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

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.