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14-12 From historical data, Harry’s Car Wash estimates that dirty cars arrive at the rate of 10 per hour all day Saturday

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14-12 From historical data, Harry’s Car Wash estimates that dirty cars arrive at the rate of 10 per hour all day Saturday. With a crew working the wash line, Harry figures that cars can be cleaned at the rate of one every 5 minutes. One car at a time is cleaned in this example of a single- channel waiting line. Assuming Poisson arrivals and exponential ser-vice times, find the (a) average number of cars in line. (b) average time a car waits before it is washed. (c) average time a car spends in the service system. (d) utilization rate of the car wash. (e) probability that no cars are in the system.

Answer Arrival rate λ = 5average service rate μ= 10a. Average number of cars in washingΡ= λ/μ= 5/10=1/2N= ρ/(1-ρ)=(1/2)/(1-1/2)=1b. Waiting time= T = 1/(μ-λ)=1/(10-5)=1/5=0.2c....