Consider the queuing network on the figure. The arrival processes to queues 1 and 2 are Poisson, the service times in all the queues are exponentially distributed and the buffer capacity is infinite. After the service in queue 1 or queue 2, tasks are randomly forwarded to queue 3 or 4 with the given probabilities.
1. Collect all the properties and theorems that are required to prove that the arrival process to queue 3 is Poisson. Give the arrival intensity.
2. Express the probability that in the entire queuing network there is one single customer.
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