NEW YORK — US Senators grilled a Southwest Airlines executive Thursday over December’s winter storm troubles that affected some two million customers, resulting in a hellish holiday travel meltdown for the ages.

Southwest had canceled more than 16,700 flights over a 10-day stretch beginning on December 21, hit by breakdowns partly stemming from the use of obsolete computer scheduling systems that became overwhelmed during the storm.

“Do you understand the public’s frustration with this?” asked Senator Maria Cantwell, a Washington state Democrat who chaired the hearing.

Cantwell — who also noted that Southwest had not sent its CEO for the high-profile once-over — and other lawmakers told myriad horror stories of passengers whose holiday vacations were ruined.

These included a woman who missed her own wedding, a family that was stranded in arctic Chicago without coats and a stage-four cancer patient who missed treatment.

“Let me be clear: we messed up,” Chief Operating Officer Andrew Watterson said at the outset of the hearing. “In hindsight, we did not have enough winter operational resiliency.”

Watterson described the storm as a “historic event with a combination of challenges we hadn’t experienced before,” leaving the company without adequate deicing capacity in Denver and Chicago, two key airports from which the problems spread.

Exacerbating the issue was an obsolete crew scheduling system that stranded workers around the country and inadequate customer service phone lines that led to endless wait times for affected travelers.

Senators asked why Southwest had not upgraded its flight scheduling software in response to pilot and flight attendant unions who had warned of a crisis due to bad weather.

Watterson acknowledged that the unions had correctly diagnosed part of the problem, but described the lack of adequate cold weather equipment as the root cause of the crisis.

He said some of the software problems from late December had been addressed, and that the company was in the process of a comprehensive review. This will point towards further actions that will include additional investments.

Later in the hearing, Watterson said the company realized its relationships with unions had “atrophied,” adding that it will reform some management practices.

But Senator Ed Markey, a Massachusetts Democrat, pressed Watterson on why Southwest would not provide cash instead of 25,000 reward points to affected customers as a complementary “goodwill” gesture.

For passengers who do not want to fly Southwest again, “it’s nothing but an empty gesture,” Markey said.

Senator Tammy Duckworth, an Illinois Democrat, recounted incidents of consumers unable to reach a human on the phone after hours on hold during the crisis.

Watterson said passengers normally reach a person within nine minutes of wait time, but that “there’s no way we can staff at that level” during a meltdown with thousands of canceled flights.