What you really need to do here is to ... get to know networking and queueing. :-)

In other words, your website would be used to create and submit jobs to a batch-processing system on the same or on a different server, and to monitor the status of the jobs as they are completed. There are many batch and cluster management systems out there, and your website would serve as an interface to one.

Furthermore, you will discover that nearly all of these batch management systems already have a web-interface, so the entire need for your existing website may prove to be ... nonexistent.