【作者】 田瑞玲；

【导师】 岳德权；

【作者基本信息】 燕山大学 ， 运筹学与控制论， 2006， 硕士

【摘要】 随着通讯与计算机技术的迅猛发展，各种各样复杂的排队系统也随之不断地出现。尤其是带有止步、状态相依和休假等类型的排队系统模型，在制造系统、计算机系统与通信网络等领域中有着广泛的应用，具有重要的实际意义。论文研究了带有止步、状态相依、超指数服务和多重休假的三个排队模型。这些模型是已有文献中相关模型的推广。首先，研究了等待空间有限的带有止步和状态相依的M／H_k／1／L排队系统。通过将转移率矩阵写成分块矩阵的形式，给出了系统稳态概率的非常简便的迭代计算公式，这些迭代公式过程简洁，计算量小。此外，建立了费用模型，通过数值方法分析了系统各参数对最优临界值和最优费用的影响。其次，研究了系统等待空间无限的带有止步和状态相依的M／H_k／1排队系统。通过拟生灭过程和矩阵几何解，给出了系统的平衡条件和稳态概率的矩阵几何解。在一般情况下，给出了率阵R的简便的迭代计算程序；在特殊情况下，得到了率阵R的精确表达式。此外，还给出了系统的一些性能指标的精确计算公式。最后，研究了等待空间无限的带有止步和N-策略的M／H_k／1多重休假排队系统。利用拟生灭过程和矩阵几何解法给出了系统的平衡条件和系统稳态概率的矩阵几何解。在一般情况下，给出了率阵R的简便的迭代计算程序；在特殊情况下，得到了率阵R的精确表达式。此外，还给出了系统的一些性能指标的精确计算公式。在此基础上，建立了系统的费用模型，并进行了数值分析。更多还原

【Abstract】 With the quick development of the communication systems and computer techniques, there are many kinds of complicated queuing systems. The queuing systems are widely applied in the manufacture system, computer system and communication network, especially those with balking, state-dependent and vacations, so they have more practical significance.In this paper, we mainly analyze three queuing systems with balking, state-dependent, hyper-exponential service and multiple vacations. They are expansions of other models in the documents. The main result of this paper has three parts.Firstly, we investigate a finite waiting room M/H_k/1/L queuing system with balking and state-dependent. By writing the transition rate matrix as block matrix, we get the very simple iterative computation formula of the steady-state probabilities, which process is succinct and computation load is small. In addition, we established the cost model, and analyze the influence of the parameters of the system to the optimal cost and critical value.Secondly, we investigate an infinite M/H_k/1 queuing system with balking and state-dependent. By the quasi-birth-death process and the matrix geometric solution, we obtain the equilibrium condition of the system and the steady-state probability distribution. In ordinary situation, we get the iterative computation formula of matrix R, and also get the explicit expression of matrix R in special situation. In addition, we get some explicit computation formula of performance measures of the system.Finally, we deal with an infinite waiting room M/H_k/1 queuing system with balking, N-policy and multiple vacations. By using the quasi-birth-death process and the matrix geometric solution, we obtain the equilibrium condition of the system and the steady-state probability distribution. In ordinary situation, we get the iterative computation formula of matrix R, and also get the explicit expression of matrix R in special situation. In addition, we get the explicit expression of system performance measures and develop a cost model, the numerical analysis is also presented.更多还原