Periodic orbits in a class of re-entrant manufacturing systems

Queue changes associated with each step of a manufacturing system are modeled by constant vector fields (fluid model of a queueing network). Observing these vector fields at fixed events reduces them to a set of piecewise linear maps. It is proved that these maps show only periodic or eventually periodic orbits. An algorithm to determine the period of the orbits is presented. The dependence of the period on the processing rates is shown for a 3(4)-step, 2-machine problem.