Ah, I see. Thanks for the clarification.
So as independent says, we not subject to a fixed limit of CPU here at Dreamhost - either on the web servers or the mysql servers. This doesn't mean that support doesn't have a guideline for CPU usage that they use to target sites as having "impact" on other sites, just that this guideline involves their own judgment about the frequency of such impact and such.
Performance analysis is a complex and difficult undertaking. Most people aren't up to the challenge. Heck, most developers aren't up to the challenge and just code things the best they know how and deliver their applications to the operations department for them to analyze.
There are certainly tools out there for you to determine the performance profile of your forum - especially since you've got the ability to add diagnostic code yourself since you're the developer!
Beyond that, you can always contact pre-sales support using the pre-sales contact form to find out what their guidelines are for this sort of thing - they have much more experience with this than us customers. But you might also consider opening a trial account. If you use a credit/debit card or Google Checkout, you will have 97 days to do your performance analysis and still be able to get your money back should you figure out that your needs are beyond shared web hosting.
But speaking of which, what's your alternative. I think all shared web hosts limit their usage to that which doesn't impact other customers on their shared servers. The difference is that they are either case-by-case or have hard CPU limits. Generally, the case-by-case ones are more generous in their interpretation of the limits (but as a result I think they sometimes have more support calls due customers who are hosting stuff that way too much for shared hosting), but it's certainly the case that the ones with hard limits have slight differences in their limits.
Beyond shared web hosts are the VPS and dedicated hosting options. In each case, you decide how much server you need and pay for it. Even Dreamhost has their Private Servers option in addition to dedicated hosting. With either of these types of hosting you can host stuff that's beyond what you can host on shared hosting - and generally get better performance characteristics as well.
The only other option you have is home-based hosting. I find this to be:
3. less reliable
4. have lower bandwidth
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