the characterization of cooperating stochastic models in product-form. Although these results have been used to prove several well-known theorems (e.g., Jackson queueing network and G-network solutions) as well as novel ones, to the best of our knowledge, an automatic tool to derive the product-form solution (if present) of a generic cooperation among a set of stochastic processes, is not yet developed. In this paper we address the problem of solving the non-linear system of equations that arises from the application of RCAT. We present an iterative algorithm that is the base of a software tool currently under development. We illustrate the algorithm, discuss the convergence and the complexity, compare it with previous algorithms defined for the analysis of the Jackson networks and the G-networks. Several tests have been conducted involving the solutions of a (arbitrary) large number of cooperating processes in product-form by RCAT.
|Data di pubblicazione:||2009|
|Titolo:||A general algorithm to compute the steady-state solution of product-form cooperating Markov chains|
|Titolo del libro:||Proc. of Int. Conf. MASCOTS 2009|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1109/MASCOT.2009.5366744|
|Appare nelle tipologie:||4.1 Articolo in Atti di convegno|
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