【作者】 赵晓华；

【导师】 田乃硕；

【作者基本信息】 燕山大学 ， 运筹学与控制论， 2009， 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、中途退出和工作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。论文研究了等待空间有限的带有止步、中途退出和多重工作休假的两个排队模型。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M/M/1/N多重工作休假排队系统。根据马尔可夫过程理论导出了稳态概率所满足的方程组,并通过将转移率矩阵写成分块矩阵的形式,求出了系统稳态概率的矩阵形式解,并给出了具体的算法。此外,还针对N=3的特殊情况,利用Matlab数学计算软件的符号计算功能,得到了稳态概率的明显表达式。最后通过数值方法分析了系统各参数对系统性能指标的影响。其次,研究了系统等待空间有限的带有止步和中途退出的M/M/1/N多重工作休假排队系统。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矩阵形式解。然后以N=3为例建立了一个以服务员正规忙期的服务率μb为控制变量的单位时间的稳态费用模型。由于费用函数的表达式非常复杂,难以求出最优服务率的明显表达式,所以采用数值方法计算最优服务率和单位时间最优费用。最后,通过费用模型的几个数值例子,分析了系统各参数对最优服务率、最优费用以及系统各个性能指标的影响。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, reneging and multiple working vacations, so they have more practical significance.In this paper, two finite buffer queuing systems with balking, reneging, and multiple working vacations are analyzed. They are expansions of other models in the documents. The main result of this paper has two parts.Firstly, we investigate a finite buffer M/M/1/N queuing system with multiple working vacations. First, we derive the steady-state equations by the Markov process method .By writing the transition rate matrix as block matrix, we get the matrix form solution of the steady-state probabilities and present a algorithm for calculating the steady-state probabilities. In addition, using the symbol function of Matlab, we get the explicit expression of the steady-state probabilities for the special case of N=3. Finally, we analyze the influence of the parameters of the system to the system performance measures .Secondly, we investigate a finite buffer M/M/1/N queuing system with balking, reneging and multiple working vacations. First, by writing the transition rate matrix as block matrix, we get the matrix form solution of the steady-state probabilities . In addition, we develop a steady-state cost model where the busy service rateμb is the control variable. However, the expression of the cost function is too complex to get the explicit expression of the optimal service rate, so we use the numerical method to get the optimal service rate and the optimal cost. Finally, we investigate the effect of the parameters of the system on the optimal service rate, the optimal cost and the system performance measures by several numerical examples.更多还原