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# 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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Cited literature [1 references]

https://hal.inria.fr/inria-00073634
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Submitted on : Wednesday, May 24, 2006 - 1:23:06 PM
Last modification on : Friday, February 4, 2022 - 3:08:10 AM
Long-term archiving on: : Sunday, April 4, 2010 - 11:52:42 PM

### Identifiers

• 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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