Further Studies on Two Queues in Parallel

This paper presents some further results related to a queueing model originally suggested by the author: “Two queues in parallel” (J. Boy. Statist. Soc, Ser. B, 31, 432–445, 1969). A detailed study of the model under the imposition of finite waiting rooms when each queue can accommodate at most two customers illustrates the complexity of the problems involved. However, this study leads to some results concerning the nature of the equilibrium probabilities in the more general finite waiting room cases. A study of the correlation between the input distributions and the correlation of the queue size distributions gives rise to some general conjectures concerning these relationships.