3. The Friendly Neighbor Grocery Store has a single checkout stand with a full-time cashier. Customers arriverandomly at the stand at a mean rate of 20 per hour. The service-time distribution is exponential, with a meanof 2 minutes. This situation has resulted in occasional long lines and complaints from customers. Therefore,because there is no room for a second checkout stand, the manager is considering the alternative of hiringanother person to help the cashier by bagging the groceries. This help would reduce the expected timerequired to process a customer to 1.5 minutes, but the distribution still would be exponential.The manager would like to have the percentage of time that there are more than two customers at thecheckout stand down below 25 percent.(a) Use the formulas for the M/M/1 model to calculate L, W, W₁, Lq, Po, P₁, and P₂ for the current mode ofoperation. What is the probability of having more than two customers at the checkout stand?(b) Repeat part (a) for this alternative.(c) Which approach should the manager use to satisfy her criteria as closely as possible?

Find the Calculation methods below: P0 = 1-λμLq = λ2(μ*(μ-λ))L = Lq + λμWq = LqλW = Wq + 1μPw =…

Answered: The Friendly Neighbor Grocery Store has…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.5: Analytic Steady-state Queueing Models

Problem 30P

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