After Gov. Andrew M. Cuomo declared a state of emergency for New York City’s subways last year, transit officials unveiled an emergency repair plan to address the most pressing needs quickly. Yet the plan invests a relatively modest amount in the equipment that many experts say is the backbone of the subway: the signaling system, which dates to before World War II.

Of the $378 million the Metropolitan Transportation Authority has so far set aside for the plan, 15 percent, or about $58 million, is dedicated to the signals that direct traffic on one of the world’s busiest systems, according to financial statements the agency released this month. The original cost of the subway action plan was $836 million, but that number was based on New York City providing half the cost. Mayor Bill de Blasio has so far refused to do so, arguing that people who live or work in New York City already contribute 70 percent of the state-run agency’s revenue.

“Given the amount of controversy around the subway action plan and who pays, governor or mayor, does the subway action plan spending match up with the problems causing the delays right now?” asked John Kaehny, of Reinvent Albany, a government watchdog group. “It raises the question — and this is an open question — is the subway rider getting the biggest bang for the buck here in terms of reducing delays?”

Moving the subway away from its antiquated method known as block signaling to a more modern and reliable technology is essential if the system is to become more dependable and capable of carrying a growing city into the future, experts and officials said. Under the current system, which in some cases includes cloth-covered cables, trains have to be spaced out a safe distance apart because the signals cannot pinpoint exactly where trains are.