Question

17.6-9. The Friendly Neighbor Grocery Store has a single check- out stand with a full-time cashier. Customers arrive randomly at the stand at a mean rate of 30 per hour. The service-time distribu- tion is exponential, with a mean of 1.5 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 hiring another person to help the cashier by bagging the groceries. This help would re- duce the expected time required to process a customer to I minute 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 the checkout stand down be- low 25 percent. She also would like to have no more than 5 per- cent of the customers needing to wait at least 5 minutes before be- ginning service, or at least 7 minutes before finishing service. (a) Use the formulas for the M/M/I model to calculate L W. W L Pa. Pi, and P: for the current mode of operation. What is the probability of having more than two customers at the check out stand? T (b) Use the Excel template for this model to check your answers in part (a). Also find the probahility that the waiting time hefore beginning service exceeds 5 minutes, and the prob- ability that the waiting time before finishing service exceeds 7 minutes. (c) Repeat part (a) for the alternative being considered by the manager (d) Repeat part (h) for this altermative. (e) Which approach should the manager use to satisfy her criteria as closely as possible?

Answer 1

3 3