Optimal flow control of a class of queueing networks in equilibrium

The problem of optimum flow control of a class of queueing systems which appears as a model of datagram and virtual circuit computer communication networks is investigated. This class "intuitively" has the property that by increasing the load on the network, both the average throughput and the average time delay also increase. It is shown that the control that achieves the maximum throughput under a bounded average time delay criterion can be specified by a "window" flow control mechanism (bang-bang control). The window size , the maximum number of unacknowledged packets in the system, can be easily derived from the preassigned upper bound on the time delay , the Norton equivalent of the queueing system μ, and the maximum admissible total load on the network .