Question: At Martha's café, Martha herself operates the espresso machine. Customers arrive and demand cups of espresso according to a Poisson process with an average rate of 30 cups/h. The time it takes for Martha to make a cup of espresso is exponential with a mean of 75 s.
a. Determine L, Lq, W, and Wq for this queuing system. Show that the results are the same if you use the expressions available for M/M/1 and M/G/1 systems, respectively.
b. Assume that Martha buys a new fully automated espresso machine that makes a cup of espresso in exactly 75 seconds always. Determine L, Lq, W, and Wq under these new conditions.
c. Determine the ratio of the mean time in the queue, Lq, for the systems in (a) and (b). What are your conclusions?