Hello everyone

I am given a problem and asked to formulate a model describing the system. I have problems determining the right process to use and was hoping someone had an idea.

We consider a system of finite capacity $\displaystyle N$, and at a fixed time every day, a number of new units arrive according to Poisson process with mean $\displaystyle \mu$. Also, units

leave the system before the next arrival time with probability $\displaystyle \mathcal{P}$. If the remaining units in the system and the new arrivals exceeds the capacity $\displaystyle N$,

the exceeding units are just disregarded. The question is then what process can be used to model the number of units just before new arrivals?

Thanks in advance