A Queuing Model for the Utilisation of Machines under Random Parallel Loading

Abstract

In a system consisting of many identical machines, any set of machines may be reserved from any other machine in order that the set may carry out a production job simultaneously. A simple queuing model, entailing various approximations, is used to give formulae for utilisation, holding time and other parameters of the system. The model suggests that a practical system designed on these lines would become congested at between one-tenth and one-fifth of full loading.