On optimal switching interactive decentralized control of networked manufacturing systems

The paper considers standard fluid models of multi-product multiple-server production systems where setup times are incurred whenever a server changes product. Concerned is the general approach to the problem of optimizing the long-run average cost per unit time that offers to first determine an optimal steady state (periodic) behavior and then to design a feedback scheduling protocol ensuring convergence to this behavior as time progresses. The second part of this program is treated and a systematic presentation of a novel approach to it is offered. This approach gives rise to protocols that are cyclic and distributed: the servers do not need information about the entire system state. Each of them proceeds basically from the local data concerning only the currently served queue, although a fixed finite number of one-bit notification signals should be exchanged between the servers during every cycle. The approach is illustrated by simple albeit instructive examples concerning polling systems, single server systems with processor sharing scheme, and the re-entrant two-server manufacturing network with non-negligible setup times introduced by Kumar and Seidman. For the last network considered in the analytical form, the optimal steady-state (periodic) behavior is first determined. Based on the desired steady state behavior and the presented theory, we designed simple distributed feedback switching control laws for all examples. These laws not only obtain the required behaviors but also make them globally attractive, irrespective of the system parameters and initial state.