Marsha operates an expresso stand. Customers arrive according to a Poisson process 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 M/G/1 model to find L, Lq, W, and Wq.
(b) Suppose Marsha is replaced by an expresso vending machine that requires exactly 75 seconds for each customer to operate. Find L, Lq, W, and Wq.
(c) What is the ratio of Lq in part (b) to Lq in part (a)?
(d) Use trial and error with the Excel template for the M/G/1 model to see approximately how much Marsha would need to reduce her expected service time to achieve the same Lq as with the expresso vending machine.