Monotonicity of the Throughput in Single Server Production and Assembly Networks with Respect to the Buffer Sizes

摘要

The single-server tree-shaped production and assembly network with arbitrary arrival streams, Markovian routing, and nonzero, independent, and generally distributed service times is considered. It is shown that the throughput is monotone in the sizes of the local buffers, using sample path comparison. Most of the assumptions can be relaxed, such as independent service times and Markovian routing.