The Long Island Rail Road will be 80 percent operational for Monday morning’s commute — with seven of its 12 lines running — and its president said full restoration of service after near-record snowfall Saturday was hampered by a decision not to shut down the system sooner.

The LIRR’s “big four” branches — Port Washington, Huntington, Ronkonkoma and Babylon — that together carry nearly three-fourths of all LIRR riders are expected to run on normal schedules, railroad chief Patrick Nowakowski said Sunday. But no trains will operate on the Long Beach, Far Rockaway, Hempstead and West Hempstead lines or to or from Brooklyn’s Atlantic Terminal, effectively stranding tens of thousands of commuters.

Nowakowski said he did not expect to restore full service until Tuesday morning at the earliest. Customers also should expect significant crowding, as commuters from the suspended lines are likely to use other stations to catch a train.

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In the meantime, Nowakowski said, work crews were working around the clock to clear the snow, which accumulated “over the third rail everywhere” — disrupting trains’ electricity source. The severe weather also froze track switches in some places and caused tall snow drifts in segments of tunnels along the Brooklyn line that some snow-removal equipment can’t reach.

And in retrospect, Nowakowski said, it would have been better to halt service sooner on Saturday once it became apparent the storm would be far worse than originally forecast.

“In hindsight, we probably should have made the call, the time that we selected for canceling service, sooner,” said Nowakowski, adding that he put off suspending service until late in the afternoon in an effort to avoid stranding passengers who had traveled from their homes earlier Saturday. “Once you transport them, you sort of have an obligation to take them home.”

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As a result, “We still had trains stranded throughout the right of way that we spent all night and a good part of this morning and early afternoon removing from tracks,” he said. “That hindered our ability to do some of the cleaning efforts because we had people and equipment tied up trying to get those trains off the tracks and out of the way.”

About 1,000 passengers on 10 trains were stranded for up to four hours. To avoid such situations, his predecessor Helena Williams in 2010 instituted a policy of suspending service when 10 or more inches of snow accumulated on tracks. The plan came in response to a December 2009 incident in which a Ronkonkoma-bound train carrying broke down in a storm, leaving 150 passengers for three hours without power or working toilets.

As late as Friday, LIRR officials expressed confidence that the storm would have only minimal impact on service. Nowakowski said that by early Saturday, it was apparent the storm would be far more severe that forecast.

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“The forecast was changing dramatically. But the one luxury that we sort of had was that, being a Saturday and given the way it was falling, most people were staying home,” Nowakowski said. “So we felt that we could monitor the weather, keep monitoring the forecasts and make that call when that call needed to be made. Unfortunately, it intensified rather quickly on us.”

By early Saturday afternoon, the LIRR announced it would shut down service around 4 p.m. But by about 3 p.m., several trains carrying passengers were getting stranded, disabled by the mounting snow.

Trains broke down near Hicksville, Bethpage, Little Neck, Syosset, Lawrence, Westbury, Merillon Avenue Station, Floral Park, and Syosset. Riders on four of those trains needed to be evacuated onto “rescue trains” that pulled up alongside them. Other trains stopped running at stations.

Well into Sunday afternoon, the LIRR was still efforting to remove some of the stranded trains, which blocked snow-removal equipment from clearing some parts of the system. Crews battled drifts as high as 3 feet

.

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The railroad also deployed a 53-foot-long, 80-ton steel snow-removal vehicle, nicknamed “Darth Vader” for its resemblance to the “Star Wars” villain’s prow, from Ronkonkoma to Greenport. Darth Vader will be put back at work Monday if needed, an official said.

A critical task was sweeping snow-blanketed rail yards such as Harold Interlocking, the Sunnyside yard where every branch intersects before entering tunnels beneath the East River into Manhattan. It was finally cleared by afternoon, an official said.

In the meantime, stranded riders hoping to get on a train waited on Sunday — and waited.

Orlanzo Williams, 51, of Wyandanch, got stuck in the city after coming into work at the New York Botanical Garden in the Bronx, where he helps oversee maintenance.

By midday, Williams said, he had been waiting at Penn Station for three or four hours hoping service would resume, and railroad employees had no information for him.

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“Absolutely nothing — no information, no suggestions. You think the LIRR, 12 hours after it stopped snowing, they would be able to run some trains,” Williams said.

At the Hicksville LIRR stop, about a dozen riders waited for trains that weren’t coming Sunday. Every few minutes, another would-be passenger approached an information window to be told the same thing: “Service is suspended until further notice.”

Inside the waiting room, a group of six commuters tried to arrange via mobile phone for a taxi to take them to the city.

“I worked since Friday,” said Marie Joseph, 60, of Brooklyn, an employee of an assisted living facility in Oyster Bay. “I’m tired.”

Looking ahead to Monday, Nowakowski asked customers to “bear with us. There’s going to be crowding. Allow some extra time. But we have good hopes that we are going to run well.”

With Rebecca Harshbarger, Emily Ngo and Ted Phillips