Question: the daughter of the owner of a local hamburger restaurant...
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 Poisson 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.
a. What service rate is needed to keep the average number
of customers in the service system (waiting line and being
served) to four?
b. For the service rate in part (a), what is the probability that
more than four customers are in line and being served?
c. 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?