Optimal hop-by-hop control with multiple transmitters

We formulate the problem of hop-by-hop flow control in a computer network as a Markov decision process where the objective is to minimize the number of untransmitted messages in the system, subject to the evolution of the state and to the buffer constraints. The control action consists of an allocation of the receiving node´s buffers among the transmitting nodes. When the message generation processes at each transmitting node are independent and identically distributed, we find an expression for the optimal control and show that it is the outcome of a myopic policy.