Efficiency of Traffic Routing When Some Users Are Controlled in Grid Traffic Networks

Considering the situation in which some users are controlled while the others still chase their least cost so that the user equilibrium is formed,the efficiency is 1 if the latency functions are linear;and is 1 if 1≤A≤2;and is(A-1)2 if A2 when the latency functions are nonnegative,non-decreasing and differentiable,where A≥1 is the comparability coefficient of Jacobian matrix of latency functions.