How to implement the concept of particles entering an open network according to a Poisson process with a rate different from the rate in the network

Question

[Poisson Process with different rates][1] [Poisson Process with different rates][2]

! [1]: https://i.stack.imgur.com/LJ87x.png

![2]: https://i.stack.imgur.com/xJsB4.png

How do I choose if the next poisson clock a particle is going to enter the network or go through the network?