During that three-month shift, trains will be more crowded, Mr. Corbett said. He said the Morris & Essex train he regularly rides home from his office in Newark is one of the trains that will be removed from the schedule next month.

He and other New Jersey Transit officials showed reporters how the equipment was being installed on 12 of the agency’s train cars at a contractor’s repair shop in this central New Jersey town. Workers crouched on rails beneath the cars, consulting manuals as they turned wrenches and sprayed lubricant on the parts they attached to the undercarriages.

The system involves transponders that receive signals to warn engineers when their trains are exceeding the speed. If an engineer does not respond to the warning tone or flashing light, the system will apply the brakes to slow or stop the train.

Installing the equipment is a complex task that has vexed several passenger railroads in the region. The Federal Railroad Administration, which is monitoring progress on the installation, reported that at the end of June, New Jersey Transit had outfitted just 26 percent of its locomotives, compared with 100 percent for the Long Island Rail Road, 82 percent for Amtrak and 77 percent for Metro-North Railroad.

Mr. Corbett admitted that New Jersey Transit had lagged behind several other commuter railroads coming into 2018. But he said that the agency has narrowed the gap and could catch up to its competitors in the next few months. He said most of the commuter railroads, like New Jersey Transit, would seek a two-year extension from federal regulators that would allow them until the end of 2020 to have Positive Train Control working on all of their trains throughout their networks of tracks.

Mr. Corbett said the additional curtailment of service, scheduled to begin Oct. 14, was an admission that the agency’s new management underestimated how detrimental the installation project would be to New Jersey Transit’s ability to maintain its service.

The trains being removed from the schedule include eight on the Morris & Essex line, four on the Main/Bergen County line, three on the Northeast Corridor, two on the North Jersey Coast Line and one on the Montclair-Boonton line. The Morris & Essex line will also have all of the weekend train service on its Gladstone Branch replaced with buses for the three months, though the trains will operate on three holidays: Thanksgiving, Martin Luther King Jr. Day and Presidents’ Day.

The Dinky, which shuttles passengers between the campus of Princeton University and the Princeton Junction station on the Northeast Corridor, will be replaced with buses from mid-October to mid-January, New Jersey Transit said.