Stochastic theory of a fluid model of multiple failure-susceptible producers and consumers coupled by a buffer.

A central topic in manufacturing is the complex interdependence of realized production rate and inventory. The role of inventory is to buffer the vicissitudes of machine failures/repairs and service times. The fluid model considered here operates in the considerably slower time scale associated with the former random phenomenon. This paper analyzes, derives efficient computational procedures and numerically investigates the following model: m producing machines supply a buffer, n consuming machines feed off it. Each machine independently alternates between exponentially distributed random periods in the "in service" and "failed" states. Producers/consumers have their own failure/repair rates and working capacities. When the buffer is either full or empty some of the machines in service are not utilized to capacity; otherwise they are fully utilized.