A semi-open decomposition approach for an open queueing network in a general configuration with a kanban blocking mechanism

We consider an open queueing network in a general configuration with a kanban blocking (KB) mechanism. The system is composed of many stations such as an entrance station, workstation, a common station and an exit station, that are arranged in a general configuration. The work-in-process (WIP) at a workstation is controlled by the kanban mechanism. The function of the common station is to store blocked jobs temporarily. A semi-open decomposition approach is applied to the queueing network as a technique which decomposes each workstation as a semi-open queueing network. Then the blocking probabilities for jobs when they are routed to the workstations are obtained by an algorithm of calculating a set of fixed point problems. A numerical example shows that the quality of the solution generated by the algorithm is satisfactory. Based on obtained blocking probabilities, the system performances can be easily measured.