Optimal Control for an MX/G/1/N + 1 Queue with Two Service Modes

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 246)

Abstract

A finite-buffer queueing model is considered with batch Poisson input and controllable service rate. A batch that upon arrival does not fit in the unoccupied places of the buffer is partially rejected. A decision to change the service mode can be made at service completion epochs only, and vacation (switch-over) times are involved in preparing the new mode. During a switch-over time, service is disabled. For the control of this model, three optimization criteria are considered: the average number of jobs in the buffer, the fraction of lost jobs, and the fraction of batches not fully accepted. Using Markov decision theory, the optimal switching policy can be determined for any of these criteria by the value-iteration algorithm. In the calculation of the expected one-step costs and the transition probabilities, an essential role is played by the discrete fast Fourier transform.

Keywords

Finite-buffer model Value iteration Fast Fourier transform 

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Copyright information

© Springer India 2014

Authors and Affiliations

  1. 1.Department of EconometricsVrije UniversiteitAmsterdamThe Netherlands

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