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When Andy Byford, the New York City subway leader, met with Amazon executives during the summer, Mr. Byford boasted that Long Island City in Queens was a transit wonderland ready to serve their army of workers.

The reality is far less rosy.

Long Island City does have half a dozen subway lines, the Long Island Rail Road, buses and ferry boats. But the picture Mr. Byford painted glosses over the enormous challenges facing the city’s transportation network, which regularly struggles to get millions of New Yorkers where they are going.

The subway is still maddeningly unreliable more than a year after it was declared to be in a state of emergency. Last week, a relatively modest snowstorm paralyzed traffic across the region. That same day, the Metropolitan Transportation Authority, which oversees the subway and buses, announced it was facing a budget crisis and might have to drastically raise fares or cut service.

Still, Mr. Byford was optimistic about the system’s ability to handle a potential influx of 25,000 workers in Long Island City, the site Amazon picked for one of two new locations, along with a suburb in Virginia.