The method of moments for higher moments and the usefulness of formula manipulation systems

Though often not explicitly stated, the method of moments is one of the heavily used methods in queueing analysis. By tracing a typical, tagged customer as it proceeds through the system 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. Starting from general considerations, the problems in dealing with higher moments are insulated, and solutions are presented. These results give a deep insight into the nature of the method of moments. It is difficult to handle the complex formulae for higher moments without the help of a formula manipulation system such as SCRATCHPAD II The tool was particularly useful to make first steps to find hypothetical formulae, then start proof (e.g. by induction) and to perform complex derivations, e.g. for comparison. The use of the tool gives deep insight into the potential use of computer algebra systems for queueing analysis.