Migrations have happened throughout the entire pre-history and history of humankind. They continue to happen today.
Nevertheless, some periods of time experience very significant migratory movements with far-reaching historical consequences. From a eurocentric perspective, one of these periods has come to be called the "Migration Period". It is usually taken to mean the time span of the 4th to 7th centuries of OTL, when Huns, Awars, Alani, Goths, Franks, Suebians, Vandals and Langobards migrated and pushed each other Westwards, bringing about the collapse of the Western Roman Empire and the order of Late Antiquity and the establishment of Roman-Germanic feudal kingdoms and the transition to medieval structures.
The above-mentioned migratory movements in OTL are only the European section of a larger picture. The initial impulse which got the ball rolling needs yet to be determined: climatic change affecting Central Asia? Chinese military campaigns against nomads? Military advances (the stirrup? better crossbows? larger horses?) by some the steppe nomads?
Either way, the migratory movements began in Eastern Central Asia: in the Gansu corridor, the Tarim basin, Dsungaria and Sogdiana. From Eastern Central Asia, they spilled Southwards and Westwards (because to the North, there were only endless forests). In OTL, Kidarites, Xionites and later Hephtalites exerted pressure on the Sassanid Empire and brought down the Gupta Empire in Northern India. Those who moved Westwards encountered other nomads in the Caspian and Pontic steppes. Overcrowding caused newly composed second, third etc. waves - led by "the Huns" or later "the Awars", labels which describe heterogeneous confederacies forming and transforming for and during migratory movements and the military events brought about by them. Migration, displacement and militarisation caught one group after the other in their avalanche and maelstrom. Repeatedly, groups attempted to build new state structures in the cultural areal where statehood was the norm, and repeatedly, Migration Period states like the Ostrogothic Kingdom in the Balkans, Magna Hungaria or Great Bulgaria were overthrown by yet another wave of migration. While most of Western, Central and Southern Europe were spared from further migratory waves from the 6th century onwards, the Balkans and Eastern Europe as well as Central Asia experienced many more Westward mass migrations for more than half a millennium.
In this timeline, the Roman Republic and the Sassanid Empire keep peace with each other. While Rome is politically much more stable than in OTL, the Sassanids are militarily much more powerful than in OTL. The Sassanids prevent the Southward migration from the 4th century on and commit a genocidal bloodbath among the nomads who had invaded Bactria, Transoxania and Sogdia. The Romans, in turn, stop the Westward migration a few decades later and commit an equally gruesome genocide in the Pontic steppe.
Thus, Romans and Sassanids not only saved themselves from imminent danger, but bought themselves two centuries of peace. The depopulation of the Western half of the Central Asian steppe dramatically deflated population pressure North of the Empires. For two centuries, new migratory movements found plenty of unoccupied space and came to a halt.
Here is a short table comparing the fate and location of various groups in OTL vs. Abrittus TL:
|Kidarites||short-lived empire in Southern Central Asia, subdued and assimilated by Hepthalites||defeated and enslaved by Sassanids|
|Xionites||see Kidarites||see Kidarites|
|Hephtalites||plundered much of Sassanid Empire, overran Kushano-Sassanids, defeated the Guptas; short-lived large empire in Southern India broke into pieces, which became "Indianised"||defeated, killed or enslaved by Sassanids; small rest employed as Sassanid soldiers, who assimilated themselves|
|North-West Indians||Late Classical empires broke down; emergence of a militarised aristocracy (e.g. Rajputs); end of Northern dominance on the subcontinent||continuous Sassanid influence and West-East-contacts, consolidating and growing urban elites|
|Sassanids||alternating conflicts on all fronts, militarised state, Northern regions often plundered, concentration on the Persian core lands||expansion, stable rule, mutual influence with post-Hellenistic Central Asian and North-Western Indian civilizations|
|Black / European Huns||subdued Alani and Goths, plundered Eastern Europe in a first confederacy; several groups serving different masters, then united in a second confederacy under Attila, short-lived empire, defeated by a Germanic confederacy, falls apart, merged into new alliances and confederacies||subdued Alani and some Goths, plundered Eastern Europe, defeated a Germanic confederacy, then annihilated or enslaved by the Romans: no Huns left in the steppe after 370 CE|
|Awars||new confederacy formed from Huns and other steppe nomads, migrated into the Balkans, erected an empire, became sedentary, after military defeats against the Frankish Empire subdued and assimilated by Danubian Bulgars and Southern Slavs||steppe depopulated in the 5th century, no confederacy forms|
