This is why I like mathematicians - they create a model and analyze it without taking into account conditions of the real world... and suddenly come to a conclusion that doesn't make much sense.

As we know, block space is limited and confirmation of a single transaction depends on how many unconfirmed transactions are pending. Hence we can't use Poisson process that doesn't have memory. Hence your model can't be described as such a process. Try another model or extend the existing one.