Marsha operates an espresso stand. Customers arrive randomly at a mean rate of 30 per hour. The time needed by Marsha to serve a customer has an exponential distribution with a mean of 75 seconds.
a. Use the Excel template for the M/G/ 1 model to find L, Lq, W, and Wq.
b. Suppose Marsha is replaced by an espresso vending machine that requires exactly 75 seconds to operate for each customer. Find L, Lq, W, and Wq.
c. What is the ratio of L q in part b to Lq in part a?
d. Use trial and error with the template to see approximately how much Marsha would need to reduce her expected service time to achieve the same L q as with the espresso vending machine.
e. Use the template to generate a data table that gives the value of Lq when Marsha is serving with the following values (in seconds) for her expected service time: 75, 70, 65, 64, 63, 62, 61, 60?