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DALLAS (CBSDFW.COM) – Many Southwest Airlines passengers are still patiently waiting to get to their destinations after nearly 24 hours of delays and cancellations.

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The problems began with intermittent computers issues Wednesday afternoon. But as the hours past the dozens of delays and hundreds of cancellations left thousands of people stranded.

This morning the airline said all of the computer systems had been “stabilized” and that workers were now in recovery mode trying to get displaced passengers to their destinations as quickly as possible.

Linda Rutherford, the Vice President of Public Relations and Community Affairs for the Dallas-based airline, issued a statement this morning that said, in part:

“I want to start off by once again apologizing to our Customers and reiterating that your experience throughout the past 24 hours is not the service you should expect from Southwest Airlines. Most of our systems are back online this morning following yesterday’s technology outages, but recovery will take some time.”

At Dallas Love Field Airport things had improved dramatically since the early morning, but there were still scores of people in line before the lunch hour. Passengers burst into applause this morning at the sight of more Southwest ticket agents arriving.

Sharon McDonald’s flight was canceled Wednesday and she spent the night frustrated and truing to sleep on the floor of the airport. “It’s really been a rough situation for us and not just us – everybody,” she said.

Southwest had sent out a warning that anyone with a flight booked for today should check the status online and get to the airport extra early.

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Sarah Beck and her husband followed instructions and got bad news about their long-planned trip to Denver to celebrate turning 30-years-old. “I checked [flight status] last night and it was still scheduled. Then we woke up at 4 a.m. to a text saying your flight was cancelled,” she recalled. “I called Southwest and we were on hold for two hours, so we decided to just head to the airport and hope to talk to a real person.”

The Beck’s are among the thousands of people trying to rebook their flight. The airline reportedly canceled as many as 700 flights yesterday, but had cleared and rebooked more than 200 of those by 6:30 this morning.

The Southwest Airlines homepage has an advisory that says, in part –

“Thank you for your patience today as we recover from yesterday’s technology outage.”

Rutherford said the airline takes responsibility for the delays and cancellations. “We know we disappointed customers today and we’re really, really sorry about that. That’s unacceptable,” she said.

The airline said they were “offering flexible accommodations for those passengers needing to rebook their travel. Affected travelers have the opinion of getting a refund, airline credit or rebooking their flight, within two weeks, free of charge.

As it stands, officials with Southwest say phones calls are still flooding in. Anyone having a hard time reaching someone by phone can also try reaching out on social media – the company was regularly responding to customers on Twitter early Thursday.

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