We study the convergence properties of some rational approximants for stocha-stic discrete event systems. Examples of the systems considered include computer and communication systems and general distributed and parallel processing systems. Diiculties often arise in the analysis of such systems due to the so-called \curse of dimensionality" in calculating some integer-parameterized functions, where the integer parameter represents the system size or dimension. Our basic idea is to develop global approximants for such functions by exploring the properties of the systems. Various examples in a previous paper have demonstrated the application of the approach. In this paper we analyze the convergence rates of these approximants.
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