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

(b) Suppose Marsha is replaced by an expresso vending machine that requires exactly 75 seconds for each customer to operate. Find

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(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.

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