In this paper, we design adaptive traffic signal control policies for urban traffic networks. Vehicles at the end of an approach to an intersection queue up in separate lanes, with finite flow capacities, corresponding to different possible turn maneuvers according to static route choice behavior. We analyze stability of such traffic networks under signal control policies that, at every intersection, give green light to at most one incoming lane at any time. We particularly focus on a class of minimalist distributed policies, under which traffic signal control at an intersection requires information only about the occupancy levels on the lanes incoming at that intersection, and does not require information about turn ratios, flow capacities or the external arrival rates to the network. We show that such a minimalist policy that exhibits monotonicity in the green light durations with respect to the occupancy levels is maximally stabilizing for acyclic network topologies, and admits a globally asymptotically stable equilibrium. Our results rely on novel tools developed recently for stability analysis of monotone dynamical systems with conservation of mass. We also present simulations to compare the stability conditions under static and dynamic route choice.