What is the probability that a passenger will have to wait before being checked for weapons?

ach airline passenger and his luggage must be checked to determine whether he is carrying weapons onto the airplane. Suppose that at Gotham City Airport, 2.6 passengers per minute arrive, on average. Also, assume that inter-arrival times are exponentially distributed. To check passengers for weapons, 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 three 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.

a. Why is an M/M/1 , not an M/M/2, model relevant here?

b. What is the probability that a passenger will have to wait before being checked for weapons?

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

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

Are you looking for a similar paper or any other quality academic essay? Then look no further. Our research paper writing service is what you require. Our team of experienced writers is on standby to deliver to you an original paper as per your specified instructions with zero plagiarism guaranteed. This is the perfect way you can prepare your own unique academic paper and score the grades you deserve.

Use the order calculator below and get started! Contact our live support team for any assistance or inquiry.