【作者】 刘书新；

【导师】 艾尼·吾甫尔；

【作者基本信息】 新疆大学 ， 应用数学， 2005， 硕士

【摘要】 带吸收状态的M/M/2排队系统在交通,服务行业等领域中有广泛应用。因此对其进行动态分析不但在理论上而且在实际中具有重要的意义。本文对该系统进行动态分析。首先用概率论的有关知识建立该排队系统的数学模型,第二步将该模型化成Banach空间中的抽象Cauchy问题,第三步运用C₀—半群理论证明该模型存在唯一的概率瞬态解,第四部通过研究该模型的主算子的谱特征得到该模型解的渐近性质。更多还原

【Abstract】 M/M/2 queueing system with absorbing state have been widely used in many fields such as transportation and service profession. So dynamic analysis of the system is important in view of theory and practice. In this thesis, we will do dynamic analysis for the system. First by using the probability theory we will establish the mathematical model of the system, second we will convert the model into an abstract Cauchy problem in a Banach space, third by using C₀-semigroup theory we will prove that the model has a unique positive time-dependent solution which satisfies probability condition, fourth through studying spectral properties of the operator corresponding to the model we will obtain asymptotic property of the solution of the model.更多还原