Question: Consider an M/M/1/ queue for which = 1 and = 3. Every customer going through the system pays an amount $15, but costs

Consider an M/M/1/∞ queue for which λ = 1 and µ = 3. Every customer going through the system pays an amount $15, but costs the system $6 per unit time it spends in the system.

(a) What is the average profit rate of this system?

(b) A bright young OR analyst from a prestigious middle Atlantic state university tells management that the profit can be increased by shutting off the queue at a certain point, that is, by preventing customers from entering whenever the queue gets to a certain size. Do you agree, and if so, what is the optimal point at which to prevent arrivals from joining?

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