Question

A gas station with two pumps does not allow drivers to pump their gas and has a service attendant for each pump. Potential customers (i.e. cars) arrive according to KinKo, a process at a rate of 40 cars per hour. If the two pumps are busy, then arriving cars wait in a single queue to be served in the order of arrival by the first available pump. However, cars cannot enter the station to wait if there are already two cars waiting for gas, in addition to the two cars getting their gas pumped. Cars that cannot enter the station to wait leave and get their gas elsewhere. Suppose that the amount of time required to service a car is exponentially distributed with a mean of two minutes.
a) What fraction of the time are neither of the attendants busy?

b) What is the average number of cars having their gas pumped?

c) What is the average amount of time, in minutes, for a car to get gas at this station?

d) What fraction of cars don’t enter the gas station because the queue is too long? (i.e. full)

e) What is the effective rate at which cars get completely served at this gas station?

f) The owner of Kinko's is considering making modifications so that any number of cars can wait. If the owner must pay back the money they borrow to make the modifications two years after the modifications are complete, what should be the most the owner should be willing to spend on the modifications? Assume the average profit per car is $5, and the gas station is open 16 hours per day, 365 days a year.

Answer 1