What symbol represents Hermes' speed?

the winged shoe He used to deliver messages.

The caduceus or something, it's like a cane with two snakes entwined on it and wings coming out of the top. It is sometimes featured on the sides of ambulances because of Hermes' quickness.

Actually, Hermes is also the patron god of doctors and all in medical professions, so the Caduceus is featured on ambulances because it represents medicine.