Equilibrium principle application to routing control in packet data transmission networks

Annual exponential growth of data flows in large scale networks impels to search not only network hardware improvements but also more perfect routing control algorithms. In networks, it is impossible to use centralized algorithms of routing control. Parallel algorithms choice must be based on the principles of functional effectiveness and stability (equilibrium). In large-scale networks, there is a huge number of users' pairs trying to achieve the maximally possible rate of data transmission by routing control. Thus, control must be based on multicriteria optimization ideas and methods. The Nash equilibrium (game formulation of the routing problem) formally presents optimality of transmission control in distributed systems. In the present paper, the equilibrium routing is proved to exist under general conditions. The solution is additionally shown to be effective in Pareto sense and computationally stable. An effective (quick and parallel) game theory algorithm is suggested and its convergence is proved.