How can I calculate metrics of 2 independent M/M/1/K systems?

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I know how to calculate those metrics if there is a single M/M/1/K queueing system.

but what if the entire system is a splitting Poisson process(has 2 independent M/M/1/K queueing systems in parallel)? Given the probability of going to the first queue is p, and the probability of going to the second queue is (1-p).

How can I calculate blocking probability, average number of packets, average delay, and average throughput of the entire system? It is not correct to just find the average of the two queueing systems.

I am really confused.