附有不可靠服务台和无等待能力的M/G/1/1排队模型时间依赖解的渐近性分析(英文)

Asymptotic Analysis of the Time-Dependent Solution of the M/G/1/1 Queue with Unreliable Server and No Waiting Capacity

本文研究附有不可靠服务台和无等待能力的M/G/1/1排队模型时间依赖解的渐近行为.首先利用强连续算子半群理论证明此排队系统模型正时间依赖解的存在唯一性.然后通过研究该模型相应主算子的谱,分别得到0是其主算子及其共轭算子的几何重数为1的特征值与虚轴上除了0外其他所有点都属于该模型主算子的豫解集.最后将上述结果结合在一起推出该模型的时间依赖解强收敛于其稳态解.

In this paper, we study the asymptotic behavior of the time-dependent solution of the M/G/1/1 queue with unreliable server and no waiting capacity. First, by using the strong continuous semigroup theory, we prove the existence and uniqueness of the nonnegative time-dependent solution of the system model. Next, by studying spectral properties of the operator corresponding to the system model, we obtain that zero is an eigenvalue of the operator and its adjoint operator with geometric multiplicity one and all points on the imaginary axis except zero belong to the resolvent set of the operator. Thus,by combining the above results, we deduce that the time-dependent solution of the system model converges strongly to its steady state solution.