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

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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.

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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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Authors and Affiliations

  1. School of Science, Yanshan University, Qinhuangdao, 066004, China

    Xiuli Xu & Huining Wang

Authors
  1. Xiuli Xu
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  2. Huining Wang
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Correspondence to Huining Wang.

Additional information

Xiuli Xu is a professor of statistics in the School of Science, Yanshan University, China. Her research interests are queueing theory, fluid model and its application. She has published many papers on these topics in the international journals, conference proceedings as well as book chapters.

Huining Wang is a master of statistics in the School of Science, Yanshan University, China. Her research interest is queueing theory.

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Xu, X., Wang, H. Analysis of Fluid Model Modulated by an M/PH/1 Working Vacation Queue. J. Syst. Sci. Syst. Eng. 28, 132–140 (2019). https://doi.org/10.1007/s11518-018-5396-2

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  • DOI: https://doi.org/10.1007/s11518-018-5396-2

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