Empire slavery has always seemed to me as being lord/serf style where the lord has a bit more totalitarian authority. The ability to trade slaves is a bit more power than the typical lord/serf relationship, however I think the dynamic would be similar after this many generations. The lord of the house/land/etc... has to maintain control of the serf population via various means; the choice method seems to be (this is opinion) via religious indoctrination, with a side of power and occasional fear mongering.
As for estates that I've ran, it's very much a self-contained community/town/city. Slaves are given their orders by foremen who are slaves themselves that have earned a certain status from service/loyalty. Doctors have been bought, dedicated to the treatment of their 'brothers in bonds', everything from deskwork organizing a small 'department' to cleaning toilets to security is covered by the slave population. Outside access is restricted without clearance, and typically painted as the surrounding area would likely try to take them away from their families if they aren't careful (causing a dependence on the estate for fear of losing their loved ones).
I think the best way to describe the method I use would be to loosely refer to it as a feudal commune; a single 'ruler' or ruling family that looks out for the interests of the whole commune as a singular entity, but the ruler/ruling family still answer to another [distant] authority as well as being the 'face' for interacting with the other entities (whether they be other communes, individuals, corporations, etc..). Obviously, there are benefits to being the ruler/ruling family, and there are benefits/consequences within the commune to 'following the rules'/'being bad' (highly over-simplified, but the idea is the same).