17.7-4. Marsha operates an expresso stand. Customers arrive ac-cording to a Pois

Question

17.7-4. Marsha operates an expresso stand. Customers arrive ac-cording to a Poisson process at a mean rate of 25 per hour. The time needed by Marsha to serve a customer has an exponential distribution with a mean of 90 seconds. (a) Use the M/G/I model to find L,Lq, W, and Wq. (b) Suppose Marsha is replaced by an expresso vending machine that requires exactly 90 seconds for each customer to operate. Find L, Lq , W, and W4. (c) What is the ratio of L, in part (b) to Lq in part (a)? T (d) Use trial and error with the Excel template for the M/G/l model to see approximately how much Marsha would need to reduce her expected service time to achieve the same Lq

Explanation / Answer

SOLUTION:

? = 25/hour

? = 60 / 90 *.60 = 40 customers/ hour

TN exponential (u)

(T) = 1 / ?^2 = 1 / 40^2 = ?^2           

A)

P = ? / ? = 25 /40 = 0.625

P0 = 1

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