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The Spectral Gap for quasi-birth and death processes

Acta Mathematica Sinica,English Series 2012年第5期28卷 1075-1090页

作者： Yong Hua MAO Liang Hui XIA School of Mathematical Sciences LMCSMinistry of EducationBeijing Normal University Department of Mathematics Ji'nan University

For a reversible quasi-birth and death process, we generalize and refine the decomposition method, by constructing a birth-death process and a sequence of restriction processes. The spectral gap for the quasi-birth and death process is estimated in terms of the spectral gaps for these processes, and in some special cases, the estimation is sharp. With the aid of the symmetrization procedure, the result is also applied to two queueing models： M/M/1 in random environment and MIMIc with synchronous vacation.

关键词： quasi-birth and death process spectral gap birth-death process M/M/1 in random environment MIMIc with synchronous vacation

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Ergodicity of quasi-birth and death processes(Ⅰ)

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Acta Mathematica Sinica,English Series 2007年第2期23卷 201-208页

作者： Zhen Ting HOU Xiao Hua LI School of Mathematics Central South University School of science Beijing University of Posts and Telecommunications

quasi-birth and death processes with block tridiagonal matrices find many applications in various areas. Neuts gave the necessary and sufficient conditions for the ordinary ergodicity and found an expression of the stationary distribution for a class of quasi-birth and death processes. In this paper we obtain the explicit necessary and sufficient conditions for/-ergodicity and geometric ergodicity for the class of quasi-birth and death processes, and prove that they are not strongly ergodic. Keywords ergodicity, quasi-birth and death process.

关键词： ergodicity quasi-birth and death process Markov chain matrix geometric solutions

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Analysis on D2D Heterogeneous Networks with State-Dependent Priority Traffic

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Computers, Materials & Continua 2023年第2期74卷 2981-2998页

作者： Guangjun Liang Jianfang Xin Linging Xia Xueli Ni Yi Cao Department of Computer Information and Cyber Security Jiangsu Police InstituteNanjingChina National and Local Joint Engineering Laboratory of Radio Frequency Integration and Microassembly Technology Nanjing University of Posts and TelecommunicationsNanjingChina School of Intelligent Engineering Nanjing Institute of Railway TechnologyNanjingChina Jiangsu Province Electronic Data Forensics and Analysis Engineering Research Center NanjingChina Department of Electrical and Computer Engineering University of WindsorWindsorONN9B 3P4Canada

In this work,we consider the performance analysis of state dependent priority traffic and scheduling in device to device(D2D)heterogeneous *** are two priority transmission types of data in wireless communication,such as video or telephone,which always meet the requirements of high priority(HP)data transmission *** there is a large amount of low priority(LP)data,there will be a large amount of LP data that cannot be *** situation will cause excessive delay of LP data and packet dropping *** order to solve this problem,the data transmission process of high priority queue and low priority queue is *** the priority jump strategy to the priority queuing model,the queuing process with two priority data is modeled as a two-dimensionalMarkov chain.A state dependent priority jump queuing strategy is proposed,which can improve the discarding performance of low priority *** quasi birth and death process method(QBD)and fixed point iterationmethod are used to solve the causality,and the steady-state probability distribution is further ***,performance parameters such as average queue length,average throughput,average delay and packet dropping probability for both high and low priority data can be *** simulation results verify the correctness of the theoretical ***,the proposed priority jump queuing strategy can significantly improve the drop performance of low-priority data.

关键词： Stochastic geometry queuing theory D2D heterogeneous networks quasi-birth and death process

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