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. a. Why is an MyMy1, not an MyMy2, 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)?
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.
a. Why is an MyMy1, not an MyMy2, 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)?
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