### Abstract

Original language | English |
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Place of Publication | Eindhoven |

Publisher | Eurandom |

Number of pages | 24 |

Publication status | Published - 2012 |

### Publication series

Name | Report Eurandom |
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Volume | 2012020 |

ISSN (Print) | 1389-2355 |

### Fingerprint

### Cite this

*Dynamic server assignment in an extended machine-repair model*. (Report Eurandom; Vol. 2012020). Eindhoven: Eurandom.

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*Dynamic server assignment in an extended machine-repair model*. Report Eurandom, vol. 2012020, Eurandom, Eindhoven.

**Dynamic server assignment in an extended machine-repair model.** / Dorsman, J.L.; Bhulai, S.; Vlasiou, M.

Research output: Book/Report › Report › Academic

TY - BOOK

T1 - Dynamic server assignment in an extended machine-repair model

AU - Dorsman, J.L.

AU - Bhulai, S.

AU - Vlasiou, M.

PY - 2012

Y1 - 2012

N2 - We consider an extension of the classical machine-repair problem. The machines, apart from receiving service from a single repairman, now also supply service themselves to queues of products. The extended model can be viewed as a two-layered queueing network, in which the queues of products in the ¿rst layer are generally correlated, due to the fact that the machines have to share the repairman’s capacity in the second layer. We are concerned with the dynamic control problem how the repairman should allocate his capacity to the machines at any point in time so that the long-term average (weighted) sum of the queue lengths of the ¿rst-layer queues is minimised. Since the optimal policy for the repairman cannot be found analytically due to the correlations in the queue lengths, we propose a near-optimal policy. We do this by combining intuition and results from queueing theory with techniques from Markov decision theory. Speci¿cally, we study the relative value functions for several policies for which the model can be decomposed in less complicated subsystems, and we combine the results with the classical one-step policy improvement algorithm. The resulting policy is easy to apply, scalable in the number of machines and is shown to be highly accurate over a wide range of parameter settings.

AB - We consider an extension of the classical machine-repair problem. The machines, apart from receiving service from a single repairman, now also supply service themselves to queues of products. The extended model can be viewed as a two-layered queueing network, in which the queues of products in the ¿rst layer are generally correlated, due to the fact that the machines have to share the repairman’s capacity in the second layer. We are concerned with the dynamic control problem how the repairman should allocate his capacity to the machines at any point in time so that the long-term average (weighted) sum of the queue lengths of the ¿rst-layer queues is minimised. Since the optimal policy for the repairman cannot be found analytically due to the correlations in the queue lengths, we propose a near-optimal policy. We do this by combining intuition and results from queueing theory with techniques from Markov decision theory. Speci¿cally, we study the relative value functions for several policies for which the model can be decomposed in less complicated subsystems, and we combine the results with the classical one-step policy improvement algorithm. The resulting policy is easy to apply, scalable in the number of machines and is shown to be highly accurate over a wide range of parameter settings.

M3 - Report

T3 - Report Eurandom

BT - Dynamic server assignment in an extended machine-repair model

PB - Eurandom

CY - Eindhoven

ER -