Grumio, Petruchio's manservant, is the first servant to appear, and his characterisation is in line with the traditional comic master-servant relationship. Grumio fails to understand (or, perhaps, pretends not to understand) his master, Petruchio's request, and consequently is given a box on the ears. He then, silenced and sulky, resorts to making sarcastic comments on the scene, and the conversation which follows.

In the same scene, we also see Lucentio treated as a servant by Gremio, though in fact, we know that he is actually a nobleman himself:

Hark you, sir: I'll have them very fairly bound:
All books of love, see that at any hand;
And see you read no other lectures to her.

And - to complete the equation - we also see Tranio, a servant, for the first time acting like the noble "Lucentio", in a burst of flowery, formal language:

Gentlemen, God save you. If I may be bold,
Tell me, I beseech you, which is the readiest way
To the house of Signior Baptista Minola?

"What roles...?" is actually a very good way of phrasing the question. I'd argue Grumio plays, initially, the role of a friend, and then the role of a wounded caustic commentator, while Lucentio (not a servant) plays the role of a servant, and Tranio (a servant) the role of a noble.