At a local fast food joint, cars arrive randomly at a rate of 12 every 30 minutes.The fast food joint takes exactly 2 minutes (this is constant).The average total time in the system is
A)5.4 minutes.
B)6.0 minutes.
C)8.0 minutes.
D)2.5 minutes.

Question

Quizplus · Accepted Answer

The arrival rate is 12 cars per 30 minutes, which is 0.4 cars per minute. The service rate is 1 car every 2 minutes, or 0.5 cars per minute. Using the formula for the average time in the system in an M/M/1 queue, which is 1/(service rate - arrival rate), we get 1/(0.5 - 0.4) = 10 minutes. However, since the service time is constant, the average time in the system is the service time plus the average waiting time, which is 2 + (1/(0.5 - 0.4)) = 6 minutes.

At a Local Fast Food Joint, Cars Arrive Randomly at a Rate