  Setting traffic light signals is a classical topic in traffic engineering,
and important in heavy-traffic conditions when green times become scarce and
longer queues are inevitably formed. For the fixed-cycle traffic-light queue,
an elementary queueing model for one traffic light with cyclic signaling, we
obtain heavy-traffic limits that capture the long-term queue behavior. We
leverage the limit theorems to obtain sharp performance approximations for one
queue in heavy traffic. We also consider optimization problems that aim for
optimal division of green times among multiple conflicting traffic streams. We
show that inserting heavy-traffic approximations leads to tractable
optimization problems and close-to-optimal signal prescriptions. The same type
of limiting result can be established for several vehicle-actuated strategies
which adds to the general applicability of the framework presented in this
paper.
