Migrants who arrived from Hungary walk inside tents on the Austrian side of the border near Nickelsdorf on Sept. 27. (Csaba/EPA)

In Austria, they’re fighting chaos with neatly lettered signs.

As asylum seekers arrived at the border in waves of 400 or 500 on a recent afternoon, some running, they were greeted with directional posters in German, Arabic and English.

“Welcome to Austria,” a soldier intoned through a loudspeaker, also speaking in three languages. “On the right, you will find food. On the left are taxis. The taxis cost money; please check your money. Behind are buses. Buses are free.”

Migrants and refugees who had been on a pell-mell northward dash for weeks filed through a lane formed by traffic cones, dutifully lining up to enter Austria, a country struggling to impose some of its love for order on a thoroughly disordered situation.

Used to processing 20,000 asylum applicants a year with flowchart efficiency, Austrian officials have been deluged with 100,000 newcomers in the past three months. Tucked between a Hungary that is stiff-arming the asylum seekers and a Germany that is accepting them in fits and starts, Austria has become Europe’s waiting room, a choke point for the mass of humanity straining northward.

Most of the refugees fleeing mayhem in the Middle East and South Asia want to carry on to countries such as Germany and Sweden, which have offered generous benefits. But Germany, overwhelmed, has suspended most passenger rail service between Vienna and Munich, allowing in only a few thousand migrants a day on special trains.

With the backup building across the country, Austria is straining to keep pace. Emergency shelters in stadiums and empty office buildings fill up as fast as agencies can set them up. The federal government has rushed through a law that, starting last Thursday, allows it to force local mayors across the country to house more asylum seekers.

Through it all, Austrians are keen to apply what method they can to the migration madness.

At the border with Hungary, soldiers ladled garlic soup for young Syrian men in one line. In another, mothers picked through clothes that Austrian Red Cross volunteers had carefully sorted into piles of children’s things, women’s things and outerwear.

At the end of the longest line, a police officer talked to a couple with three children and held up five fingers, like a hotel doorman. Another officer then spoke into his radio, and a minivan cab detached itself from an ad hoc taxi stand that stretched more than a half-mile. Most of the more than 200 drivers had come 45 miles from Vienna to make 170 euros (about $190) for the drive back with a carload of asylum seekers.

“That’s what the Taxi Drivers’ Association has set as the rate,” Ludwig Beil, a driver, said with a shrug as he pocketed the money from a group of Syrians and Afghans. One of his passengers, Alshet Azahara from Kabul, said in halting English that they were heading for Germany at last.

A look at the numbers behind the stream of refugees flowing into Europe as political leaders struggle to ease the burden. (Jason Aldag/The Washington Post)

But Beil said he was taking them to the Westbahnhof train station in Vienna. And since Germany had cut off most passenger rail service, the station was mostly a clearinghouse for one of the emergency shelters, now housing more than 12,000 refugees in the city.

“No Germany?” Azahara asked as Beil shut the door.

Uncertainty still reigns at the border. Taxis are for those who can afford to pay to go where they want, or at least to dead-end stations in Vienna or Salzburg. The chartered buses are free, but they stop only at one of the 38 other shelters across the country, many of them far from the cities.

Still, the scene is far more systematic than during the first weeks of the crisis, when shouting throngs of frustrated arrivals nearly crushed a fence, and some set off by foot for Vienna.

Even critics who say the government ignored months of warning that the wave of migrants and refugees was coming acknowledged that officials, with lots of help from civilian volunteers, have achieved at least a patina of order.

“All in all, they are handling this situation surprisingly well and calmly,” said Georg Buerstmayr, a veteran immigration lawyer.

Upended asylum process

Enama Najm, a 22-year-old student from Homs, Syria, said the situation at the border was a relief, even if no one could tell her how to apply for asylum.

“They just pointed us to the taxis, but at least they were ready for us and everyone was working very hard,” Najm said. “They are nice. We are not used to nice policemen in Syria.”

Najm, who crossed the border with her husband after traveling for 15 days, had originally set out for Germany. But now they have decided to try their luck here. “The place of Austria on the map is great, right in the middle of Europe,” she said. “And it is calm here. Drivers stop at the traffic lights.”

Officials say they expect most of the asylum seekers to pass through this country, but all of them have to be housed until they are allowed to proceed. As many as 85,000, they estimate, will seek permanent residence in Austria this year, more than four times the norm.

Before, that was a step-by-step process. First, asylum seekers would have their fingerprints and a photograph taken at a border police station. Within 48 hours, word would come from databases in Brussels on whether they had already applied for asylum in any other European Union member country. If so, they would be sent back to that country in accordance with E.U. treaties.

If they hadn’t applied elsewhere, they would be interviewed a second time to determine their eligibility for asylum in Austria. Applicants were barred from working or leaving the country during the six to eight months it typically took to rule on their applications, but the government fed and housed them during that time at Traiskirchen, a former army base.

“Now the bureaucracy can’t even register them all,” Buerstmayr said. “I find myself prefacing everything I say with: ‘In normal times, it would work like this.’ But now, who knows?”

The country’s national asylum office is hiring at a breakneck speed, seeking to double its 780-member staff. The agency is borrowing interpreters from the federal court system.

“I myself worked 78 hours of overtime in September,” said Walter Ruscher, director of the Traiskirchen facility.

Nothing has been more challenging than feeding and housing the asylum seekers. The government has vowed to keep them from sleeping in parks and on sidewalks. But the first tent city that officials erected next to Traiskirchen led to a public outcry, even though it features plank sidewalks, heated tents, numerous hand-washing stations and regular litter patrols.

“They said, ‘This is Austria? We are a rich country and we need tents?’ ” Alexander Marakovits, an Interior Ministry spokesman, said as he walked between the neat rows of white nylon structures where more than 700 asylum seekers are living.

In a nearby cafeteria line, where a poster of a pig with an X through it assured the mostly Muslim asylum seekers that no pork was being served, two young men tried to sneak to the front of the line. Instantly, two security guards in orange vests blocked their way and pointed to the end of the line. In Austria, no one butts ahead.

Providing beds

On arriving in Vienna, Najm and her husband were given numbered armbands and subsequently were told to be at an office in the coming days to have their fingerprints taken, a week after crossing the border.

For several nights, they slept on cots at the Vienna Stadthalle — site of the Vienna Open tennis tournament — with hundreds of others. But they were kicked out to make room for a mineral trade show and were given a map to a new shelter, in an abandoned newspaper office.

“I have a pink bracelet now,” Najm said, holding up her arm as the couple were escorted to the office where they would sleep. “I don’t know what it means.”

Volunteers were still setting up cots for 300 migrants, with more than 40 beds in the old newsroom alone. Families were being ushered into glass-walled editorial offices.

Once the newcomers have been approved to formally apply for asylum, they are eligible for longer-term housing. Historically, the government has distributed them across the country, and by law each province is required to accept refugees equaling at least 1.5 percent of its population.

But mayors across Austria have balked at putting up the thousands of applicants who will need beds for months, if not longer.

Now the federal government has changed the law, giving itself the power to override local objections in many cases, a move that the Association of Austrian Cities and Towns called “a coercive measure that is without precedent.”

Joachim Maislinger knows what that feels like. The chief magistrate of Wals-Siezenheim, a town of about 13,000 near the German border, was outraged in August when he got one day’s notice that the government was putting up 50 tents on a local army base. Within a week, 250 asylum seekers had arrived.

“We weren’t even asked,” Maislinger said. “It’s not the refugees. It’s the entire organization around them.”

Nicole Lundeen contributed to this report.

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