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The Impact of Priority Policy in a Two-Queue Markovian Polling System with Multi-Class Priorities

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Queueing Theory and Network Applications (QTNA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10591))

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Abstract

In this paper, we consider a two-queue Markovian polling system attended by a single server. For this model, multiple-class customers with priorities are concerned in each queue. We first present the exact LST (Laplace-Stieltjes transformation) expressions and means of the waiting times of each type customers by utilizing the concept of delay-cycle. Furthermore, we prove that prioritizing customers with smaller mean service times could shorten the mean response time, especially in the heavy traffic regime. With the LSTs of waiting times, we also concentrate on the derivation of the exact asymptotics of the scaled delay in the heavy-traffic scenario. It is illustrated that the priority policy generates a mixture distribution of the limiting scaled delay in comparison with the non-priority policy. Lastly, simulations are used for validation of the limiting results and the impact of priority policy.

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Acknowledgements

This work is partially supported by the National Natural Science Foundation of China (11671404) and by the Fundamental Research Funds for the Central Universities (WUT:2017IVA069). The authors also gratefully acknowledge the helpful comments and suggestions of the reviewers.

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Authors and Affiliations

  1. School of Science, Wuhan University of Technology, Wuhan, 430070, China

    Yuqing Chu

  2. School of Mathematics and Statistics, Central South University, Changsha, 410083, China

    Zaiming Liu

Authors
  1. Yuqing Chu
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  2. Zaiming Liu
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Correspondence to Yuqing Chu .

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Editors and Affiliations

  1. Konan University, Kobe, Japan

    Wuyi Yue

  2. Yanshan University, Qinhuangdao, China

    Quan-Lin Li

  3. Yanshan University, Qinhuangdao, China

    Shunfu Jin

  4. Yanshan University, Qinhuangdao, China

    Zhanyou Ma

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Chu, Y., Liu, Z. (2017). The Impact of Priority Policy in a Two-Queue Markovian Polling System with Multi-Class Priorities. In: Yue, W., Li, QL., Jin, S., Ma, Z. (eds) Queueing Theory and Network Applications. QTNA 2017. Lecture Notes in Computer Science(), vol 10591. Springer, Cham. https://doi.org/10.1007/978-3-319-68520-5_17

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  • DOI: https://doi.org/10.1007/978-3-319-68520-5_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-68519-9

  • Online ISBN: 978-3-319-68520-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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