cc 16(10): e1

Research Article

Critically loaded k-limited polling systems

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  • @ARTICLE{10.4108/eai.14-12-2015.2262578,
        author={Marko Boon and Erik Winands},
        title={Critically loaded k-limited polling systems},
        journal={EAI Endorsed Transactions on Collaborative Computing},
        keywords={polling model, k-limited, heavy traffic},
  • Marko Boon
    Erik Winands
    Year: 2016
    Critically loaded k-limited polling systems
    DOI: 10.4108/eai.14-12-2015.2262578
Marko Boon1,*, Erik Winands2
  • 1: Eindhoven University of Technology
  • 2: University of Amsterdam
*Contact email:


We consider a two-queue polling model with switch-over times and $k$-limited service (serve at most $k_i$ customers during one visit period to queue $i$) in each queue. The major benefit of the $k$-limited service discipline is that it - besides bounding the cycle time - effectuates prioritization by assigning different service limits to different queues. System performance is studied in the heavy-traffic regime, in which one of the queues becomes critically loaded with the other queue remaining stable. By using a singular-perturbation technique, we rigorously prove heavy-traffic limits for the joint queue-length distribution. Moreover, it is observed that an interchange exists among the first two moments in service and switch-over times such that the HT limits remain unchanged. Not only do the rigorously proven results readily carry over to $N$($\geq2$) queue polling systems, but one can also easily relax the distributional assumptions. The results and insights of this note prove their worth in the performance analysis of Wireless Personal Area Networks (WPAN) and mobile networks, where different users compete for access to the shared scarce resources.