A small popular restaurant at an interstate truck stop provides priority service to truckers. The restaurant has ten tables where customers may be seated. The service time averages 40 minutes once a party is seated. The customer arrival rate is 12 parties per hour, with the parties being equally divided between truckers and non-truckers.
On average, how many parties of non-truckers are waiting to be seated?
A) 0.27.
B) 0.52.
C) 0.88.
D) 1.36.
E) 1.75.

Question

Quizplus · Accepted Answer

We can use the Little's Law formula, which states that the average number of customers in a system (L) is equal to the average arrival rate (λ) multiplied by the average time a customer spends in the system (W):
L = λW
We can solve for L by finding the ratio of the arrival rate of non-truckers to the total arrival rate:
L = (12/2) * (40/60) * (1 - 1/10)
The first term represents the arrival rate of non-truckers, which is half of the total arrival rate of 12 parties per hour. The second term represents the average time a customer spends in the system, which is 40 minutes or 2/3 of an hour. The third term represents the probability that all ten tables are occupied, which is 1 minus the probability that any given table is available (9/10).
Simplifying the equation, we get:
L = 4 * 2/3 * 1/10
L = 8/15
Therefore, on average, there are 8/15 or approximately 0.533 parties of non-truckers waiting to be seated. The closest choice is D, which is 1.36.

A Small Popular Restaurant at an Interstate Truck Stop Provides