Journal of Industrial and Management Optimization (JIMO)

Stability of a cyclic polling system with an adaptive mechanism

Pages: 763 - 777, Volume 11, Issue 3, July 2015      doi:10.3934/jimo.2015.11.763

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Jeongsim Kim - Department of Mathematics Education, Chungbuk National University, 52 Naesudong-ro, Heungdeok-gu, Cheongju, Chungbuk, 361-763, South Korea (email)
Bara Kim - Department of Mathematics, Korea University, 145, Anam-ro, Seongbuk-gu, Seoul, 136-701, South Korea (email)

Abstract: We consider a single server cyclic polling system with multiple infinite-buffer queues where the server follows an adaptive mechanism: if a queue is empty at its polling moment the server will skip this queue in the next cycle. After being skipped, a queue is always visited in the next cycle. The service discipline in each queue is 1-limited. Using the fluid limit approach, we find the necessary and sufficient condition for the stability of such polling system.

Keywords:  Polling system, adaptive mechanism, stability, fluid model.
Mathematics Subject Classification:  Primary: 60K25; Secondary: 60J25.

Received: September 2013;      Revised: May 2014;      Available Online: October 2014.