Greg is making plans to open a new fast-food restaurant soon. He is estimating that customers will arrive randomly (a Poisson process) at a mean rate of 150 per hour during the busiest times of the day. He is planning to have three employees directly serving the customers. He now needs to make a decision about how to organize these employees.

Option 1 is to have three cash registers with one employee at each to take the orders and get the food and drinks. In this case, it is estimated that the average time to serve each customer would be 1 minute, and the distribution of service times is assumed to be exponential.

Option 2 is to have one cash register with the three employees working together to serve each customer. One would take the order, a second would get the food, and the third would get the drinks. Greg estimates that this would reduce the average time to serve each customer down to 20 seconds, with the same assumption of exponential service times.

Greg wants to choose the option that would provide the best service to his customers. However, since Option 1 has three cash registers, both options would serve the customers at a mean rate of 3 per minute when everybody is busy serving customers, so it is not clear which option is better.

T

(a) Use the main measures of performance—L, Lq, W, Wq—to compare the two options.

(b) Explain why these comparisons make sense intuitively.

(c) Which measure do you think would be most important to Greg’s customers? Why? Which option is better with respect to this measure?