The Federal Aviation Administration plans to reduce air traffic by 10 percent across 40 “high-volume” markets to maintain travel safety as air traffic controllers exhibit signs of strain during the ongoing government shutdown.

The affected airports covering more than two dozen states include the busiest ones across the U.S. — including Atlanta, Denver, Dallas, Orlando, Miami, and San Francisco. In some of the biggest cities — such as New York, Houston, and Chicago — multiple airports will be affected.

CBS News has a list of all the airports affected and that list includes both DFW Airport and Dallas Love Field. Other airports in Texas that would be affected include both airports in Houston — Houston Hobby and George Bush Houston Intercontinental.

The FAA is imposing the flight reductions to relieve pressure on air traffic controllers who are working without pay during the government shutdown and have been increasingly calling off work.

Controllers already have missed one full paycheck and are scheduled to again receive nothing next week as as the shutdown drags on.

The FAA has been delaying flights at times when airports or its other facilities are short on controllers.

Passengers should start to be notified about cancellations Thursday. Airlines said they would try to minimize the impact on customers, some of whom will see weekend travel plans disrupted with little notice.

United Airlines said it would focus the cuts on smaller regional routes that use smaller planes like 737s. United, Delta Air Lines, and American Airlines said they would offer refunds to passengers who opt not to fly -- even if they purchased tickets that aren’t normally refundable. Frontier Airlines recommended that travelers buy backup tickets with another airline to avoid being stranded.

Experts predict hundreds if not thousands of flights could be canceled. The cuts could represent as many as 1,800 flights and upwards of 268,000 seats combined, according to an estimate by aviation analytics firm Cirium.

Air traffic controllers have been working unpaid since the shutdown began October 1. Most work mandatory overtime six days a week, leaving little time for side jobs to help cover bills and other expenses unless they call out.

Major airlines, aviation unions, and the broader travel industry have been urging Congress to end the shutdown, which on Wednesday became the longest on record.

Staffing can run short both in regional control centers that manage multiple airports and in individual airport towers, but they don’t always lead to flight disruptions. Throughout October, flight delays caused by staffing problems had been largely isolated and temporary.

But the past weekend brought some of the worst staffing issues since the start of the shutdown.

From Friday to Sunday evening, at least 39 air traffic control facilities reported potential staffing limits, according to an Associated Press analysis of operations plans shared through the Air Traffic Control System Command Center system. The figure, which is likely an undercount, is well above the average for weekends before the shutdown.

During weekends from January 1 to September 30, the average number of airport towers, regional control centers and facilities monitoring traffic at higher altitudes that announced potential staffing issues was 8.3, according to the AP analysis. But during the five weekend periods since the shutdown began, the average more than tripled to 26.2 facilities.