The Efficiency Loss of User Equilibrium with Linear Non-separable and Asymmetric Latency Functions

Selfish routing problem in which traffic demands are revealed in n sequential games in an online fashion is discussed in this paper. In each game, the new demands form a user equilibrium and their routing remain unchanged afterwards. The efficiency loss of user equilibrium is 4n /(2n+2)-c² n-(n-1)δ when c² ≤ (n+1)/n 4n² c²/[(n+1)-(n-1)δ]² when c² > n+1/n if latency functions on the edges are linear non-separable and asymmetric, where c² ≥ 1.0 ≤ δ ≤ 0 are the degree of asymmetry and the degree of adjacence of Jacobian matrix of latency functions.