From historical data Rick\'s Car Wash estimates that dirty cars arrive at a rate

Question

From historical data Rick's Car Wash estimates that dirty cars arrive at a rate of 11 per hour all day on Saturday. With a crew working the wash line, Rick figures that cars take 4 minutes to be cleaned. One car at a time is cleaned. What type of system is this? What is the average number of cars in line waiting to be cleaned? (Enter two decimal places) What is the average time (in minutes) that a car spends in the service system? (Enter one decimal place) What percentage of the time is the crew busy washing cars? (Enter three decimal places)

Explanation / Answer

arrival rate = 11 cars per hour
Service rate = 15 cars per hour

This is first in first out type of system with single server.

Here utilization p = 11/15 = 0.7222

Average number of custromers waiting in queue are L = p^2/(1-p) = 2.0167

Wait in the queue = W1 = L/arrival rate = 2.0167/11 = 0.1833 * 60 = 10.998 = 11 mins

Wait ins system W = W1 + 1/15 = 0.1833 + 1/15 = 0.25 * 60 = 15 mins

Crew was busy for 72.22% of the time

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