Question: Consider a static admission control problem for M/M/1 system with (arrival rate ) < (service rate ). The system can control arrival rate by choosing

Consider a static admission control problem for M/M/1 system with (arrival rate ) < (service rate ). The system can control arrival rate by choosing a rejection probability p that is fixed over time. Every arriving customer will be allowed to enter the system with probability 1-p. There are two types of costs associated: (i) a rejection cost r (cost per rejection); and (ii) a holding-cost rate h (cost per unit time per customer in system). Formulate expected total cost per unit time Y(p), and find optimal rejection probability p * .

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