A generalized semi-Markov process model for the buffer allocation problem in a cyclic network

A generalized semi-Markov process model is presented for establishing relations regarding the throughput associated with different buffer allocation schemes in a cyclic queuing network. For a network with two stations it is shown that transposing the number of buffers assigned to each station does not affect the throughput. Furthermore, it is shown that the optimal buffer allocation scheme, which maximizes the throughput, is the one for which the absolute difference between the numbers of buffers assigned to each station is minimized, i.e., it becomes either 0 or 1. This optimal allocation is insensitive to any general-type service time distributions for the two stations; these distributions are in general different and can be even correlated