P9_L14_GasStation - customers i.e the loss probability b...

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OM 335 Fall 2008 8e4d29906d1f311d42ee5d1dc00be98cbf35f2cd.doc P9: Gas Station  Consider the situation of Mr. R. B. Cheney, who owns a large gas station at a highway in Vermont. In the  afternoon hours, there are on average 1000 cars per hour passing by the gas station, of which 2% would  be willing to stop for refuelling. However since there are several other gas stations with similar prices at  the highway, potential customers are not willing to wait and bypass Cheney’s gas station if all of its spots  are full. The gas station has six spots that can be used for filling up vehicles and it takes a car on average  five minutes to free up the spot again (includes filling up and any potential delay caused by the customer  going to the gas station). a) What is the probability that all six spots are taken? [Hint: this is asking the probability of losing 
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Unformatted text preview: customers, i.e., the loss probability.] b) How many customers are served every hour? Solution: The flow units are cars that come to be refueled, and the servers (resources) are the six fuel spots. 20 2% 1000 = × cars need to fill in per hour. We have the following inputs time service average min/ 5 time al interarriv average min/ 3 20 min 60 6 = = = = = = car p car car a m a) We compute 667 . 1 3 / 5 / = = = a p ρ . Then use the Erlang loss table to find that the probability that all 6 servers are utilized, 0.56%. = 0.0056 = (1.667) P 6 b) The flow rate is Flow rate=20 cars/hour *(1-0.0056) =19.888 cars/hour . / 888 . 19 ) 0056 . 1 ( / 20 hr cars hr car rate Flow =-× = 1...
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