Question: A post office in a small town has a single line for customers waiting for the postal clerk. There is only one postal clerk at

A post office in a small town has a single line for customers waiting for the postal clerk. There is only one postal clerk at the office. The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution. On average, a customer arrives at the post office every 4 minutes, and the average service time the clerk spends with each customer is 2 minutes.

What is the average length of the line?

How long does the average person spend waiting for the clerk?

What proportion of time is the clerk idle?

What is the probability that there is more than 1 customer waiting in the line?

Suppose the clerk is paid $20/hr, and the customers waiting cost in the line is $15/hr. What is the total hourly cost for the system?

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