Hi, our teacher put us this exercise, I searched the Internet and found some sim

Question

Hi, our teacher put us this exercise, I searched the Internet and found some similar problems that helped me solve it, but my answers aren't the same as the options given, so I guess I'm making some mistake.

A service station has one gasoline pump. Cars wanting gasoline arrive according to a Poisson process at a mean rate of 16 per hour. However, if the pump already is being used, then potential customers may balk (drive to another service station). In particular, if there are n cars already at the service station, the probability that an arriving potential customer will balk is n/4 for n = 1, 2, 3, 4 The time required to service a car has an exponential distribution with mean of 4 minutes.

Determine:

a) Expected waiting time for customers that do enter the gas station.

b) Expected number of customers on the queue in the system.

The problem is that those options aren't between the ones given by my teacher, so I guess I'm making some mistake. Could you please help me?

Explanation / Answer

Here is the answer: Their equations $lambda q_n p_n = mu p_{n+1}$ are clearly wrong, and your equations $lambda(1-q_n)p_n = mu p_{n+1}$ are correct. They accidentally switched $q_n$ and $1-q_n$.

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