solution

For the post office in Problem 12-17, a second drivethrough window is being considered. A single line would be formed and as a car reached the front of the line it would go to the next available clerk. The clerk at the new window works at the same rate as the current one.

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

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

(c) What is the average time cars spend waiting to receive service?

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

(e) What is the probability that there are no cars in the system?

(f) What percentage of the time are the clerks busy?

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

Problem 12-17

Automobiles arrive at the drive-through window at a post office at the rate of 4 every 10 minutes. The average service time is 2 minutes. The Poisson distribution is appropriate for the arrival rate and service times are exponentially distributed.

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

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

(c) What is the average time cars spend waiting to receive service?

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

(e) What is the probability that there are no cars at the window?

(f) What percentage of the time is the postal clerk busy?

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

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