Consider a closed Jackson network with M nodes. The service rate at each node is controllable in a decentralized manner, i.e., it will be controlled based on local information extracted from that node only. For each node, there is a holding cost and an operating cost. Assume that both costs are time-homogeneous, and that the operating cost is a linear function of the service rate. Allow, however, both costs to be arbitrary functions of the number of jobs at the node. The objective is to minimize the time-average expected total cost. The authors show that there exists an optimal control characterized by a set of thresholds (one for each node), such that it is optimal for each node to serve at zero rates if the
