When subway lines are closed in the years ahead, the routes should be replaced with dedicated bus lanes that prioritize transit riders over cars, said Joe Cutrufo, a spokesman for Transportation Alternatives, an advocacy group for bikers and pedestrians.

“The subway doesn’t share the tracks with cars — neither should buses,” he said.

While overhauling New York’s century-old subway will be disruptive, installing modern signals is the key to making the system reliable again. In London, another vast and aging system, the signals have been upgraded much faster. On one line with modern signals, trains regularly arrive every 100 seconds.

In New York, only the L train and the No. 7 line have modern signals, known as communications based train control, or C.B.T.C. The installation was plagued by delays and took nearly two decades, but the L train is now the most reliable with a 90 percent on-time rate. The No. 7 line can run 29 trains per hour during rush hour, up from 27 trains before new signals were installed. Mr. Cuomo has also urged Mr. Byford to use a new technology called ultra-wideband radio that could allow the signal work to be done faster.

On the F line, where the signals are currently being upgraded, some riders understand the need to shut down parts of the route. Patrick Smith said he watched an interview with Mr. Byford on “60 Minutes” last year that portrayed him as the subway’s cheerful savior. He supports Mr. Byford’s plan to fix the subway.

“I think the crux of the situation is, how do you modernize a 110-year-old system without grossly impacting everyday life?” said Mr. Smith, who works in information technology and lives in Brooklyn.

If the subway was closed on nights and weekends, Mr. Smith said he would be fine with taking a backup shuttle bus. “Short-term sacrifice usually pays off,” he said.

Andrew Fox, who lives in Queens and works in construction on the weekend, said the subway often ran local during repair work which made his commute a “nightmare,” turning a 30-minute trip into an hourlong ride.