Round Robin – how to determine the optimal quantum of time

Please be careful to understand that priority is not the same as order of running. As a rule, when you fork a process it runs at the same priority, unless you ask for it to be lower. The order in which parent and child run is separate.

The answer is that you cannot and should not depend on the order. In many cases after forking (or using any comparable mechanism in any other operating system), the parent will continue to run before the child starts. Or not. It all depends.

If it is important, you will have to include synchronising mechanisms to control which process runs and which waits.

In the usual terminology, processes don't arrive. Processes roughly corresponds to the programs running on a machine. What can arrive (and cause some processing to be done) are requests and/or events. I will assume you meant those when using "process" in the question.

Assuming that the processing of a request is CPU-bound (meaning that a single request keeps the CPU fully occupied for 8 seconds, with no spare time to do anything else), then your calculation of

6 requests/minute * 8 seconds processing time = 48/60 = 80% load

is a reasonable estimate for the average processor load.

If the processing of a single request isn't CPU-bound, then the 8 second response time is not a correct figure for calculating CPU load, because you need to subtract the time that the process is waiting for external systems, like the disk drive or database.