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inria-00073634, version 1

## On Polling Systems where Servers wait for Customers

Larissa G. Afanassieva, Franck Delcoigne 1, Guy Fayolle () 1

N° RR-3058 (1996)

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.

• 1:  MEVAL (INRIA Rocquencourt)
• INRIA
• Domain : Computer Science/Other
• Keywords : NETWORK / POLLING / RANDOM WALK / RECURRENCE / TRANSIENCE / CENTRAL LIMIT THEOREM
• Internal note : RR-3058
• Comment : Projet MEVAL

• inria-00073634, version 1
• oai:hal.inria.fr:inria-00073634
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• Submitted on: Wednesday, 24 May 2006 13:23:06
• Updated on: Wednesday, 25 April 2007 12:45:26