Question: Consider an (M / M / 1 / N) queue whose arrival and service rates are equal. Suppose that customers who join the queue receive

Consider an $M / M / 1 / N$ queue whose arrival and service rates are equal. Suppose that customers who join the queue receive a reward $R$ at the end of service, but pay at a rate of $C$ per unit time while they are waiting. Find inequalities that characterize the optimal waiting room size $N$ that maximizes the long-run expected profit per customer, per unit time:

AR lim P[X,

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