Question

Each airline passenger and his or her luggage must be checked. Suppose that at Jeddah City Airport, an average of 10 passengers per minute arrive (interarrival times are exponential). To check passengers, 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. A checkpoint can check an average of 15 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: 1-1. What is the probability that a passenger will have to wait before being checked for weapons? 2-2. On the average, how many passengers are waiting in line to enter the checkpoint? Attach File Browse My Computer

Answer 1

FK =10 S Solution Crien Average Arrival Rate of Lassenfels per minute Average Service Rate la 15 berminute (1) The probability that will hare to wait before being checked for Weapons lo 0.6667 M 15. a pass engel 9 = 1 = 3 (2) On average, the number of locassengers are waiting in line to entee the checkpoints Lq a = |२ 11 fúri) gel Mah) Von 10 1 15 15.10 = 20 10 x 10 To 5 T I 1.3333 15

FK =10 S Solution Crien Average Arrival Rate of Lassenfels per minute Average Service Rate la 15 berminute (1) The probability that will hare to wait before being checked for Weapons lo 0.6667 M 15. a pass engel 9 = 1 = 3 (2) On average, the number of locassengers are waiting in line to entee the checkpoints Lq a = |२ 11 fúri) gel Mah) Von 10 1 15 15.10 = 20 10 x 10 To 5 T I 1.3333 15
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