Problem:
The daughter of the owner of a local hamburger restaurant is preparing to open a new fast-food restaurant called Hasty Burgers. Based on the arrival rates at her father's outlets, she expects customers to arrive at the drive-up window according to a Poison distribution, with a mean of 20 customers per hour. The service rate is flexible; however, the service times are expected to follow an exponential distribution. The drive-in window is a single- server operation.
Required:
Question 1) What service rate is needed to keep the average number of customers in the service system (waiting line and being served) to four?
Question 2) For the service rate in part (a), what is the probability that more than four customers are in line and being served?
Question 3) For the service rate in part (a), what is the average waiting time in line for each customer? Does this average seem satisfactory for a fast-food business?
Solve the problem and show all work.