Get a new host that doesn't suck. Seriously, VPS hosting is crazy
cheap nowadays and doesn't have bizarro restrictions like "no shell
access".
I'm not sure what else is an option - the issue is that the whole
Rails stack is centered on serving requests, and there's not really a
way to say, "wait for this till time X". There are a number of "Ruby
cron"-type things, but they all ultimately rely on a real attachment
to cron - or they require persistent daemon processes, which I suspect
your current host doesn't allow *either*...
But if you're stuck where you are, you can use a "webcron" service to
periodically make a request to an action on your server, which then
fires off the process. So have a controller call "WebCron" with
actions like "calculate_stats" and call
http://your.url/web_cron/calculate_stats