附有不可靠服务台和无等待能力的M/G/1/1排队模型的进一步研究  

Further Research of An M/G/1/1 Queue with Unreliable Server and No Waiting Capacity

作　　者：阿力木·米吉提[1] 奥古丽江·艾尼 Alim MIJIT;Oghuljan AINI(Xinjiang Radio&TV University,Urumqi 830049,China;No.2 Middle School of Urumqi,Urumqi 830000,China)

机构地区：[1]新疆广播电视大学,新疆乌鲁木齐830049 [2]乌鲁木齐市第二中学,新疆乌鲁木齐830000

出　　处：《安徽师范大学学报（自然科学版）》2020年第5期415-423,共9页Journal of Anhui Normal University(Natural Science)

基　　金：国家开放大学课题项目(G18E4302Y).

摘　　要：本文考虑一个附有不可靠服务台和无等待能力的M/G/1/1排队系统模型.第一步指出此M/G/1/1排队系统的主算子生成一个正定压缩C0-半群T(t),并证明所生成的正定压缩C0-半群T(t)的拟紧性。接着推出虚轴上除了点0外的其他的全部点都属于此M/G/1/1排队模型所对应主算子的豫解集。最后通过上述结果得到该M/G/1/1排队系统模型的动态解强收敛到该M/G/1/1排队系统的稳态解。We consider an M/G/1/1 queueing model with unreliable server and no waiting capacity in this paper.Firstly we show that the underlying operator corresponding to the M/G/1/1 queueing model generates a positive contraction C 0-semigroup T(t)and verify that T(t)is a quasi-compact operator.Next,we derive that the imaginary axis points beside zero belongs to the corresponding operator s resolvent set.Thus,by these above results we conclude that the nonnegative time-dependent solution of the M/G/1/1 queueing system converges strongly to the steady-state solution of the system.

关 键 词：附有不可靠服务台和无等待能力的M/G/1/1排队系统 拟紧算子 豫解集 

分 类 号：O177.7[理学—数学]