Introducing modern coneal theory

we present the netWOrk dynamic eqUations tO describe thenetwork states in nonsational’y environment in data communication netWorks with the objective of minimax the total network delay that is given by the packets waiting in all node bibers and ones are Processing in all networknodes. Based on the I’yapunov principle

we develop a new method tO test stability Of routing decision in datanetworks after the network nonlinear state control models are approximate lineallzed by numetical method. In thestationary network environment we cochrm the conclusions of netWork optimization control such as we can getshortest commllnication path that is defined as function of link delay

and optimal routing will never form a routing link ring and so on.