The Application of Optimal Control Theory to Dynamic Routing in Data Communication Networks

The flow of messages in a message-switched data communication net-work is modeled in a continuous dynamical state space. The state vari-ables represent message storage at the nodes and the control variables represent message flow rates along the links. A deterministic linear cost functional is defined which is the weighted total message delay in the network when we stipulate that all the message backlogs are emptied at the final time and the inputs are known. The desired mini-mization of the cost functional results in a linear optimal control problem with linear state and control variable inequality constraints. The remainder of the thesis is devoted to finding the feedback solution to the optimal control problem when all the inputs are con-stant in time. First, the necessary conditions of optimality are derived and shown to be sufficient. The pointwise minimization in time is a linear program and the optimal control is seen to be of the bang