I have only watched Season 1 of the Wire so far. But, based on that limited experience, I have come to think that where Deadwood was influenced by Shakespeare, The Wire is influenced by Greek Tragedy. Most of all, the petty dealers lead by D'Angelo, sitting on an outdoors sofa in the projects, seem to me like a Greek Chorus. 'What is the smell of blood emerging from the palace?' etc.
Simon said, he and his colleagues had “ripped off the Greeks: Sophocles, Aeschylus, Euripides. Not funny boy—not Aristophanes. We’ve basically taken the idea of Greek tragedy and applied it to the modern city-state.” He went on, “What we were trying to do was take the notion of Greek tragedy, of fated and doomed people"
The article has quite a few spoilers, so I'm reading it in a sort of wincing way, skipping paragraphs that seem a bit dangerous. Fans of 'Homicide' might be interested to read it, because it gets a mention too.
Here's a good article on the dramatic function of the Greek Chorus (written in 1908).
The Chorus has been censured as an absurdity, inasmuch as, representing a crowd, it shows a secret transaction of the soul being carried on before the public--an objection which, of course, might be applied to the condemnation of the whole Tragic Drama, whereby the inmost agonies of contending souls are laid bare to crowded benches.
The Greek Chorus in The Wire is literally outdoors all the time, exposed to the public gaze.