Queueing Systems

, Volume 83, Issue 1–2, pp 13–28 | Cite as

Asymptotic independence of servers’ activity in queueing systems with limited resource pooling

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Abstract

We consider multi-class multi-server queuing systems where a subset of servers, called a server pool, may collaborate in serving jobs of a given class. The pools of servers associated with different classes may overlap, so the sharing of server resources across classes is done via a dynamic allocation policy based on a fairness criterion. We consider an asymptotic regime where the total load increases proportionally with the system size. We show that under limited scaling in size of server pools the stationary distribution for activity of a fixed finite subset of servers has asymptotically a product form, which in turn implies a concentration result for server activity. In particular, we establish a clear connection between the scaling of server pools’ size and asymptotic independence. Further, these results are robust to the service requirement distribution of jobs. For large-scale cloud systems where heterogeneous pools of servers collaborate in serving jobs of diverse classes, a concentration in server activity indicates that the overall power and network capacity that need to be provisioned may be substantially lower than the worst case, thus reducing costs.

Keywords

Resource pooling Server activity Concentration  Mean field Insensitivity Power Network capacity 

Mathematics Subject Classification

60K25 
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Notes

Acknowledgments

The authors would like to thank François Baccelli and Sanjay Shakkottai at The University of Texas at Austin, and Xiaoqing Zhu at Cisco Systems for helpful discussions which motivated this work. Virag Shah would also like to thank Anurag Kumar at Indian Institute of Science for providing him with the first exposure to mean field models.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of ECEThe University of Texas at AustinAustinUSA

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