When trains are late or subway fares increase, many New Yorkers reflexively blame the mayor. But the agency that runs the city subway system is controlled by the state, often leaving the city dependent on the whims of the governor.

Mayor Bill de Blasio has a voice on the transportation agency’s board, but that voice has been largely muted over the last year, a situation that may reflect his strained relationship with leaders in Albany.

While the mayor has four seats to fill on the Metropolitan Transportation Authority’s board, he currently has only one representative: Polly Trottenberg, the city’s transportation commissioner. Mr. de Blasio recommended three others for the 23-member board last year, but the State Senate did not approve them before the legislative session ended. Transit advocates are concerned that those nominees will again not be confirmed before the session ends next week.

At a time when subway riders face overcrowded cars, the prospect of a fare increase and the upcoming shutdown of the L train tunnel, the city is pushing for more power on the authority’s board.