According to FlightAware, which is a website that tracks flights, Southwest has canceled more than 2,500 flights, which is equivalent to 62 percent of its scheduled flights for the day. The company has estimated that it may take many days before the tangles can be untangled and regular service can be resumed.

Following the disruption to travel plans caused by a winter storm throughout the United States the previous week, Southwest’s operating structure, which is distinct from that of the majority of other major airlines, has come under heavy examination. Because Southwest was the only airline that was unable to get its aircraft back in the air after the storm, thousands of passengers were left stranded and had a difficult time rebooking flights with the airline.

On Friday, Southwest Airlines had to cancel over 1,300 of its flights, which is equivalent to approximately 34 percent of its planned flights for that day. FlightAware reports that on Friday, other airlines in the United States also had difficulties, leading to the cancellation of around 22.5 percent of all flights operated by airlines other than Southwest.

However, despite the fact that other airlines started to get back on their feet (only 13.3 percent of flights with airlines other than Southwest were canceled on Saturday, 9.7 percent on Sunday, and 5.7 percent on Monday), Southwest’s troubles continued to become worse.

On Saturday, Southwest was forced to cancel 39% of its scheduled flights. On Sunday, the percentage was at 46 percent; on Monday, it was 74 percent, and on Tuesday, it was 64 percent.

According to FlightAware, since Thursday, Southwest Airlines has been forced to cancel about 11,000 of its scheduled flights.

Pete Buttigieg, the transportation secretary, said on Tuesday that it was “an unacceptable situation”.

“We all understand that you can’t control the weather,” he said, adding that “this has clearly crossed the line from what is an uncontrollable weather situation to something that is the airline’s direct responsibility.”

In a statement released on Tuesday, Senator Maria Cantwell, who chairs the Senate Commerce Committee, stated that the committee will be examining the reasons for the collapse and that “the problems at Southwest Airlines over the last several days go beyond weather.”

“Many airlines fail to adequately communicate with consumers during flight cancellations,” she said. “Consumers deserve strong protections, including an updated consumer refund rule.”

Bob Jordan, the chief executive officer of Southwest Airlines, issued an apology to the company’s customers in the form of a video on Tuesday night. In the video, he said that resolving the “giant puzzle” of staffing might take several days.

“Our plan for the next few days is to fly a reduced schedule and reposition our people and planes,” Mr. Jordan said. “We’re making headway, and we’re optimistic to be back on track before next week.”

The problems are caused by the airline’s unconventional “point to point” operation, in which aircraft often travel from one location to another without first returning to either of the airline’s main hubs. The vast majority of airlines operate according to a model known as “hub and spoke,” in which flights generally return to a hub airport after traveling to various other locations. Hub-and-spoke airline networks are able to suspend some flights in the event that inclement weather strikes, but they do have contingency plans ready to go in case the weather improves. However, severe weather may disrupt many flights and routes in a point-to-point arrangement, making it impossible for Southwest personnel to reestablish regular operations.