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Analysis of Fluid Model Modulated by an M/PH/1 Working Vacation Queue

  • Xiuli Xu
  • Huining WangEmail author
Article

Abstract

We propose a fluid model driven by the queue length process of a working vacation queue with PH service distribution, which can be applied to the Ad Hoc network with every data group. We obtain the stationary distribution of the queue length in driving process based on a quasi-birth-and-death process. Then, we analyze the fluid model, and derive the differential equations satisfied by the stationary joint distribution of the fluid queue based on the balance equation. Moreover, we obtain some performance indices, such as, the average throughput, server utilization and the mean buffer content. These indices are relevant to pack transmission in the network, and they can be obtained by using the Laplace Transform (LT) and the Laplace-Stieltjes Transform (LST). Finally, some numerical examples have been discussed with respect to the effect of several parameters on the system performance indices.

Keywords

Fluid model M/PH/1 queue average throughput server utilization buffer content Ad Hoc network 

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Notes

Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grant No.11201408, and was supported in part by MEXT, Japan. The authors would also like to thank anonymous reviewers for their detailed and constructive comments and suggestions.

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Copyright information

© Systems Engineering Society of China and Springer-Verlag GmbH Germany 2019

Authors and Affiliations

  1. 1.School of ScienceYanshan UniversityQinhuangdaoChina

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