Dynamic programming for optimal packet routing control using two neural networks

We propose a dynamic programming model for optimal packet routing control using two neural networks within the framework of statistical physics. An energy function for each neural network is defined in order to express competition between a queue length and the shortest path of a packet to its destination node. We set a dynamics for the thermal average of the state of neuron in order to make the mean-field energy of each neural network decrease as a function of time. By computer simulations with discrete time steps, we show that the optimal control of packet flow is possible by using the proposed method, in which a goal-directed learning has been done for firm-dependent environment for packets.