Question

Snappy Lube is a quick-change oil center with a single service bay. On average, Snappy Lube can change a car's oil in 10 minutes. Cars arrive, on average, every 15 minutes. Assume Poisson arrivals and Exponential service times. The average number of cars waiting is 2 cars The average number of cars in the system is 2 cars. The average time spent waiting is 20 minutes The average time spent in the system is 30 minutes. Answer all questions to 2 decimal places. Only enter numerical values.

Answer 1

Given information: The arrival rate (λ) = 1/15 = 0.067 cars per minute

The service rate (μ) = 1/10 = 0.1 cars per minute

Average number of cars waiting (Lq) = 2

Average number of cars in the system (L) = 2Average time spent waiting (Wq) = 20 minutes

Average time spent in the system (W) = 30 minutes

Using the formula for the average number of cars in the system, we have:L = λWSince
`L = 2, λ = 0.067`, we can solve for W as:W
`= L/λW = 2/0.067W ≈ 29.85` minutes

Using the formula for the average number of cars waiting, we have:Lq = λ²Wq / μ(μ-λ)

Since Lq = 2, λ = 0.067, μ = 0.1, we can solve for Wq as:Wq =
`Lq(μ-λ) / λ²Wq = 2(0.1-0.067) / 0.067²Wq ≈ 19.54` minutesTherefore, the average number of cars waiting is 2 cars, and the average time spent waiting is 19.54 minutes.

To know more about