In this paper we present DALI, a distributed, collaborative multi-agent Traffic Signal Timing system (TST) for highly dynamic traffic conditions. In DALI, intersection controllers are augmented with software agents which collaboratively adapt signal timings by considering the feedback of all controller agents that may be affected by a change. The model is based on a real-world TST and is intended to be deployed with minimal changes to the infrastructure. DALI has been validated on a simulated model of the City of Richardson, Texas, comprising 128 signalized intersections. The experimental results show that it outperforms the conventional traffic operation modes as well as an RL-based TST in highly dynamic scenarios.