Speedy Oil provides a single-server automobile oil change and lubrication service

Business Aug 22, 2020

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.
b. What is the average time that a car waits for the oil and lubrication service to begin?

Expert Solution

b). Computation of the average time that a car waits for the oil and lubrication service to begin:-

Average number of cars in waiting line = (Arrival rate^2) / (Service rate * (Service rate - Arrival rate))

= (2.5^2) / (5*(5-2.5))

= 6.25 / 12.5

= 0.50

Average time = Average number of cars in waiting line / Arrival rate

= 0.50 / 2.5

= 0.20 hours Or 12 minutes

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