How can we model the process scheduling mechanism in Linux using queueing theory models?

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Assuming the arrival and processing times of processes in the system both follow a Poisson distribution, and with c independent logical cores present, this represents an approximate M/M/c model.

The issue arises in that, within this model, each task is executed sequentially in a first-come-first-served manner until completion, whereas in reality, Linux employs a Round-robin scheduling approach (excluding the effects of Completely Fair Scheduler - CFS). Given this discrepancy, how should I calculate the average waiting time for each process?

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