In this paper, we mainly study the M/G/l queuing system with multiple working vacation and vacation interruption. First, we convert the mathematical model corresponding to this system into an abstract Cauchy problem. Second, we prove that the operator corresponding this queuing model generates a positive contraction Co-semigroup T(t). Then we show that T(t) is isometric operator. Last, we conclude that this model has a unique nonnegative time-dependent solution.%主要研究工作休假和休假中止的M/G/1排队系统,首先将对应于此系统的数学模型转化为抽象Cauchy问题,其次证明对应于此排队模型的主算子生成正压缩C0半群T(t),然后证明T(t)是局部等距的,最后证明此模型存在唯一的非负时间依赖解.
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