I am hosting a website that is currently run on Google Cloud Storage, and a completely static interface. I am considering upgrading it to allow for better plotting tools, which will require it to run a server, in this case a Java Servlet. The specific technology is Webmathematica, if it matters. My website hast mostly a steady demand averaging around 1K visitors at a time, but has had a peak of over 40K. My hunch is that a single server would not be enough to host such a service, that it would crash. Right now being hosted with a purely static website, I have been okay, but I'm worried about what might happen if I switch to a servlet system and I receive another huge spike in traffic.
What I would like to know is if there is a system in place that will allow me to host my website with java servlets that will scale as required. I would rather not pay for the high demand load all of the time, but I would like the option to turn on a few extra servers if the spare capacity should be required. I think I am okay if the site goes down for a minute while the servers turn on, but not much longer then that.
Is there such a host? What exactly is the name of this capacity so I can price things out? And is there anything else that I should know?