Problem 3. 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 20 per hour. The service-time distribution is exponential, with a mean of 2.5 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 reduce the expected time required 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 the checkout stand down below 25 percent. She also would like to have no more than 5 percent of the customers needing to wait at least 5 minutes before beginning service, or at least 7 minutes before finishing service. Compute L, Lq, W, Wq, P0, P1, P2 for both the current mode of operation and the considered alternative.
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Chai S.
Pete's Market is a small local grocery store with only one checkout counter. Assume that shoppers arrive at the checkout lane according to a Poisson probability distribution, with an arrival rate of 18 customers per hour. The checkout service times follow an exponential probability distribution, with a service rate of 20 customers per hour. The manager's service goal is to limit the waiting time prior to beginning the checkout process to no more than five minutes. Also, the manager of Pete's Market wants to consider one of the following alternatives for improving service. Calculate the value of Wq for each alternative. a. Hire a second person to bag the groceries while the cash register operator is entering the cost data and collecting money from the customer. With this improved single-server operation, the service rate could be increased to 28 customers per hour. Round your answer to three decimal places. Do not round intermediate calculations. Wq = _______ minutes b. Hire a second person to operate a second checkout counter. The two-server operation would have a service rate of 20 customers per hour for each server. Note: Use P0 values from Table 11.4 to answer this question. Round your answer to three decimal places. Do not round intermediate calculations. Wq = ____________ minutes
Sri K.
Pete's Market is a small local grocery store with only one checkout counter. Assume that shoppers arrive at the checkout lane according to a Poisson probability distribution, with an arrival rate of 9 customers per hour. The checkout service times follow an exponential probability distribution, with a service rate of 15 customers per hour. The manager's service goal is to limit the waiting time prior to beginning the checkout process to no more than five minutes. Also, the manager of Pete's Market wants to consider one of the following alternatives for improving service. Calculate the value of Wq for each alternative. A. Hire a second person to bag the groceries while the cash register operator is entering the cost data and collecting money from the customer. With this improved single-server operation, the service rate could be increased to 19 customers per hour. Round your answer to three decimal places. Do not round intermediate calculations. Wq= B. Hire a second person to operate a second checkout counter. The two-server operation would have a service rate of 15 customers per hour for each server. Note: Use P0 values from Table 11.4 to answer this question. Round your answer to three decimal places. Do not round intermediate calculations. Wq=
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