Relations between probabilities of high states describing the bottleneck of a certain inventory system and the dynamic parameters of an aggregated input

The authors investigate a bottleneck in an inventory system composed of the following subsystems: production, transport, storage, and receiver. In order to obtain a mathematical description of the bottleneck in the system, the authors derive a system of differential equations which is satisfied by the probabilities of the high states of a process controlled by an aggregated product supply process.