### Abstract

Original language | English |
---|---|

Pages (from-to) | 1072-1089 |

Number of pages | 18 |

Journal | Performance Evaluation |

Volume | 70 |

Issue number | 12 |

DOIs | |

Publication status | Published - 2013 |

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*Performance Evaluation*,

*70*(12), 1072-1089. https://doi.org/10.1016/j.peva.2013.09.005

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*Performance Evaluation*, vol. 70, no. 12, pp. 1072-1089. https://doi.org/10.1016/j.peva.2013.09.005

**Analysis of a two-layered network by means of the power-series algorithm.** / Dorsman, J.L.; Mei, van der, R.D.; Vlasiou, M.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Analysis of a two-layered network by means of the power-series algorithm

AU - Dorsman, J.L.

AU - Mei, van der, R.D.

AU - Vlasiou, M.

PY - 2013

Y1 - 2013

N2 - We consider an extension of the classical machine-repair model, also known as the computer-terminal model or time-sharing model. As opposed to the classical model, we assume that the machines, apart from receiving service from the repairman, supply service themselves to queues of products. The extended model can be viewed as a two-layered queueing network, of which the first layer consists of two separate queues of products. Each of these queues is served by its own machine. The marginal and joint queue length distributions of the first-layer queues are hard to analyse in an exact fashion. Therefore, we apply the power-series algorithm to this model to obtain the light-traffic behaviour of the queue lengths symbolically. This leads to two accurate approximations for the marginal mean queue length. The first approximation, based on the light-traffic behaviour, is in closed form. The second approximation is based on an interpolation between the light-traffic behaviour and heavy-traffic results for the mean queue length. The obtained approximations are shown to work well for arbitrary loaded systems. The proposed numerical algorithm and approximations may prove to be very useful for system design and optimisation purposes in application areas such as manufacturing, computer systems and telecommunications. Keywords: Layered queueing networks; Light-traffic behaviour; Machine-repair model; Queue-length approximations

AB - We consider an extension of the classical machine-repair model, also known as the computer-terminal model or time-sharing model. As opposed to the classical model, we assume that the machines, apart from receiving service from the repairman, supply service themselves to queues of products. The extended model can be viewed as a two-layered queueing network, of which the first layer consists of two separate queues of products. Each of these queues is served by its own machine. The marginal and joint queue length distributions of the first-layer queues are hard to analyse in an exact fashion. Therefore, we apply the power-series algorithm to this model to obtain the light-traffic behaviour of the queue lengths symbolically. This leads to two accurate approximations for the marginal mean queue length. The first approximation, based on the light-traffic behaviour, is in closed form. The second approximation is based on an interpolation between the light-traffic behaviour and heavy-traffic results for the mean queue length. The obtained approximations are shown to work well for arbitrary loaded systems. The proposed numerical algorithm and approximations may prove to be very useful for system design and optimisation purposes in application areas such as manufacturing, computer systems and telecommunications. Keywords: Layered queueing networks; Light-traffic behaviour; Machine-repair model; Queue-length approximations

U2 - 10.1016/j.peva.2013.09.005

DO - 10.1016/j.peva.2013.09.005

M3 - Article

VL - 70

SP - 1072

EP - 1089

JO - Performance Evaluation

JF - Performance Evaluation

SN - 0166-5316

IS - 12

ER -