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The new Fore and Aft Marina is to be located on the Ohio River near Madison, Indiana
The new Fore and Aft Marina is to be located on the Ohio River near Madison, Indiana. Assume that Fore and Aft decides to build a docking facility where one boat at a time can stop for gas and servicing. Assume that arrivals follow a Poisson probability distribution, with an arrival rate of 5 boats per hour, and that service times follow an exponential probability distribution, with a service rate of 10 boats per hour. Answer the following questions:
d. What is the average time a boat will spend at the dock?
Expert Solution
d). Computation of the average time a boat will spend in dock:-
Average time that a boat spend in dock (W) = Wq + (1 / Service rate)
= 0.10 + (1 / 10)
= 0.10 + 0.10
= 0.20 hours Or 12 minutes
Working note:-
Average number of boats in waiting line (Lq))= (Arrival rate^2) / (Service rate * (Service rate - Arrival rate))
= (5^2) / (10*(10-5))
= 25 / (10*5)
= 25 / 50
= 0.50
= 0.50
Average time a unit spends in the waiting line (Wq) = Lq / Arrival rate
= 0.50 / 5
= 0.10 hours Or 6 minutes
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