Question: Consider a static service rate control problem for M/M/ system with arrival rate . The system can choose a service rate that is common to

Consider a static service rate control problem for M/M/ system with arrival rate . The system can choose a service rate that is common to all the servers and fixed over time. There are two types of costs associated: (i) a service-cost rate c (cost per unit time per unit service rate); and (ii) a holding-cost rate h (cost per unit time per customer in system). Note that the service-cost rate here is the cost rate for all servers together.

What is the optimal service rate * ?

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