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A general algorithm to compute the steady-state solution of product-form cooperating Markov chains

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2 Author(s)
Andrea Marin ; Dipartimento di Informatica, Università Ca' Foscari di Venezia, Venice, Italy 30172 ; Samuel Rota Bulò

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.

Published in:

2009 IEEE International Symposium on Modeling, Analysis & Simulation of Computer and Telecommunication Systems

Date of Conference:

21-23 Sept. 2009