|Sabirs||some went with the Huns, others lived outside the Sassanid Empire in Northern Caucasus and clashed with Awars; both groups assimilated into Bulgars and Chasars||some went with the Huns and were killed or enslaved, others lived within the larger Sassanid Empire and assimilated in the 5th century|
|Bulgars||emerged from earlier nomadic configurations, formed several empires in the Pontic steppe, along the Volga and on the Balkans||steppe depopulated in the 5th and early 6th century, Old Great Bulgaria never forms|
|Alani||subdued by the Huns, many went with them and merged later into other confederacies, rest remained as small tribes in the Northern Caucasus and settled down||subdued by the Huns, many went with them and were killed or enslaved; rest remained as small tribes in the Northern Caucasus and settled down|
|Magyars||left their settlements along the Volga in the Chasar Empire and moved into OTL Ukraine, then, pushed by Bulgars and Pechenegs, into Pannonia||remained on the Volga and settled down, became integrated into Great Perm|
|Goths||poured over the Danube into the Roman Empire, erected kingdoms in Italy and Spain, which were conquered by other Germanic kingdoms later||defeated by Decius; one half is settled in a controlled manner in Dacia, secures the province and is Romanised; the other half flees from the Huns to Tauris (OTL Crimea), assimilates to its Jewish Hellenised culture and becomes a global seafaring nation|
|Romans||overrun by Germanic tribes, their empire disintegrated, although its cultural legacy lingered on; Eastern Roman Empire persisted for another millennium with a Greek Orthodox twist||stable Second Republic is established, which continues to modernise and remains a globally powerful force|
|Vandals||poured into the Roman Empire in the early 5th century, established a kingdom in North Africa, which was defeated by the Byzantine Empire||remained North of the Danube, joined a Germanic confederacy (Alliance of Five Nations), later left it, one half Romanised, the other absorbed into Corvatia|
|Markomanni||absorbed by other tribes in the late 4th/early 5th century||remained North of the Danube, joined a Germanic confederacy (Alliance of Five Nations),developed a syncretic Roman-Christian-Germanic cult (Lausai), joined the Roman Republic in the 7th century; Romanised|
|Gepids||subdued by the Huns, later part of a confederacy which defeated the Huns, became absorbed by other tribes||defeated by Decius, settled in Roman Dacia, Romanised|
|Langobards||moved into formerly Roman land already held by other Germanic groups; established kingdom in Italy, which was defeated by Charlemagne and integrated into HRE||under pressure of migrants from the East during the Hun Wars joined the Alliance of Five Nations, fused with the Burgundians, ended up in the separate Kingdom of Burgundy|
|Burgundians||crossed the Rhine in 406, occupied parts of Gaul, then subdued by the Merowingian Franks||under pressure of migrants from the East during the Hun Wars joined the Alliance of Five Nations, fused with the Langobards, formed separate kingdom in OTL Czech Republic|
|other Suebians||some merged into the Thuringians, others into the Bavarians, others into yet other groups||same here, but the Bavarians never formed, instead, a few civitates in "Boicum" joined the Roman Republic in the 6th century|
|Alemanni||occupied the Agri Decumates and other parts of Germania Superior, Raetia and Alpes, lost their political independence to the Merowingian Franks||occupied the Agri Decumates, but stopped at the Rhine by the Imperium Romanum Galliarum, developed into a half-Romanised Empire|
|Franks||occupied much of Gaul, established a large empire which claimed the legacy of West Rome||stopped at the Rhine by the Imperium Romanum Galliarum; petty kingdoms overthrown by peasant rebellion which unifies Franconia as a republic in the late 6th century, under Gallo-Roman influence|
|Slavs||migrated into the Balkans and into depopulated lands between Baltic Sea and Carpathians as well as Northwards into Uralic lands, formed various polities, many of which have successor states in the present||confined at the Roman borders, with which they engage in trade instead. In the North-West, influenced by Scandinavians, in the East, mixed with "Ostrogoths". Establishment of three sizable polities which have successor states in the present|
In OTL, the migration period of the 4th-7th centuries left the old empires (Rome, Sassanids, North India) weakened, which paved the way to power for less sedentary powers like Turks and Arabs. The establishment of their various empires resulted in new migratory movements throughout the Middle Ages.
In this timeline, stable empires and power blocs continued to prevent and contain migration even in the centuries that followed. Trade and cultural and technological dissemination took the function of integrating new groups into the developing civilizations, which in OTL was often achieved by migration.
Even the discovery of new continents led to less migrations than in OTL because by the time of their discovery, Eurasian and African women had found efficient methods of birth control, and imperial states provided a minimum of social security outside of the family, so birth rates were sinking by the 11th and 12th centuries, and Eurasia and Africa did not experience a population pressure which their continents could not absorb.