单重工作休假M/M/c排队驱动的流体模型分析  

Analysis of the Fluid Model Driven by M/M/c Queue with Single Working Vacation

作　　者：李子坤 徐秀丽[1] 岳德权[1] Li Zikun;Xu Xiuli;Yue Dequan(School of Science,Yanshan University,Hebei Qinhuangdao 066000)

机构地区：[1]燕山大学理学院,河北秦皇岛066000

出　　处：《数学物理学报（A辑）》2021年第1期254-268,共15页Acta Mathematica Scientia

基　　金：国家自然科学基金(71971189);河北省自然科学基金(A2019203313);河北省高等学校科学研究重点项目(ZD2019079)。

摘　　要：该文在M/M/c排队驱动系统中加入工作休假策略,研究了单重工作休假多服务台排队驱动的流体模型.利用拟生灭过程和矩阵几何解法得到驱动系统稳态队长分布.构建净输入率结构,导出流体模型的稳态联合分布函数满足的的矩阵微分方程组,进而利用Laplace-Stieltjes变换(LST)方法得到稳态下缓冲器库存量的空库概率及均值表达式.最后,给出模型在多信道无线Mesh网下的应用,通过数值例子展示参数变化对系统性能指标的影响.In this paper,introducing working vacation strategy into an M/M/c queue,the fluid model driven by a multi-server queue with single working vacation is studied.Using quasi birth-and-death process and matrix-geometric method,the steady-state distribution of the queue length is obtained.The net input rate structure is constructed,and the matrix differential equations satisfied by the joint stationary distribution of the fluid model are derived.Furthermore,by using Laplace-Stieltjes Transform(LST)method,the probability of the empty buffer content and the mean of the buffer content in the stable case are obtained.Finally,the application of the model in multi-channel wireless Mesh network is presented,and the influence of parameter on system performance index is demonstrated in numerical examples.

关 键 词：流体模型 单重工作休假 库存量 无线MESH网 

分 类 号：O226[理学—运筹学与控制论]