Human behavior and interaction in road traffic is highly complex, with many open scientifi?c questions of high applied importance, not least in relation to recent development efforts toward automated vehicles. In parallel, recent decades have seen major advances in cognitive neuroscience models of human decision-making, but these models have mainly been applied to simplified laboratory tasks. Here, we demonstrate how variable-drift extensions of drift diffusion (or evidence accumulation) models of decision-making can be adapted to the mundane yet non-trivial scenario of a pedestrian deciding if and when to cross a road with oncoming vehicle traffic. Our variable-drift diffusion models provide a mechanistic account of pedestrian road-crossing decisions, and how these are impacted by a variety of sensory cues: time and distance gaps in oncoming vehicle traffic, vehicle deceleration implicitly signaling intent to yield, as well as explicit communication of such yielding intentions. We conclude that variable-drift diffusion models not only hold great promise as mechanistic models of complex real-world decisions, but that they can also serve as applied tools for improving road traffic safety and efficiency.