A small baqala has a single checkout 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 minutes. The baqala owner would like to improve the performance of its store by setting the following goals:

• to have less than 25 percent of the time that there are more than two customers at the checkout stand.

To achieve the goals, the baqala owner is considering the alternative of hiring another person to help the cashier by bagging the groceries (because there is no room for a second checkout stand). This helper would reduce the expected time required to process a customer to 1.5 minutes, but the distribution still would be exponential.

1. [5 Marks] Show the various queuing characteristics of such baqala, before and after hiring a helper (Wq, W, L, Lq, P0, P1, and P2)
2. [1 Marks] Can the baqala owner achieve the goals upon hiring a helper?

ANSWER