Question: Queuing System

Automobiles arrive at the drive-through window at a post office at the rate of four every ten minutes. The average service time is two minutes. Arrival behavior can be measured using a Poisson distribution, and the service time is believed to be exponentially distributed. Given above information, please provide answer (list parameters’ values and detailed formulas as well as calculations) following questions:

(a) How long on average takes a car in the system?

(b) What is the average number of cars in the system?

(c) What is the average number of cars in line behind the customer receiving service?

(d) What is the probability that there are exactly two cars in the system?

If assume that a second drive-through window is being opened. A single line would be formed and as a car reached the front of the line it would go the next available clerk. The clerk at the new window works at the same service level as the current one.

(e) What is the average time a car spends in the system?

(f) What is the average number of cars in line behind the customers receiving service?