It really depends on what resolution of repeat interval you require, and what platform your server is running, but here's some thoughts:
I believe the shortest repeat interval for UNIX Cron tasks and Windows Task Scheduler tasks is every 1 minute. Given that you're talking about actions that last one hour, is this not sufficient resolution?
If you need something more frequent then you could create some sort of daemon or service running on the server that constantly polls the current time in a loop and calls the corresponding actions as necessary. Be careful though - badly written daemons are an easy way to kill a server (and you'll need to own the server on which it's running - shared hosts generally don't let you run ongoing processes). The way to write the daemon would obviously depend on the server OS.
My only other thought is that I'm assuming you're using a database to manage the job queue, in which case, you should check whether the database has inbuilt scheduling functionality. For example, SQL Server has an agent that lets you call a stored procedure on a schedule that can be repeated every second (if you *really* want to run it every second). That procedure can check the queue table, and process jobs accordingly. I don't know, but I guess that other databases come with equivalent scheduling functionality.