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Unformatted text preview: Practice Questions: Managing Uncertainty 1. To support national health week, the American Heart Association plans to install a free blood pressure testing booth in South Coast Plaza for a week. Previous experience indicates that, on the average, 10 persons per hour request a test. Assume the inter-arrival times are exponentially distributed. The blood measurements take a constant time of 4.8 minutes. a. What is the utilization of the blood pressure machine? 8 . 6 8 . 4 = = b. What is the average number of people in the system (sum of those waiting and those getting their blood pressure checked)? customers C C L s a s q 6 . 1 5 . * 2 . 8 . 2 1 2 . 8 . 2 1 2 4 2 2 ) 1 ( 2 = = + = + = + customers L L q s 4 . 2 8 . 6 . 1 = + = + = c. How long, on average, do people spend in the system (waiting + service time)? From Littles rule we know 4 . 14 24 . * 60 24 . 10 4 . 2 = = = = hours W s min d. What is the average waiting time (before you see a nurse)? min 6 . 9 16 . * 60 16 . 10 6 . 1 = = = = hours W q e. What is the average number of people waiting in line? 1.6 customers 2. At the California border inspection station, vehicles arrive at the rate of 10 per minute. The inter-arrival times are exponentially distributed. For simplicity assume the there is only one lane and one inspector, who can inspect at the rate of 12 per minute in an exponentially distributed fashion. a. What is the average number of cars waiting to be inspected? 6 5 12 10 = = customers C C L s a s q 17 . 4 6 25 2 1 1 ) 6 / 1 ( ) 6 / 5 ( 2 1 4 2 2 ) 1 ( 2 = = + = + = + b. What is the average number of cars in the system either waiting or being inspected? customers N L l s 5 83 . 17 . 4 = + = + = c. How long, on average, does a car spend in the system waiting + inspection? min 5 . 10 5 = = = s s N W d. What is the average waiting time (before inspection)? min 417 . 10 17 . 4 = = = l q N W 3. Since the deregulation of the airline industry, fierce competition has forced Global Airlines to reexamine their operations for efficiency and economy. As part of their campaign to improve customer service, they have focused on passenger check-in operations at the terminal. Global operates a common check-in system wherein passengers for all Globals flights line up in a single snake line. The arrival rate is estimated to be 52 passengers per hour. The check-in process takes an average of three minutes. Agents are paid $20 an hour. The customer relations department estimates that every minute a customer spends waiting in line to be checked in, it costs Global $1 due to missed flights, customers dissatisfaction, and loss of future business....
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- Fall '07