The rules and regulations adopted and promulgated by the State University at Binghamton council and set forth in this Part are effective throughout the year, from September 1st to August 31st, including all recess and intersession periods. They apply to students, employees, faculty and staff of the university, and all other persons who operate or park or whose vehicles are operated or parked at any time on the grounds of the university, including visitors, officers and employees of other agencies whose vehicles are operated and parked regularly on the grounds of the university. The Vehicle and Traffic Law shall apply upon such premises notwithstanding any references in such law to public highways, streets, roads or sidewalks. No person shall drive a vehicle on university streets, roads or highways at a speed greater than is reasonable and prudent under the conditions and having regard to the actual and potential hazards then existing, but in no event shall a person drive a vehicle in excess of 20 miles per hour unless a different speed is authorized and indicated by the university.