成批到达GI/G/1排队系统的收敛问题
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摘要
GI／G／1排队系统是一种非常经典的排队系统模型,本文主要研究的是具有成批到达特性的GI／G／1系统的收敛问题。文章首先介绍了排队论的起源与马尔可夫骨架的相关知识。然后在此基础上给出了具有成批到达特性的GI／G／1排队系统队长的转移函数。最后研究了该系统的收敛性问题。
GI/G/1queuing system is a very classic queuing system model. This paper studies the convergence problem of GI/G/1system with batch arrival.Firstly,this paper introduces the origin of the queuing theory and the basic knowledge of Markov skeleton processes.Then we found the transition function of the batch arrival GI/G/1queuing system.Finally,we study the convergence problem of this system.
GI/G/1queuing system is a very classic queuing system model. This paper studies the convergence problem of GI/G/1system with batch arrival.Firstly,this paper introduces the origin of the queuing theory and the basic knowledge of Markov skeleton processes.Then we found the transition function of the batch arrival GI/G/1queuing system.Finally,we study the convergence problem of this system.
引文
[1]侯振挺,刘国欣.马尔可夫骨架过程及其应用.科学出版社.2005,1-13
[2]徐光辉.随机服务系统.科学出版社.1988
[3]孙荣恒,李建平.排队论基础.科学出版社.2002
[4]田乃硕,徐秀丽,马占友.离散时间排队论.科学出版社.2002
[5]刘晓红.马尔可夫骨架过程在两类GI／G／1排队系统中的应用：[硕士学位论文]。长沙：中南大学,2007.
[6]王益民.马尔可夫骨架过程在GI／G／1排队系统中的应用：[博士学位论文]。长沙：中南大学,2003.
[7]王梓坤.生灭过程与马尔可夫链,科学出版社,1980.
[8]华洪涛.成批到达带休假的排队系统：[硕士学位论文]。郑州：郑州大学,2011.
[9]徐光辉.GI／M／n的瞬时分布性质。应用数学学报,1965,15,91-120
[10]Finch,P.D.,On the queuing system GI/G/1,J.Aust.Math.Soc.,1961,2,217-228.
[11]Takacs,L.Delay distributions for simple trunk groups with recurrent input and exponential service times。Bell Syst.Tech.J.,1962,41,311-320.
[12]唐应辉,唐小我.排队论：基础与分析技术,科学出版社,2006：120-124.
[13]侯振挺,何宁卡.马氏骨架过程与一个排队系统的瞬时队长.铁道科学与工程学报,2004,02,107-110.
[14]Kendall,D.G.Some problem in the theory of queues.J.Roy.Statist.Soc.,B,1951,13:150-185.
[15]Hou Zhengting,Liu Guoxin.Markov Skeleton Process and Their Application.Boston:International Press,2005,92-124.
[16]Hou Zhengting.Markov Skeleton Process and Application to queuing systems.Acta,Mathematic Application Sinica, English Series,2002,18(4):537-552.
[17]Finch,P.D.,On the busy period in the queuing system GI/G/1,J.Aust.Math.So.,1961,2,217-228.
[18]Attahiru Sule Alfa.Discrete-time analysis of the GI/G/1 system with Bernoulli retrials:An alpporithmic approach, Springer.2006(01).
[19]Hou Zhengting,Li Min.The Transinet Behavior of the Length of GI/G/1 Queueing Sys-tem.Mathematical Theory and Application.2003(01).
[20]Cohen J W.The Single Server Queue.New York:North-Holland Publishing Company,1982.
[21]Neuts,M,F..Probability distributions of phase type,in Liber Amicorum prof.Belguim Uni.Of Louvain,1975.173-206.
[2]徐光辉.随机服务系统.科学出版社.1988
[3]孙荣恒,李建平.排队论基础.科学出版社.2002
[4]田乃硕,徐秀丽,马占友.离散时间排队论.科学出版社.2002
[5]刘晓红.马尔可夫骨架过程在两类GI／G／1排队系统中的应用：[硕士学位论文]。长沙：中南大学,2007.
[6]王益民.马尔可夫骨架过程在GI／G／1排队系统中的应用：[博士学位论文]。长沙：中南大学,2003.
[7]王梓坤.生灭过程与马尔可夫链,科学出版社,1980.
[8]华洪涛.成批到达带休假的排队系统：[硕士学位论文]。郑州：郑州大学,2011.
[9]徐光辉.GI／M／n的瞬时分布性质。应用数学学报,1965,15,91-120
[10]Finch,P.D.,On the queuing system GI/G/1,J.Aust.Math.Soc.,1961,2,217-228.
[11]Takacs,L.Delay distributions for simple trunk groups with recurrent input and exponential service times。Bell Syst.Tech.J.,1962,41,311-320.
[12]唐应辉,唐小我.排队论：基础与分析技术,科学出版社,2006：120-124.
[13]侯振挺,何宁卡.马氏骨架过程与一个排队系统的瞬时队长.铁道科学与工程学报,2004,02,107-110.
[14]Kendall,D.G.Some problem in the theory of queues.J.Roy.Statist.Soc.,B,1951,13:150-185.
[15]Hou Zhengting,Liu Guoxin.Markov Skeleton Process and Their Application.Boston:International Press,2005,92-124.
[16]Hou Zhengting.Markov Skeleton Process and Application to queuing systems.Acta,Mathematic Application Sinica, English Series,2002,18(4):537-552.
[17]Finch,P.D.,On the busy period in the queuing system GI/G/1,J.Aust.Math.So.,1961,2,217-228.
[18]Attahiru Sule Alfa.Discrete-time analysis of the GI/G/1 system with Bernoulli retrials:An alpporithmic approach, Springer.2006(01).
[19]Hou Zhengting,Li Min.The Transinet Behavior of the Length of GI/G/1 Queueing Sys-tem.Mathematical Theory and Application.2003(01).
[20]Cohen J W.The Single Server Queue.New York:North-Holland Publishing Company,1982.
[21]Neuts,M,F..Probability distributions of phase type,in Liber Amicorum prof.Belguim Uni.Of Louvain,1975.173-206.