The 3 segments of the brainstem are the midbrain, pons & this, which regulates coughing & sneezing
The brainstem is made of three regions: the medulla oblongata, the pons, and 
... Vomiting, sneezing, coughing, and swallowing reflexes are coordinated in this 
.... substantia nigra of the midbrain to regulate and control muscle movements.