General Formulation

Abstract

With but a few exceptions, the existing literature on multiple-channel service systems has not been very useful in the analysis of typical practical problems for at least three reasons. First, despite the existence of a few thousand papers and a dozen or more books on queueing theory and related subjects, the range of problems that have been studied is rather narrow. Secondly, in the mathematical formulations, people usually make many idealizations (Poisson arrivals, stationary behavior, independent service times, etc.) which are of such doubtful validity that it is difficult to judge the accuracy with which any conclusions can be applied to practical problems. Thirdly, particularly for non-stationary behavior, the “solutions” describing the evolution of even the simplest systems are usually so complicated as to be useless for computation.