A marina operates with two machines that put boats into the water. Each machine has a...
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A marina operates with two machines that put boats into the water. Each machine has a separate line. Boat owners arrive according to a Poisson process, and randomly choose one of the two lines to join, with the probability of choosing a particular line equal to the probability of choos- ing the other line. Once a customer enters a line, it is not possible for the customer to maneuver his/her way into the other line. Each machine operates as follows. Boat owners reverse their trailers into the machine, which op- erates like a large sling and lowers the boat into the water. The time to serve a customer at a ma- chine follows an exponential distribution. On average, a customer spends 40 minutes waiting in the line, and 10 minutes in service. In other words, a customer spends, on average, 50 minutes from entering the line till the completion of the service by a machine. a) (3 points) What is the probability that a customer can be served immediately upon his/her arrival, without waiting? A marina operates with two machines that put boats into the water. Each machine has a separate line. Boat owners arrive according to a Poisson process, and randomly choose one of the two lines to join, with the probability of choosing a particular line equal to the probability of choos- ing the other line. Once a customer enters a line, it is not possible for the customer to maneuver his/her way into the other line. Each machine operates as follows. Boat owners reverse their trailers into the machine, which op- erates like a large sling and lowers the boat into the water. The time to serve a customer at a ma- chine follows an exponential distribution. On average, a customer spends 40 minutes waiting in the line, and 10 minutes in service. In other words, a customer spends, on average, 50 minutes from entering the line till the completion of the service by a machine. a) (3 points) What is the probability that a customer can be served immediately upon his/her arrival, without waiting?
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To find the probability that a customer can be served immediately upon arrival without waiting we need to consider the arrival pattern of the customers and the service pattern of the machines Given th... View the full answer
Related Book For
Introduction To Probability And Statistics
ISBN: 9781133103752
14th Edition
Authors: William Mendenhall, Robert Beaver, Barbara Beaver
Posted Date:
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