On the modeling and optimal flow control of the Jacksonian network

The modeling and optimal flow control of a Jacksonian network in equilibrium is investigated. The model employed consists of a controller node cascaded with the Jacksonian network. Input packets arrive at the controller node with a Poissonian rate δ. For a blocking type strategy for accessing the network it is shown that the control which maximizes the average throughput of the network subject to a bounded average time delay constraint is a window flow control mechansim. The window size depends on the offered load δ, the maximum service rate of the controlling queueing system, c, and the Norton equivalent service rate of the network μ. The dependence of the average throughput and the average time delay on the control is also analyzed.