Each airline passenger and his or her luggage must bechecked to determine whether he or she is carrying weaponsonto the airplane. Suppose that at Gotham City Airport, anaverage of 10 passengers per minute arrive (interarrivaltimes are exponential). To check passengers for weapons,the airport must have a checkpoint consisting of a metal detector and baggage X-ray machine. Whenever a check-point is in operation, two employees are required. A checkpoint can check an average of 12 passengers perminute (the time to check a passenger is exponential). Underthe assumption that the airport has only one checkpoint,answer the following questions:a What is the probability that a passenger will have towait before being checked for weapons?b On the average, how many passengers are waiting in line to enter the checkpoint? 1082 CHAPTER 2 0 Queuing Theoryc On the average, how long will a passenger spend atthe checkpoint?
Each airline passenger and his or her luggage must be
checked to determine whether he or she is carrying weapons
onto the airplane. Suppose that at Gotham City Airport, an
average of 10 passengers per minute arrive (interarrival
times are exponential). To check passengers for weapons,
the airport must have a checkpoint consisting of a metal
detector and baggage X-ray machine. Whenever a check-
point is in operation, two employees are required. A
checkpoint can check an average of 12 passengers per
minute (the time to check a passenger is exponential). Under
the assumption that the airport has only one checkpoint,
answer the following questions:
a What is the probability that a passenger will have to
wait before being checked for weapons?
b On the average, how many passengers are waiting in
line to enter the checkpoint?
1082 CHAPTER 2 0 Queuing Theory
c On the average, how long will a passenger spend at
the checkpoint?
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