A system intended to prevent train collisions, and derailments caused by excessive speed, is gradually being installed across the state's Empire Corridor, the main passenger route connecting Albany with New York City and Buffalo.The route, used by dozens of Amtrak trains each day, is controlled by three different railroads — Metro-North from New York City to Poughkeepsie, Amtrak from Poughkeepsie to Hoffmans, just west of Schenectady, and CSX from Hoffmans west to Buffalo.Each is in various stages of installation, according to filings with the Federal Railroad Administration, which requires quarterly reports on Positive Train Control, or PTC, status.