Optimal control of service rates and arrivals in Jackson networks

We can represent each dynamic job shop system as a network of queues, in which each service station indicates a machine or a production department. Now, assume that we can control the service rates of these service stations and also the arrival rates to the service stations, in which the arrival rate to each service station corresponds to the total rates of demands for the products which are processed by this service station. In this paper, we develop a new model for optimal control of service rates of all service stations and also the arrival rates to these service stations in a class of Jackson networks, in which the expected value of shortest path of the network and also the total operating costs of all service stations of the network per period are minimized. The expected value of shortest path of such networks of queues is equal to the expected value of the completion time of the first product, which is an important factor in production systems. The networks of queues, which we analyze in this paper, have all specifications of Jackson networks, except they do not include M/M/C queueing systems.