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Most major airlines are back up and running, five days after severe winter weather wreaked havoc on holiday air travel. Delta Air Lines, American Airlines and United Airlines each canceled less than 40 flights. Delta had the lowest number of canceled flights.

It wasn't the same at Southwest.

More than two thirds of its flights had been canceled on Wednesday. Southwest said in a statement on Wednesday that it would cancel close to 2,500 flights a day as it tries to return to normal operations. Some passengers were unable to rebook Southwest flights, rented cars or spent hundreds of dollars on other airlines.

What made the meltdown happen?

Southwest allows passengers to fly directly from smaller cities and regions without having to stop at a central hub like Denver or New York. Travelers who aren't flying from major metro areas have an advantage by eliminating the intermediate stop.

The hub-and-spoke model is used by other large carriers like United and American.

A passenger on a United plane from Oklahoma City to Phoenix might have to stop in Denver for a while. Southwest flies direct from Oklahoma City to Phoenix.

Mike Arnot, an industry analyst, said there is a ready pool of crew members and pilots who can report to work at a major airport. It's easier to regroup after a storm. Planes are kept closer to their home airports.

When airlines serve a lot of smaller markets it can be hard to have a reserve of pilots and crew. Mr. Arnot said that there isn't usually excess crew in Syracuse.

He and other analysts said that Southwest's cancellation caused a domino effect that left planes and crews scattered across the country.

The only way to get the planes back to where they should be is to reset. Canceling a lot of flights is the only way to go.

ImageA group of passengers sits among luggage and coats on the floor of an airport. Several people are staring at their phones and a boy in the center of the photo wears a number of baseball caps and hats on top of a blue-patterned hoodie.
Zach Soda, center, with his family at Denver International Airport as their flight to Dallas was delayed along with thousands of others on Tuesday.Credit...Daniel Brenner for The New York Times
A group of passengers sits among luggage and coats on the floor of an airport. Several people are staring at their phones and a boy in the center of the photo wears a number of baseball caps and hats on top of a blue-patterned hoodie.

In a video message on Tuesday, Southwest's chief executive, Bob Jordan, likened the airline's route model to a "giant puzzle" that depends on airplanes and crews remaining in motion.

He said that because Southwest is the largest airline in 23 of the top 25 travel markets in the US, it resulted in airplanes and crew members being out of position in dozens of cities.

He said that the airline was focused on getting all the pieces back into place.

When assigning crews and pilots to flights, the scheduling system has to take into account union rules, federal regulations and airline policies.

Southwest's system couldn't keep track of where its crew members and pilots were after so many flights were canceled

The president of the Southwest Airlines Pilots Association said that pilots and crew members waited hours to speak to staff members at Southwest's overwhelmed operations center. Hundreds of pilots and crew members slept in airports with passengers and luggage.

He said that if one card fell, the whole house would fall at Southwest. Our problem is that. The cascading events made it hard for us to keep up.

Mr. Murray said the union had been urging the airline for a long time to update their infrastructure.

He said that this past weekend was the exclamation point on the growing number of meltdowns. In June of 2021, half of the airline's flights were delayed or canceled and it took days for the situation to be fixed. In October of that year it had similar issues and had to cancel more than 1,700 flights.

The scheduling system was outdated, even before this week's problems.

Mr. Jordan stated in November that they were behind. We have outrun our tools as we grow.

Southwest doesn't have a way to contact crew members who get re-assigned. He said someone needed to call them or chase them down in the airport.

ImageRows and rows of luggage stretch across an airport arrivals hall and two people search among the bags as more people can be seen in the background.
Travelers look for their bags in the baggage claim area at Dallas Love Field Airport in Texas.Credit...Emil Lippe for The New York Times
Rows and rows of luggage stretch across an airport arrivals hall and two people search among the bags as more people can be seen in the background.

Southwest doesn't have agreements with other airlines that allow passengers to fly on other airlines' planes when there is a cancellation. Most low cost carriers don't have these agreements in place.

Southwest passengers are compensated if their flights are canceled. Passengers are rebooking on the same airline flight.

In the last few days, that was not an option for thousands of Southwest passengers.

The McNamaras, an art director from Brooklyn, visited family in Mississippi for the holiday with her husband and two children.

When their flight was canceled, they couldn't find any other flights on Southwest's website.

They paid a lot of money for tickets to New York. Ms. McNamara was waiting for Southwest to call customer service so she could try to get the extra cost covered. Customers were told to rebook flights on the airline's website.

She doesn't think they're answering their phones right now.

Southwest said that requests for reasonable reimbursements would be reviewed on a case by case basis.

Ms. McNamara, who has used Southwest for years for direct flights to visit family in Texas, New Mexico and Mississippi, said the current fiasco won't stop her from booking with the airline again.