Solving Signal Control Problems with Second-Order Sensitivity Information of Equilibrium Network Flows

Abstract EN

The equilibrium network signal control problem is represented as a Stackelberg game.

Due to the characteristics of a Stackelberg game, solving the upper-level problem and lower-level problem iteratively cannot be expected to converge to the solution.

The reaction function of the lower-level problem is the key information to solve a Stackelberg game.

Usually, the reaction function is approximated by the network sensitivity information.

This paper firstly presents the general form of the second-order sensitivity formula for equilibrium network flows.

The second-order sensitivity information can be applied to the second-order reaction function to solve the network signal control problem efficiently.

Finally, this paper also demonstrates two numerical examples that show the computation of second-order sensitivity and the speed of convergence of the nonlinear approximation algorithm.