Designs of optimal switching feedback decentralized control policies for re-entrant queueing networks: A case study

We study the problem of optimal feedback switching control of two-server re-entrant manufacturing network with nozero setup times introduced by Kumar and Seidman. The optimal steady-state (periodic) behavior is determined for the system in the analytical form. A simple feedback switching control law is proposed under which the process in the system converges to the optimal steady state behavior irrespective of the initial state. This law is 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 framework of Kumar-Seidman model is used for presentation of a methodology of both design of a switching policy and justification of its convergence.