N-策略M/G/1排队系统的推广研究

【作者】 刘晓燕；

【导师】 唐应辉；

【作者基本信息】 电子科技大学 ， 运筹学与控制论， 2008， 硕士

【摘要】 目前对于可修排队系统和休假排队系统的研究,大多数文献都假设满足休假或可修其中一个方面,并且已得到了深入的研究,而把这两者结合起来进行研究的文献还比较少。在可修系统的研究当中,一般都假设修理设备是完全可靠的,但在实践中经常会碰到修理设备在修理故障部件时其本身也可能发生失效,这时只有将修理设备更换后它才能继续修理故障部件。在本文中首先考虑的是修理设备可更换的N-策略M/G/1可修排队系统。首先,研究了队长的瞬态和稳态性质。通过引进“服务员忙期”和使用全概率分解技术,导出了在任意时刻t瞬态队长分布的拉普拉斯变换的递推表达式和稳态队长分布的递推表达式,以及平稳队长的随机分解。其次,考虑的是该系统的可靠性指标。通过引入服务台的“广义忙期”和修理设备的“广义忙期”,采用随机分解法,得到了服务台以及修理设备的一些重要的可靠性指标。另外,系统的输入率与服务员是否在岗是有关的,即在服务员假期中到达系统的顾客不一定要进入系统。基于此,在本文中又考虑了另一类N-策略M/G/1排队系统,其中在服务员休假中到达的顾客以概率p(0＜p≤1)进入系统。采用一种较简单的分析方法,得到了队长瞬态分布的拉普拉斯变换的递推表达式和稳态分布的递推表达式。更多还原

【Abstract】 The research about one aspect of the repairable queueing system and the vacation system has been done by many references and obtained in-depth research. But there has been little of the research about the union of them. During the research of the repairable system, it is usually assumed that the repair facility is reliable completely. But it is usual that the repair facility may be invalid during repairing trouble unit in practice. It will not keep on repairing a trouble unit until the repair facility has been changed.In this paper we consider the M/G/1 repairable queuing system with N-policy and a replaceable repair facility. First, we study the transient and equilibrium properties of the queue length. By introducing the server busy period and using the total probability decomposition technique we derive the recursion expression of the L-transformation of the transient queue length distribution at any time t, and also the expressions of the distribution and stochastic decomposition of the queue length at a random point in equilibrium. Especially we obtain some corresponding results under some special cases. Second, we consider some important reliability indexes of this system. The generalized busy periods of the service station and repair facility are defined, and the stochastic decomposition is provided to obtain some important reliability indexes of the service station and the repair facility.In addition, the import-rate of the system is usually related with whether the server is on guard or not. Customers who arrived the system did not always enter the system during the vacation of server. Based on the above, in this paper we consider another M/G/1 queue with N-policy in which the customers who arrive during server vacation enter the system with probability p (0 < p≤1). By using a simple method, the recursion expression of the Laplace transform of the transient queue-length distribution and equilibrium queue-length distribution are obtained.更多还原