I am a performance engineer for a tier one mobile phone manufacturer in their web browser division. We run virtual mozilla browsers to fetch, process, render, and scale web pages for our users' mobile phones - millions of users all over the world. This situation (slowdown during peak hours) is not uncommon, and has many contributing causes, from the capacity of the phone company (carrier), to our capacity to process the users' requests efficiently, to the capacity of the web sites being accessed. Needless to say, Facebook, Twitter, and Google are those with the biggest loads (and pipes/capacity). But, all things have their limits! That is why we are studying ways to cache those most commonly accessed pages during busy hours so we can provide our users with the snappiest performance possible. We monitor latencies (time to get service and relevant data) at all links in the chain, from the handset to the carrier, to our data centers, to the target web sites, between our server components, and back to the handset, and we exert a LOT of effort to improve the experience continuously.
So, I think my point is, is that there is no simple answer here. Peak times == peak loads == slowest performance. That's just the way it is, unfortunately... :-( Sorry, but our quantum tunneling, time compression technology is just not yet ready for prime (or any other) time! :-)