工作休假的流体故障排队的优化策略分析  

Analysis of the Optimization Strategy for a Fluid Queue with Working Vacations and Breakdowns

作　　者：张怡通 徐秀丽[3] ZHANG YITONG;XU XIULI(School of Economics and Management,Yanshan University,Qinhuangdao 066004,China;School of Science,Tianjin University of Commerce,Tianjin 300134,China;School of Science,Yanshan University,Qinhuangdao 066004,China)

机构地区：[1]燕山大学经济管理学院,秦皇岛066004 [2]天津商业大学理学院,天津300134 [3]燕山大学理学院,秦皇岛066004

出　　处：《应用数学学报》2025年第2期153-183,共31页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(批准号:62171143);河北省自然科学基金(批准号:G2024203008)资助项目。

摘　　要：本文在完全可见情形下对带有故障维修和工作休假的流体排队模型进行均衡策略研究,其中缓冲器在忙期,工作休假期和故障维修期三种状态之间交替运行.运用更新过程理论和常微分方程组的标准型理论揭示了流体水平的纳什均衡行为规律和稳态概率分布,进而利用经典的拉普拉斯变换导出稳态下缓冲器的平均流体水平.基于经济学和效用原理构建线性社会收益函数,通过数值分析找到全局最优止步阈值下社会福利的极值.考虑以流体全局最优止步阈值和入场单价为联合决策变量构建入场费收益模型,研究全局最优止步阈值对最大入场费收益的影响.结合认知无线网络信息传输过程中的节点失效和节点半休眠的特点,研究相应的参数优化策略和社会收益问题,对于提升认知无线网络的安全传输性能至关重要,仿真结果可为无线网络资源的优化配置提供理论支撑.This paper studies the equilibrium strategy of a fluid queue with breakdowns and working vacations in the fully observable case,where the buffer switches alternately in the busy period,working vacation period,and fault maintenance period.Based on the renewal process and the standard theory of linear ordinary differential equations,the Nash equilibrium behavior of the fluid and the steady-state probability distribution are obtained,then the expected buffer content can be derived by using the classical Laplace-Stieltjes Transform(LST)method.Based on the economics and utility theory,the expected social benefit function is constructed reasonably and the global balking thresholds that maximize the social welfare can be obtained by some numerical examples.The admission fee revenue model can be constructed with the globally optimal thresholds and admission fees as joint decision variables,and the effect of the global optimal thresholds on the maximal admission fee revenue can be illustrated.The parameter optimization strategies and social benefit problems are crucial for improving the secure transmission performance of cognitive wireless networks,where the nodes fail and become semi-dormant.Simulation results can provide a theoretical basis for the optimal allocation of limited wireless network resources.

关 键 词：流体排队 故障可修 工作休假 止步策略 入场费用 

分 类 号：O226[理学—运筹学与控制论]