London ? Europe’s busiest airport reopened Tuesday as air traffic across the continent lurched back to life. But the gridlock created by Iceland’s volcanic ash plume was far from over: Officials said it would be weeks before all stranded travelers could be brought home.

Passengers wept with relief as flights took off from Paris’ Charles de Gaulle Airport, Amsterdam and elsewhere. A jetliner from Vancouver, British Columbia, was the first to land at London’s Heathrow airport, the continent’s busiest, since the volcano erupted last week.

British Airways said it expected about two dozen flights from the United States, Africa and Asia to land by early today.

Travelers cheered as the first European flights took off.

Jenny Lynn Cohen, waiting at Charles de Gaulle to travel to San Francisco, had a boarding pass but could hardly believe she was going to fly.

“I am a little afraid — I am hopeful that the plane will take off, and that it won’t meet with any volcanic ash,” she said.

Chris James, arriving at Heathrow from Mauritius, told the British Broadcasting Corp. that passengers on his flight didn’t know they would land in London until 45 minutes before their plane touched down.

“Initially it was quite a stressful situation, we didn’t know what was happening,” James said.

The Eurocontrol air traffic agency said it expected just under half of the 27,500 flights over Europe to go ahead Tuesday, a marked improvement over the last few days. The agency predicted close to normal takeoffs by Friday.

It was the first day since the April 14 eruption of Iceland’s Eyjafjallajokull (ay-yah-FYAH-lah-yer-kuhl) volcano — dormant for nearly 200 years — that travelers were given a reason for hope.

“The situation today is much improved,” said Brian Flynn, deputy head of operations at the Brussels-based agency.

Conditions changed fast. Airspace in Germany remained officially closed, but about 800 flights were allowed at low altitude.

Rita and Peter Meyer said they had to share a hotel room with two strangers in Singapore while waiting to find a way home to Germany. News that they could fly to Frankfurt airport came as they slept.

“Just after midnight — after an hour’s sleep — the phone rang (and they said), ‘Everyone downstairs, get in taxis to the airport,'” Rita Meyer said.

But with more than 95,000 flights canceled in the last week alone, airlines faced the enormous task of working through the backlog to get passengers where they want to go — a challenge that could take days or even weeks.

Passengers with current tickets were being given priority; those who had been stranded for days were told to either buy a new ticket or take their chances using the old one — a wait that could be days or weeks for the next available seat.

“Once your flight’s canceled, you go to the back of the queue,” said Laurie Price, director of aviation strategy at consultant Mott Macdonald, who was stranded in Halifax, Canada. “It seems intrinsically unfair.”

The volcano that prompted the turmoil continued to rumble, and tremors could be heard and felt as far as 15 miles from the crater.