Cooperative flow dynamics in production lines with buffer level dependent production rates

We study, in the fluid flow framework, the cooperative dynamics of a buffered production line in which the production rate of each work-cell does depend on the content of its adjacent buffers. Such state dependent fluid queueing networks are typical for people based manufacturing systems where human operators adapt their working rates to the observed environment. We unveil a close analogy between the flows delivered by such manufacturing lines and cars in highway traffic where the driving speed is naturally adapted to the actual headway. This close analogy is thoroughly explored. In particular, by investigating the dynamic response of small perturbations around free flow stationary regimes, we can draw a ‘phase diagram’. This diagram exhibits two different flow patterns, namely the free and jamming production regimes. The transitions between these regimes are tuned by the production control parameters (i.e. the buffer capacities, the reaction sensitivity, the control sampling time, etc.). We finally extract a dimensionless dynamic parameter directly relevant for design purposes.