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This paper considers a multi-server delay queue with finite additional waiting spaces and time-varying arrival rates, where the customers waiting in the buffer may abandon. These are features that arise naturally from the study of service systems such as call centers. Moreover, the authors assume rewards for successful service completions and cost rates for service resources. Finally, the paper considers service level agreements that constrain both the fractions callers who abandon and the ones who are blocked. Applying the theory of Lagrangian mechanics to the fluid limit of a related Markovian service network model, the authors obtain near profit-optimal staffing and provisioning schedules.
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