工作休假和休假中止的M/M/1排队系统时间依赖解的渐进性质  

Asymptotic Property of the Time-Dependent Solution of the M/M/1 Queueing System with Multiple Working Vacation and Vacation Interruption

作　　者：周学良 吴晓云[2] ZHOU Xue-liang;WU Xiao-yun(Department of Public Education,Xinjiang Industrial Vocational and Technical College,Urumqi 830022 China;School of Public Education,Bayingol Vocational and Technical College,Korla 841000,China)

机构地区：[1]新疆工业职业技术学院公共教学部,新疆乌鲁木齐830022 [2]新疆巴音郭楞职业技术学院公共教育学院,新疆库尔勒841000

出　　处：《数学的实践与认识》2018年第16期150-161,共12页Mathematics in Practice and Theory

摘　　要：研究工作休假和休假中止的M/M/1排队系统时间依赖解的渐近性质.通过研究该模型主算子的共轭算子的豫解集得到在虚轴上除了0点外其它所有点都属于该主算子的豫解集,并得到0是主算子及其共轭算子几何重数为1的特征值,由此推出当时刻t趋向于无穷时模型的时间依赖解收敛于其稳态解.The asymptotic property of the time-dependent solution corresponding to the M/M/1 queueing system with multiple working vacation and vacation interruption has been studied. Through studying the resolvent set of the adjoint operator of this operator the resolvent set of this operator has been obtained, all points on the imaginary axis except for zero belong to the resolvent set of this operator, and obtain that 0 is an eigenvalue of the operator and its adjoint operator with geometric multiplicity one, Thus we derive that the time-dependent solution of the queueing model converges strongly to its static solution as time tends to infinite.

关 键 词：工作休假和休假中止排队系统 共轭算子 C0-半群 稳态解 

分 类 号：O226[理学—运筹学与控制论]