General network equilibrium analysis
Shu‐Cherng Fang, Elmor L. Peterson · International Journal of Systems Science · 1983
Network equilibrium problems, such as electric, hydraulic, traffic and economic equilibrium problems, are very common topics in real world situations. Equilibrium solutions can be characterized by various flow laws which govern the feasible flows on the underlying network, the dependent index quantity which is resulted by feasible flows, and the equilibrium principles which put the network system in a stable state. In this paper, a generalized complementary model is established for the general network equilibrium problems. Due to the nature of conical duality and complementary characterization of equilibrium solutions, under some monotonicity assumptions, the equilibrium problem is equivalent to the extremality conditions of a generalized geometric programming problem. Hence geometric programming methods can be applied to the network equilibrium analysis. Furthermore, the recent studies of Fang and Peterson (1982) in generalized variational inequalities can be adopted to handle more complicated cases. In order to compute equilibrium solutions, fixed-points computation concepts are also introduced.