Commercial trucks traveling through Monument, Colorado must stop at a weigh station. Trucks arrive at the...

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Commercial trucks traveling through Monument, Colorado must stop at a weigh station. Trucks arrive at the station at an average rate of 16 per hour (Poisson distributed), and it takes on average of 2.8 minutes to weigh each truck (following an exponential distribution) on the single scale. WEIGH STATION a. What is the average number of trucks waiting to be weighed? b. How long, on average, does a truck spend at the weigh station (including the time in line, and the time being weighed)? c. The weigh station can operate safely with up to 8 trucks in the system. What is the probability that this capacity will be exceeded? d. A national trucking association estimates that the cost of an idle truck is $39 per hour. In an 8 hour day, what does the weigh station cost the trucking industry? e. Adding another person to work at the weigh station would cost $22 per hour, and would allow trucks to be processed in 2.4 minutes. Should the trucking industry offer to pay for this additional worker? Hint: For parts d and e, note that a truck is essentially "idle" during the entire time it is in the system. Commercial trucks traveling through Monument, Colorado must stop at a weigh station. Trucks arrive at the station at an average rate of 16 per hour (Poisson distributed), and it takes on average of 2.8 minutes to weigh each truck (following an exponential distribution) on the single scale. WEIGH STATION a. What is the average number of trucks waiting to be weighed? b. How long, on average, does a truck spend at the weigh station (including the time in line, and the time being weighed)? c. The weigh station can operate safely with up to 8 trucks in the system. What is the probability that this capacity will be exceeded? d. A national trucking association estimates that the cost of an idle truck is $39 per hour. In an 8 hour day, what does the weigh station cost the trucking industry? e. Adding another person to work at the weigh station would cost $22 per hour, and would allow trucks to be processed in 2.4 minutes. Should the trucking industry offer to pay for this additional worker? Hint: For parts d and e, note that a truck is essentially "idle" during the entire time it is in the system.

Answer rating: 100% (QA)

To solve these questions we can use concepts from queueing theory specifically the MM1 queue model Poisson arrival exponential service Lets go through each part step by step a Average Number of Trucks ... View the full answer