I am running some very small sites that recieve a lot of traffic in bursts. The content served is < 2MB per user but there have been upto 8000 connections at a single time, this would probably be sustained for 2 or 3 hours but would rise and fall. I'm not certain 8000 would be the upper limit because so far I've been hosting on shared webhosting accounts and they've not taken too kindly to the large amount of traffic and have suspended service.
My question is, in order to comfortably handle this amount of traffic should I be looking at a VPS or a dedicated server?
I don't need to have much diskspace at all. Does anyone have any suggestions on cost-effective solutions, bearing in mind that the traffic is spread fairly evenly between the US and Europe at any given time.