While looking around the internet, I came across Victoria Fleischer's 3 April 2014 PBS Newshour Art Beat piece "What Does a Medieval Literature Scholar Read into Game of Thrones?" In it, Fleischer reports and comments on a monologue from Prof. Brantley Bryant of Sonoma State University (noted as one of the Chaucer bloggers) in which Bryant discusses in brief possible medieval literary antecedents for the characters in Martin's increasingly famous fantasy series. It is a useful example of popular scholarship, taking something very much in the contemporary popular mind and using it as a bridge to begin consideration of appropriations of the medieval.
Of note to my mind is Bryant's attempt to connect Stannis Baratheon and Melisandre to Arthuriana, specifically Arthur and Nimue. There is some connection present between Martin's work and the primary piece of Arthurian legend in English, Malory's Le Morte d'Arthur. For one, Douglas A. Anderson asserts in his introduction to Tales before Tolkien: The Roots of Modern Fantasy that Arthurian legend underlies all fantasy literature--which would include the tales of Westeros. Too, the civil unrest depicted in the Song of Ice and Fire series echoes the Wars of the Roses, in which Malory fought and which culminated in one of the understood ends of the English Middle Ages. And there is the tentative character connection Bryant suggests--although I am not convinced of its strength, thinking the relationship of Stannis and Melisandre more like that of Accolon and Morgan than of Arthur and Nimue. There is also a stronger structural parallel, that of the interwoven narrative. One of the key features of Malory's text is that it switches among plots, moving from one character to another in ways that are occasionally ragged except for their simultaneity, antecedent to cross-cutting in films. Martin's books do the same thing, with each volume of the Song of Ice and Fire moving among several characters' individual stories. They meet and part, and sometimes their deeds run as one for a while before they become separate threads again. To my mind, it is one of the more notable mimicries of medieval literature in Martin's series, although I can understand why it is not among the comments Fleischer reports.
As a means to begin discussion, then, the piece is worth attention. As is perhaps unavoidable given the constraints on the piece, it does not go as far as it could or as it ought; there is far more to discuss than Fleischer, or those of Bryant's comments Fleischer offers, present.
(Yes, this piece makes use of informal citation. I tend to follow MLA, but tend to does not mean always.)