In queueing theory, the research on gi / g / l queue have been continued for decades of years . by the end of last century, the integral representation of its transient distribution of the queue length has been obtained . in this integral representation, the integrated term can be determined recursively by a system of kolmogorov differential equation 在排队理论中,关于gi/g/1排队系统的研究,延续了几十年,直至上个世纪末,方得到了它的瞬时队长分布的积分表示,在这个积分表示中,其被积项可以由一组柯尔莫洛夫偏微分方程递归地确定。
We then consider the n policy m / g / 1 queueing model with two priorities . by using the supplementary variable method to analyze the state probability equations, we derive the generating function of queueing length distribution and the mean queue length in the buffer of the communications network . and through further discussing for the queue with various priorities, we derive the generating function of queueing length distribution and the stationary queueing length in queue models with various priorities 其次研究带有两个优先权的n策略mg1排队模型,利用补充变量法对状态概率方程组进行分析,得出了此排队系统队长分布母函数及通信网缓冲器中的平均队长,并对不同优先权队列的进一步讨论,得出了不同优先权队列的队长分布母函数及稳态队长。
We then consider the n policy m / g / 1 queueing model with two priorities . by using the supplementary variable method to analyze the state probability equations, we derive the generating function of queueing length distribution and the mean queue length in the buffer of the communications network . and through further discussing for the queue with various priorities, we derive the generating function of queueing length distribution and the stationary queueing length in queue models with various priorities 其次研究带有两个优先权的n策略mg1排队模型,利用补充变量法对状态概率方程组进行分析,得出了此排队系统队长分布母函数及通信网缓冲器中的平均队长,并对不同优先权队列的进一步讨论,得出了不同优先权队列的队长分布母函数及稳态队长。
We then consider the n policy m / g / 1 queueing model with two priorities . by using the supplementary variable method to analyze the state probability equations, we derive the generating function of queueing length distribution and the mean queue length in the buffer of the communications network . and through further discussing for the queue with various priorities, we derive the generating function of queueing length distribution and the stationary queueing length in queue models with various priorities 其次研究带有两个优先权的n策略mg1排队模型,利用补充变量法对状态概率方程组进行分析,得出了此排队系统队长分布母函数及通信网缓冲器中的平均队长,并对不同优先权队列的进一步讨论,得出了不同优先权队列的队长分布母函数及稳态队长。
We then consider the n policy m / g / 1 queueing model with two priorities . by using the supplementary variable method to analyze the state probability equations, we derive the generating function of queueing length distribution and the mean queue length in the buffer of the communications network . and through further discussing for the queue with various priorities, we derive the generating function of queueing length distribution and the stationary queueing length in queue models with various priorities 其次研究带有两个优先权的n策略mg1排队模型,利用补充变量法对状态概率方程组进行分析,得出了此排队系统队长分布母函数及通信网缓冲器中的平均队长,并对不同优先权队列的进一步讨论,得出了不同优先权队列的队长分布母函数及稳态队长。
The primary works and innovations of this paper include but not limited to : ( 1 ) considering the nonlinear, time-varying and uncertain characteristics of networks, a new active queue management ( aqm ) algorithm, i . e . nnpc-aqm was proposed based on predictive control theory, which requires less model accuracy . in order to realize fast control, a predictor was constructed using two-layer linear neural network to predict the future queue length, and a controller was composed using two layers of nonlinear neural network to optimize the next control volume, i . e . drop probability 本文研究的主要内容及创新点如下:(1)针对网络的非线性、时滞、不确定特点,结合预测控制理论提出一种新型主动队列管理(aqm)策略nnpc-aqm,该算法基于单值预测控制思想,为了实现快速控制,采用两层神经网络构造预测器,估计未来时刻队列长度;采用两层非线性神经网络组成控制器,实现对下一步丢弃概率的优化。
In this paper, the repairable queuing system with police is studied . some important queuing quantities and reliability quantities are in detail discussed as follows : ( 1 ) using the renewal process theory and the method of stochastic decomposition, both the transient and equilibrium distributions of the queue length from any state are discussed, and the recursion expression of the equilibrium distribution is given by furthermore, the generating function of equilibrium queuing length distribution is given by ( 2 ) the distribution of waiting time is discussed, and the mean waiting time is given by ( 3 ) the departure of the system is discussed, and the mean value of departure customers when is given by 具体如下:(1)利用更新过程理论和随机分解方法,讨论了从任意初始状态出发队长分布的瞬态解和稳态解,得到了队长平稳分布的递推公式:并进一步求得了系统的稳态队长分布的母函数(2)讨论了稳态等待时间分布,求得了平均等待时间:(3)讨论了系统的输出过程,求得了长期单位时间内离去顾客的平均数:(4)讨论了服务台的不可用度,得到了稳态不可用度:(5)讨论了内服务台平均故障次数,求得了长期单位时间内的平均故障次数
In this paper, the repairable queuing system with police is studied . some important queuing quantities and reliability quantities are in detail discussed as follows : ( 1 ) using the renewal process theory and the method of stochastic decomposition, both the transient and equilibrium distributions of the queue length from any state are discussed, and the recursion expression of the equilibrium distribution is given by furthermore, the generating function of equilibrium queuing length distribution is given by ( 2 ) the distribution of waiting time is discussed, and the mean waiting time is given by ( 3 ) the departure of the system is discussed, and the mean value of departure customers when is given by 具体如下:(1)利用更新过程理论和随机分解方法,讨论了从任意初始状态出发队长分布的瞬态解和稳态解,得到了队长平稳分布的递推公式:并进一步求得了系统的稳态队长分布的母函数(2)讨论了稳态等待时间分布,求得了平均等待时间:(3)讨论了系统的输出过程,求得了长期单位时间内离去顾客的平均数:(4)讨论了服务台的不可用度,得到了稳态不可用度:(5)讨论了内服务台平均故障次数,求得了长期单位时间内的平均故障次数
It is shown that the nonlinear characteristics change frequently with the slight variations of parameters, and the border collision results in remarkable oscillations of queue length and the parameter sensitivity to increase the end-to-end delay and reduce the link utilities, thus it is necessary to avoid sub-critical bifurcation as designing system parameters 研究结果表明,系统参数的微小变化会导致系统动力学特性的频繁改变;边界碰撞分岔导致队列长度的大幅度振荡,在增大端到端的时延抖动、降低链路利用率的同时,使得系统对参数表现出极端敏感性;在配置系统参数时,应尽量避免亚临界分岔的发生。