Modeling for flexible manufacturing systems (FMS) with an FMS blocking mechanism and a blocking depended static Markov job routing

We consider a Flexible Manufacturing System (FMS) which is composed of a set of workstations, a common buffer and a Material Handling System (MHS). Each workstation includes a limited input buffer, several machines and a limited output buffer. The MHS consists of several carts moving jobs among the workstations according to the process paths required by the jobs. The carts treat blocked jobs in accordance with a new blocking mechanism, called ‘FMS blocking mechanism’. The function of the common buffer is to temporarily store blocked jobs. Such an FMS is formulated as an open queueing network, in which the MHS is modeled as a central station routing jobs to the workstations. In the model, the machines process jobs with an exponentially distributed processing time, and the carts route jobs to the workstations following a ‘Blocking Depended Static Markov (BDSM) job routing’ with an exponentially distributed routing time and treat blocked jobs in accordance with the FMS blocking mechanism. It is shown that the equilibrium state distribution of the model has a product-form solution. The blocking probabilities are obtained by computing a fixed point problem whose solution is revealed by an iterative algorithm. Moreover, it is shown that the throughputs of the workstations are independent of the spaces on the local buffers at the workstations. Several numerical examples are presented.