A drive-through car-wash service has one station for washing cars. Cars arrive according to a…

A drive-through car-wash service has one station for washing cars. Cars arrive according to a Poisson process with rate ʎ= 10 per hour.

(a) If the time to wash a car is approximately a fixed value of 4 minutes, what is the expected wait in queue?

(b) You are thinking of buying a new car wash that senses the amount of dirt on the car and washes the car only as long as necessary. The new car wash is slightly faster on average, but there is variability in the time to wash each car. The time to wash a car has a mean of 3.5 minutes and a standard deviation of 2 minutes. Using an Erlang approximation for the service distribution, what is the expected wait in queue for the new car wash? Is it longer or shorter than with the existing car wash?