Optimal Control of a Single-Server Queue with Balking and Reneging

Joseph D. Blackburn

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Advanced Queuing Theory Analysis Optimization and Search Problems Age of Information Optimization

Abstract

We consider the problem of controlling a single-server queue by turning the server on and off. In addition to a Poisson arrival process and general service-time distribution, provisions for balking and reneging are included in the models, yielding a variety of applications. Stationary optimal policies which maximize expected discounted reward over an infinite horizon are shown to have a simple critical-number characterization. Algorithms for computing the critical numbers are described.

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1968Optimal Operating Policies for M / G /1 Queuing Systems 1963Some Queuing Problems with Balking and Reneging. I 1963Elements of Queueing Theory: With Applications.1971Characterization and Computation of Optimal Policies for Operating an M/G/1 Queuing System with Removable Server 1969Optimal Average-Cost Policy for a Queue with Start-Up and Shut-Down Costs 1957Queuing with Impatient Customers and Indifferent Clerks

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1974Optimal Pricing for an Unbounded Queue 1976Optimal control of batch service queues with switching costs

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