Question

Each airline passenger and his luggage must be checked for security. Suppose that at Gotham City Airport, 3.6 passengers per minute arrive, on average. Also, assume that interarrival times are exponentially distributed. To check passengers for security, the airport must have a checkpoint consisting of a metal detector and baggage X-ray machine. Whenever a checkpoint is in operation, two employees are required. These two employees work simultaneously to check a single passenger. A checkpoint can check an average of 4.2 passengers per minute, where the time to check a passenger is also exponentially distributed. Under the assumption that the airport has only one checkpoint, answer the following questions.

What is the probability that a passenger will have to wait before being checked for weapons? If needed, round your answer to one decimal digit.

On average, how many passengers are waiting in line to enter the checkpoint? If needed, round your answer to one decimal digit.

On average, how long will a passenger spend at the checkpoint (including waiting time in line)? If needed, round your answer to one decimal digit.

Answer 1

Given

= 3.6

= 4.2

The probability that a passenger will have to wait before being checked for weapons

= 3.6/4.2

= 0.857 ~ 0.8 (Round to one decimal place)

On average, how many passengers are waiting in line to enter the checkpoint

On average, how long will a passenger spend at the checkpoint (including waiting time in line)

Average time at checkpoint W = Expected no.of customers (L) /

customers or passengers