System optimal dynamic traffic assignment: solution structures of the signal control in non-holding-back formulations

This paper devises locally optimal traffic Signal Control (SC) settings in a Non-Holding-Back Dynamic Traffic Assignment with SC (NHB DTA-SC) formulation for single destination (i.e. one source to one destination and many sources to one destination) networks. To this end, we apply temporal-spatial dual decomposition method and decompose the NHB DTA-SC problem into intersection cells and non-intersection cells. Then we further decompose the intersection cells into different subproblems, i.e. Occupancy Minimization (OM), Flow Maximization (FM), and SC. To study the optimal SC structures, we examine the Karush-Kuhn-Tucker (KKT) optimality conditions of the decomposed SC subproblem. Finally, we obtain the locally optimal SC structures under different network conditions that include over-saturated, under-saturated, and queue spillback traffic scenarios. We also present several numerical results to verify the optimality structures found by our theoretical derivations.