The Method of Moments for Higher Moments { Problems , Solutions , and
نویسندگان
چکیده
Though often not explicitly stated, the method of moments is one of the heavily used methods in queueing analysis. A typical, tagged customer is traced as it proceeds through the system and the components of its delay are individually analyzed. Using the moments of these components, moments of the sojourn and waiting times of an arbitrary customer can be derived. By this method, expected values for a wide range of systems, especially single server systems with Poisson arrivals, have been obtained in the last decades. This paper investigates the suitability of the method of moments to derive higher moments. Sums of random variables, Little's law for higher moments, and conditional remaining service times play an important role. Starting from general considerations, the problems in dealing with higher moments are insulated, and some solutions are presented. These results give a deep insight into the nature of the method of moments. The complex formulae for higher moments are handled with the help of the formula manipulation system SCRATCHPAD II. It is demonstrated, how such a system can be used as a tool for handling complex formulae in queueing theory.
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