Barrer的一个排队模型的进一步研究

本文进一步研究Barrer的一个排队模型，首先证明该模型的主算子是dispecsive算子，然后将 此结果与已有结果结合得到核算子生成一个正压缩C0-半群，由此推出该模型存在唯一的概率态解，第三步证明0是此主算子的主因子算子的代数贡数为1的特征值，最后此结果与已有结果合并后得到该模型的时间依赖解强收敛于该模型的稳太解.

Further Resaearch of the Barrer＇s Queuing Model

In this paper, based on some other study results, we further study the Barrer＇s queuing model. First we prove that the operator corresponding to this model is a dispersive operator, second, by combining our resuhs with other resuhs we observe that the operator generates a positive contraction C0-semigroup and therefore we deduce that this model has a unique positive time-dependent solution that satisfies the probability condifion. Third, we prove that 0 is an eigenvalue of the ajoint poperator of this operator with algebraic muhiplicity one. Finally. by using this result and the other results we obtain the time--dependent solution of this model converging strongly to its steady--state solution.