Queueing model - expected outflow Can anybody please help me how to tackle this question?
We have one server.
The service time is random with mean 1 minute
The arrival rate is constant with 3 customers/minute, but they leave if the server is occupied.
A)
Assume the server is empty. How long would it take before one enters the system?
B)
What is the expected number of customers served after 1 hour?
I have a hard time of figuring out how to estimate the fraction of time the server is empty; and obviously then there is not served 1 customer per minute on average.

The arrival rate is $3$ per minute, so $1$ every $20$ seconds. That means you have to wait on average $10$ seconds for the next customer. Each customer takes $60$ seconds of time, so in total, thats $1$ customer every $70$ seconds. Per hour, you get $\frac 1{70}\cdot3600=\frac{360}7$.
Not that I am assuming that arrival rates are constant, but because serving time is random, two consecutive waiting times are not correlated.
