# On Polling Systems where Servers wait for Customers

Abstract : In this paper, a particular polling system with $N$ queues and $V$ servers is analyzed. Whenever a server visits an empty queue, it waits for the next customer to come to this queue. A customer chooses his destination according to a routing matrix $P$. The model originates from specific problems arising in transportation networks. A global classification of the process describing the system is given under general assumptions. It is shown that this process can only be {\em transient} or {\em null recurrent}. In addition, a detailed classification of each node, together with limit laws (after proper time-scaling) are obtained. The method of analysis rel= ies on the central limit theorem and a coupling with a reference system in which transportation times are identically zero.
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Type de document :
Rapport
[Research Report] RR-3058, INRIA. 1996
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https://hal.inria.fr/inria-00073634
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Soumis le : mercredi 24 mai 2006 - 13:23:06
Dernière modification le : vendredi 25 mai 2018 - 12:02:05
Document(s) archivé(s) le : dimanche 4 avril 2010 - 23:52:42

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• HAL Id : inria-00073634, version 1

### Citation

Larissa G. Afanassieva, Franck Delcoigne, Guy Fayolle. On Polling Systems where Servers wait for Customers. [Research Report] RR-3058, INRIA. 1996. 〈inria-00073634〉

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