Lord of the Fliers: Will Anarchy Break Out Among Throngs of Stranded Air Travelers? This weekend's blizzard is likely to cost the airlines millions of dollars.

Dec. 28, 2010 -- The nightmare continued Tuesday for travelers trying to fly to or from the Northeast. Airports opened but there were plenty of delays, even more lines and fears that delays could stretch on for days.

Even passengers whose flights got through amid the weekend's ferocious snowstorm suffered, with some international travelers to New York spending hours on the tarmac waiting to disembark.

Several fliers described the situation at various airports as chaos, with passengers jockeying for any available seat on a plane or even to rest at the gates.

Ted Canova, with son Brendan, 18, boarded a plane at New York's LaGuardia Airport Tuesday only to find somebody already in his seat. Indeed, there were several people on the Delta flight to Minneapolis assigned to the same seats. Three spare pilots trying to get back to Minnesota were kicked off the flight and the Canovas, who awoke at 4 a.m. to try and squeeze on standby, were on their way home.

In Chicago, there were similar reports of people fighting for spots on flights to New York. One frequent flier said "O'Hare feels a bit like 'The Lord of the Flies' this morning ... at least for those trying to get to NYC."

"You could feel the tension in the air as passengers who had been stranded since Sunday began to realize today might not be their lucky day," Heather Mikesell said. "When a couple of passengers tried to cut the line, those who were patiently waiting their turn revolted."

Police officers in Cleveland were called to at least one gate to maintain some kind of order.

"While boarding, tensions rose as everyone tried to get onto the plane at once and there was mass confusion about ticketing, what boarding passes would work, what wouldn't," ABC News producer Dawn Piros said.

Things arguably were worse for passengers on four international flights into New York's Kennedy Airport who had to spend the night aboard planes on the tarmac because airport and customs officials were not equipped to accept the passengers.

One of those flights, Cathay Pacific Flight 830, left Hong Kong bound for New York Monday morning but was diverted to Canada because of the weather. After waiting 11 hours in Toronto, the plane finally took off for New York, arriving at 11 p.m. Monday. But the passengers had to wait another seven hours, until 6 a.m., because there weren't any gates available. Next, they had to wait again -- almost three more hours -- until 8:45 a.m. Tuesday, when there finally was customs and immigration staff available to process them.

Rules forbid airlines from keeping passengers waiting aboard airplanes on tarmacs for more than three hours, but those apply only to domestic flights.

There also was the family returning from Florida that made it to Buffalo only to find no buses or other means to get home to Long Island, the New York Times reported. So instead, they took a 13-hour, $900 cab ride.

Airlines said passengers stranded in the Northeast by this weekend's blizzard might have to wait until the end of the week to make it home.

Flights slowly started to return to the air Monday night but the backlog created by the storm might take days to clear as airlines struggle during one of the busiest times of the year to reposition airplanes and crew, and find seats on already-crowded planes for stranded passengers.

"You are trying to put them on planes that are already packed. There isn't a lot of room to re-accommodate folks," AirTran Airways spokesman Christopher White said.

AirTran is hoping to return to normal operations by late Wednesday or early Thursday.

Those with confirmed tickets for flights Tuesday, Wednesday or Thursday typically get priority over passengers whose flights were canceled earlier in the week.

New York's three area airports restarted some operations Monday night.

LaGuardia Airport officials in New York said they planned to open a second runway Tuesday morning.

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For airlines, the problem might not be whether planes can take off and land but whether there will be enough staff at the airport to load baggage, take tickets and do security screenings of passengers.

Ed Martelle, an American Airlines spokesman, said the airline put up a lot of its staff near the New York airports in anticipation of the storm. But as shifts change, it might still be hard to get replacement staff to the airports, given the poor condition of the roads.

"Can they get there? That's a huge question right now," he said. "It's like trying to do a jigsaw puzzle but the pieces keep changing. This is just phenomenally complicated."

Take American Eagle's flights between New York's LaGuardia and Detroit. One of the planes used on that route was diverted overnight to Rochester, N.Y., because LaGuardia was closed. So before a new group of passengers could board the plane to head to Detroit, that aircraft has to leave Rochester and make it to LaGuardia.

Airlines Budget for Storms

The blizzard is probably going to cost airlines several million dollars in overtime, lost revenue and other storm-related expenses, such as de-icing planes. Airlines said they were focused on getting passengers up in the air again and didn't yet have an estimate on costs.

But if a December 2006 Denver blizzard is an indication, it won't be cheap.

Denver International Airport was closed for 45 hours by a storm that started Dec. 20. 2006.

More than 2,000 flights were canceled and about 4,700 travelers were stranded.

United Airlines said it lost about $30 million in revenue because of that storm, and Denver-based Frontier lost $13 million.

New York is home to many lucrative international routes, especially for American, Continental and Delta, making the losses greater.

Henry Harteveldt, an airline analyst with Forrester Research, noted that airlines budget for such storms.

"This happens every winter. It also happens every summer when you have thunderstorms in certain markets," Harteveldt said. "It's part of the game."

Stock prices for the parent companies of United, Continental, American, Delta and JetBlue -- all with a large Northeast presence -- were either flat or up today. US Airways was down but only slightly.

Most airlines have taken the highly unusual step of giving passengers the ability to rebook flights within a 14-day window of their original plans. Usually, it's only three or four days. That should help spread out rebookings slightly.

For airlines, the test comes in how well they communicate with their customers about the delays.

"This is where an airline proves itself," Harteveldt said. "It's been known when an airline doesn't do a good job in something like this they lose customers for life."

Robert Mann, an airline consultant and president of R.W. Mann and Co., said airlines will save a bit of money on fuel from the canceled flights but are spending a small fortune on things such as de-icing.

He said about 1,000 gallons are needed for a single-aisle jet, at about $12 a gallon of de-icing fluid.

Airlines Lose, Travelers Bear Extra Costs

The airlines' losses might be limited because there is very little business travel this time of year. Those are the travelers who typically book last-minute, high-fare tickets. Most seats this week are booked by leisure travelers who have nonrefundable tickets.

"These people have already purchased tickets, and the airlines are just trying to get them home," said David A. Castelveter, spokesman for the airlines' trade group, the Air Transport Association of America. "Where they will lose money is from trying to sell the empty seats."

On Monday, United and Continental Airlines added a one-way "peak travel day" surcharge ($20 roundtrip) for most of their domestic flights, according to airline fare watcher website FareCompare.com. The surcharge will impact all future travel dates.

American Airlines and Delta Airlines soon followed suit with a $20 (roundtrip) fare hike for a majority of its domestic routes.

Despite the weather conditions, the hikes and charges were also prompted by other factors.

"It's worth noting that these increases come on a day in which oil prices soared to a 26-month high, which impacts the airlines' jet fuel costs," Graeme Wallace of FareCompare.com said.

Then there are the costs shouldered by travelers: hundreds of extra dollars for hotel rooms, meals, clothing and distractions while stranded.

Once they get home, add in an extra day or two of parking at the airport, that extra day of having the family dog at the kennel and any lost income from missing work.

ABC News' John Donvan and Sharyn Alfonsi contributed to this report.