Question

Sharp Discount Wholesale Club II - How much time does the average customer spend in their queue? Sharp Discounts Wholesale Club has two service desks, one at each entrance of the store. Customers arrive according to a Poisson distribution at each entrance at an average of one every 7.5 minutes. Without exception, when customers finish shopping, they checkout at the service desk near the entrance where they entered the store. The negative exponentially distributed service time is 6 minutes per customer. How much time does the average customer spend in their queue?

Answer 1

Average arrival rate, λ = 1 in 7.5 minutes = (1/7.5) per minute
Average service rate, μ = 1 in 6 minutes = (1/6) per minute

So,

u =  λ/μ = (1/7.5) / (1/6) = 0.8

The average time a customer spends in the queue, T_q = {u / (1 - u)} * (1/μ) = (0.8/(1 - 0.8))*6 = 24 minutes