Traffic intersection signal control usually employ fixed-time, or periodic control policies. Yet, their optimality is unknown. Recent work has proposed queue-dependent max-weight scheduling policies that are optimal. But these are not regarded as practical and unlikely to be adopted. This paper considers the question whether there exist optimal fixed-time signal control policies. We consider a fluid model for arrivals and departures. For simplicity, only one queue is actuated at a time, though this can be generalized. Furthermore, switching the actuation from one queue to the next incurs an all-red Δ delay. We show that there exists a fixed-time signal control policy that is near-optimal. The proof is non-constructive. Nevertheless, it answers an important question and suggests the existence of approximate optimal fixed-time policies that would be practical as well.