I'm sorry, but this is a BS answer. Since H2 I've played 20,000+ games of Team Slayer online, and what is described is a host selection issue. I was in communication with part of the development team at Bungie for a while about my observations in this respect, but they never made significant corrections to the netcode. The selection filters that they used (H3?...can't remember)were a step in the right direction, but was still a flawed methodology based upon, I believe, how they ping/compare each console. It was never described to me if XBL handled this 100%, or if Bungie controlled this.
H4 is somewhat better online, but that is quickly degrading as fewer and fewer people play TS. There are simply too many gametypes for the numbers of players. I have found that whenever TS falls <20,000 participants, the chances of having connection issues increases logarithmically. Obviously with the game already released, there's not much 343 can do to improve their netcode. The only thing they can do at this point is eliminate gametypes to increase the population on the remaining games.
If you live near a large metropolitan area, or otherwise near a broadband hub, it's very likely you'd never notice connection issues. But if you live in a more suburban or rural location, and have more server hops, it will become noticeable.
I'm a stat hound, and it's very easy to see who had host, most of the time, by examing the k/ds at the end. Frequently, I see such lopsided final results that it's a clear indication of poor host selection. I'm able to tell during the game either who has host, or who has a low ping to host.