I want to study a scheduling scenario by using queuing theory.
This is the situation:
- one CPU with mean service time $1/μ$
- two infinite queues with arrival rate $λ$
- queue B has priority over queue A, i.e if the CPU is executing a job of A type, it stops (preemption) that job and executes (for all) the B job. Then if the B queue is empty it continues to execute the A jobs until a new B job/s arrives.
I would calculate some stability conditions, but I have never worked on systems like this.
If I would see the system as M/M/1 with only the queue with higher priority I could use $λ < \mu$ relation, but what about the queue A behaviour?
In the end, I have to do some simulations (with different parameters) and get some results about waiting times in the queues. I am doing some queuing theory modelling first to calibrate a bit the parameters of the system (inter-arr times and job tasks time, both exponential for both queues, CPU speed..)
I have read this question, but it is slightly different for my case/
What can I do?