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Speedy Oil provides a single-server automobile oil change and lubrication service
Speedy Oil provides a single-server automobile oil change and lubrication service. Customers provide an arrival rate of 2.5 cars per hour. The service rate is 5 cars per hour. Assume that arrivals follow a Poisson probability distribution and that service times follow an exponential probability distribution.
c. What is the average time a car spends in the system?
Expert Solution
Computation of the average time that a car spend in system:-
Average time that a car spend in system (W) = Wq + (1 / Service rate)
= 0.20 + (1 / 5)
= 0.20 + 0.20
= 0.40 hours Or 24 minutes
Working note:-
Average number of cars in waiting line (Lq))= (Arrival rate^2) / (Service rate * (Service rate - Arrival rate))
= (2.5^2) / (5*(5-2.5))
= 6.25 / 12.5
= 0.50
Average time that a car waits for the oil and lubrication service to begin (Wq) = Lq / Arrival rate
= 0.50 / 2.5
= 0.20 hours Or 12 minutes
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