Trucks come to a facility to pick up final goods for delivery to far-off markets. They must join a waiting line when they arrive and are served on an FCFS basis. Ten trucks come per hour, whereas fifteen trucks are loaded per hour. The fact that loading is exponentially distributed and arrivals are Poisson distributed are also a given. Transporters have expressed dissatisfaction about the approximately 12-hour wait time for their trucks at the factory. (A) Verify the validity of the complaint. (B) What is the probability that the loaders are idle?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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Trucks come to a facility to pick up final goods for delivery to far-off markets. They must join a waiting line when they arrive and are served on an FCFS basis. Ten trucks come per hour, whereas fifteen trucks are loaded per hour. The fact that loading is exponentially distributed and arrivals are Poisson distributed are also a given. Transporters have expressed dissatisfaction about the approximately 12-hour wait time for their trucks at the factory. (A) Verify the validity of the complaint. (B) What is the probability that the loaders are idle?
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