LJUBLJANA, Slovenia — After weeks of warnings about the dangers involved in Europe’s migrant influx, and fears about winter’s arrival, the worries of public officials and humanitarian groups were realized on Monday when thousands of asylum seekers, many of them families with small children, began to back up at crossings and were stranded in a chilly rain.

The backups came just two days after Hungary closed its border with Croatia, and occurred as countries on the north end of the Balkan route tightened border controls while states to its south quarreled over how to manage the unabated human flow into Europe.

The logjam followed a month of relative stability across the Balkans and Central Europe, as countries unofficially worked together to create a safe and relatively quick route north and west by transporting asylum seekers by bus or train from one border to the next, where they could exit on their way toward Germany, Sweden and other desired destinations.

The arrangement filled the void left by the European Union, which has talked, bickered and failed to come up with a common solution to the problem of accommodating hundreds of thousands of new arrivals, many fleeing war in Syria, Iraq and Afghanistan, or repression in places like Eritrea in northern Africa.