A state variable model for the fluid approximation of flexible manufacturing systems

We analyze discrete event dynamic processes which represent flexible manufacturing systems (FMS) characterized by unreliable machines, buffers of finite capacity, arbitrary service time distributions and deterministic sequencing and routing policies. Our main goal is the design of the FMS configuration embedded with its optimum control policy. The problem is addressed using first and second order fluid approximation obtained by splitting the process in two hierarchical layers and defining what we call micro and macro events. With an original approach this fluid approximation lends itself to a discrete-time linear stochastic state variable model which offers average values and variances of both performance measures and their gradients with respect to the most significant FMS parameters. Finally, we investigate problems concerning the non-differentiability of the performance indices with respect to certain design parameters, specifically the control parameters when they appear as structural elements of the model