A roundabout near Ballymun may mark the end of their journey for now, but the start of the Roma journey goes back more than 1,000 years to India.
While there has been much debate about the origin of the Roma, there is a consensus that they descended from groups who fled from Punjab and Rajasthan on the Indian sub-continent from about 800-950AD onwards as Islamic forces invaded.
The Roma history is not a happy one and is littered with references to persecution, ethnic cleansing, enforced sterilisation and slavery. But one of the happier stories uses the Roma's musical skills to explain their migration from India. The story claims that the king of Persia, Behram Gour, asked an Indian king to provide 12,000 musicians to entertain his subjects. The Roma were chosen for their expert lute-playing and dancing and they never went home.
Whatever the reason, the migration continued from North Africa into Spain and throughout Europe in the 14th and 15th centuries.
As they gained a foothold in Europe, persecution followed. The Roma people were targeted by the Nazis during the second World War, when an estimated 500,000 were killed in concentration camps.
During the Cold War, coercive sterilisation of Roma women went on in eastern bloc states such as Czechoslovakia and Hungary, while their children were systematically placed in care in some north European countries.
Most recently, Roma were subjected to ethnic cleansing in Kosovo in 1999, when an estimated 120,000 were displaced or forced into exile in neighbouring countries.
Skinhead violence targeting the Roma population is endemic in many European states, according to the European Roma Rights Centre, which campaigns for the rights of the Roma people.
It is difficult to put an exact figure on the number of Roma in Romania because many are undocumented, but it has been estimated that about 2.5 per cent of the 22 million-strong population is Roma.
The Roma people did not begin arriving in Ireland in any great numbers until about 1998, according to Pavee Point, which promotes the rights of Travellers. Before Romania joined the EU, there were about 3,500 Roma in Ireland but the figure is thought to have risen significantly in recent months with people joining extended families. It is thought that there are about 40,000 Romanians here. About 90 per cent of the Roma people living here came from Romania, with the remainder coming from Bulgaria and, in much smaller numbers, from Slovakia and the Czech Republic.
While Roma people may face discrimination abroad, their social standing is even lower in their home countries. They suffer routine discrimination, educational segregation and police harassment.
"Institutionalised racism faces them everywhere and it will become increasingly an issue if something isn't done at European level to tackle it," says Sara Russell, Pavee Point's Roma coordinator. Pavee Point estimates that only 30 per cent of Roma children in Ireland attend school. Some 95 per cent of Roma women cannot read or write.
Roma people marry young and women are expected to remain in the home so this can often result in girls being withdrawn from school.Several generations frequently live and travel together.
Most Roma people in Ireland are Catholic or Protestant, with a Roma community usually adopting the religion of its host country. Their language derives from Sanskrit and has some elements in common with northern Indian languages such as Hindi and Bengali.