Here is a link to an article "The Repertories of Model Melodies (Automela) in Byzantine Musical Manuscripts" by Christian Troelsgaard, dealing with notated model melodies in the Byzantine epoch mss:
P.S. I wonder what a modern reaction to chanting the 1st Ressurectional Exaposteilarion "Τοῖς μαθηταῖς συνέλθωμεν" in Mode 1 would be (as it is notated in the oldest surviving sources)
Here are two other articles: "Byzantine prosomoion singing: a general survey of the repertoire of the notated stichera models (automela)" by Irina Shkolnik, and "Melodic variation in the "marginal" repertories of Byzantine musical mss, exemplified by Apolytikia/Kontakia and Exaposteilaria Anastasima" by Christian Troelsgard (with more examples of the Exaposteilaria not in the 2nd or 3rd Mode ).
Through a detailed analysis Jung (pp. 30-33) shows that the mediaeval Byzantine melody of the hymn is closely related to the Heirmologion melos. However, her attempt to locate the origin of the hymn in the monastic environment of Palestine is unconvincing to me: I'm not sure the Sabbaitic rite at that time differed much from the Typikon of the Anastasis church in Jerusalem in its choice of hymnography and we know that the prosomoia of "Οἶκος τοῦ Ἐφραθᾶ" are absent in an excellent 9th c. source reflecting the ancient Jerusalem liturgical tradition, the Tropologion Sin. gr. ΜΓ 56-5. Likewise, I have yet to see these prosomoia in old Georgian mss, which, as far as their choice of model melodies is concerned, show strong dependence on Palestinian archetypes (from what I can judge, "Οἶκος τοῦ Ἐφραθᾶ" first appears as a model melody in printed Georgian books of the 18th-19th c., but then purely formally only: its "prosomoia" are usually metrically different from the heirmos).
