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Optimal control of a queue under a quality-of-service constraint with bounded and unbounded rates. (English) Zbl 1525.90120

Summary: We consider a simple Markovian queue with Poisson arrivals and exponential service times for jobs. The controller chooses state-dependent service rates from an action space. The queue has a finite buffer, and when full, new jobs get rejected. The controller’s objective is to choose optimal service rates that meet a quality-of-service constraint. We solve this problem analytically and compute it numerically under two cases: When the action space is unbounded and when it is bounded.

MSC:

90B22 Queues and service in operations research
60K25 Queueing theory (aspects of probability theory)
90B18 Communication networks in operations research
90C40 Markov and semi-Markov decision processes
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