### Abstract

Original language | English |
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Title of host publication | Proceedings of the 2nd International Conference on Operations Research and Enterprise Systems (ICORES 2013, Barcelona, Spain, February 16-18, 2013) |

Publisher | INSTICC Press |

Pages | 14-23 |

ISBN (Print) | 978-989856540-2 |

Publication status | Published - 2013 |

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### Cite this

*Proceedings of the 2nd International Conference on Operations Research and Enterprise Systems (ICORES 2013, Barcelona, Spain, February 16-18, 2013)*(pp. 14-23). INSTICC Press.

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*Proceedings of the 2nd International Conference on Operations Research and Enterprise Systems (ICORES 2013, Barcelona, Spain, February 16-18, 2013).*INSTICC Press, pp. 14-23.

**Cyclic-type polling models with preparation times.** / Perel, N.; Dorsman, J.L.; Vlasiou, M.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - Cyclic-type polling models with preparation times

AU - Perel, N.

AU - Dorsman, J.L.

AU - Vlasiou, M.

PY - 2013

Y1 - 2013

N2 - We consider a system consisting of a server serving in sequence a fixed number of stations. At each station there is an infinite queue of customers that have to undergo a preparation phase before being served. This model is connected to layered queuing networks, to an extension of polling systems, and surprisingly to random graphs. We are interested in the waiting time of the server. The waiting time of the server satisfies a Lindley-type equation of a non-standard form. We give a sufficient condition for the existence of a limiting waiting time distribution in the general case, and assuming preparation times are exponentially distributed, we describe in depth the resulting Markov chain. We provide detailed computations for a special case and extensive numerical results investigating the effect of the system's parameters to the performance of the server.

AB - We consider a system consisting of a server serving in sequence a fixed number of stations. At each station there is an infinite queue of customers that have to undergo a preparation phase before being served. This model is connected to layered queuing networks, to an extension of polling systems, and surprisingly to random graphs. We are interested in the waiting time of the server. The waiting time of the server satisfies a Lindley-type equation of a non-standard form. We give a sufficient condition for the existence of a limiting waiting time distribution in the general case, and assuming preparation times are exponentially distributed, we describe in depth the resulting Markov chain. We provide detailed computations for a special case and extensive numerical results investigating the effect of the system's parameters to the performance of the server.

M3 - Conference contribution

SN - 978-989856540-2

SP - 14

EP - 23

BT - Proceedings of the 2nd International Conference on Operations Research and Enterprise Systems (ICORES 2013, Barcelona, Spain, February 16-18, 2013)

PB - INSTICC Press

ER -