Good evening. I am thinking about the probabilistic queuing model M/M/n with n servers, arrival rate $\lambda$ and service rate $\mu$. The model allows to estimate the waiting time in the queue and the minimal number of servers that you need for the system not to explode (which is has to be greater then $\frac{\mu}{\lambda})$.
My question is: why we need a probabilistic model? (the minimum number of servers is intituive also without knowing probability)
The probabilistic model allows to have information about the expected waiting time?
Which is the phenomena that a probabilistic model like this one is able to capture?