Network Traffic Flow Evolution Model Based on Disequilibrium Theory

The disequilibrium theory in economics is used to depict the network traffic flow evolution process from disequilibrium to equilibrium. Three path choice behavior criteria are proposed, and the equilibrium traffic flow patterns formed by these three criteria are defined as price regulation user equilibrium, quantity regulation user equilibrium, and price-quantity regulation user equilibrium, respectively. Based on the principle of price-quantity regulation user equilibrium, the method of network tatonnement process is used to establish a network traffic flow evolution model. The unique solution of the evolution model is proved by using Picard’s existence and uniqueness theorem, and the stability condition of the unique solution is derived based on stability theorem of nonlinear system. Through numerical experiments, the evolution processes of network traffic flow under different regulation modes are analyzed. The results show that all the single price regulation, single quantity regulation, and price-quantity regulation can simulate the evolution process of network traffic flow. Price-quantity regulation is the combination of price regulation user equilibrium and quantity regulation user equilibrium, which thus can simulate the evolution process of network traffic flow with multiple user class.