§ 1623. Regulation of traffic on the grounds of state departments, institutions of the state university, state hospitals and other state institutions. (a) Upon the application of the head of any state department, upon the application of the board of trustees of the state university of New York and upon the application of the board of visitors or other similar board or body of a state hospital or state institution, the department of transportation may by order, rule or regulation prohibit, restrict or regulate traffic on or pedestrian use of any highway on the grounds of the department, institution or institutions over which the department head, board or body making such applications has jurisdiction. (b) This section shall not apply to any of the grounds referred to in section fifty-seven hundred eight of the education law.