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离散时间排队MAP/PH/3(英文) 被引量：1

The MAP/PH/3 Discrete-time Queue
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摘要 本文研究具有马尔可夫到达过程的离散时间排队ＭＡＰ／ＰＨ／３，系统中有三个服务台，每个服务台对顾客的服务时间均服从位相型分布．运用矩阵几何解的理论，我们给出了系统平稳的充要条件和系统的稳态队长分布．同时我们也给出了到达顾客所见队长分布和平均等待时间． In this paper, we study the MAP/PH/3 discrete-time queue with Markovian arrival process, there are three servers in the system, service time of each server follows phase type distribution. By using the theory of matrix-geometric solution we give the necessary and sufficient condition of the system being stable and the stationary queue length distribution of the system. At the same time, the stationary distribution of queue length seen by an arriving customer and the mean waiting time are also provided.
作者 禹海波 周家良 聂赞坎
机构地区 西安交通大学理学院
出处 《运筹学学报》 CSCD 2000年第4期63-70,共8页 Operations Research Transactions
基金 This paper is supported by National Science FOundations of China(19571055).
关键词 离散时间排队 多服务台排队 马氏到达过程 位相型分布 MAP/PH/3 Discrete-time queue, Multi-server queue, Markovian arrival process, Phase type distribution.8
分类号 O226 [理学—运筹学与控制论]
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参考文献5

  • 1[1]Bruneel,H.and Kim,B.G.,Discrete-time Models for communication Systems Including ATM.Kluwer.,Boston,1993.
  • 2[2]Roberts,J.W.,Performance Evaluation and Design of Multiserver Networks,ECSC-EECEAEC,Brussels,1992.
  • 3[3]Neuts,M.F,Matrix-Geometric Solution in Stochastic Models-an Algorithmic Approach.The John Hopkins University Press,Baltimore,1981.
  • 4[4]Ramaswami.V and Lucantoni.D.M.,Algorithms for the Multi-serve Queue with phase type service.COMMUN.STATIST-STOCHASTIC MODELS,1995,Vol.1,No.3:393-417.
  • 5[5]Neuts,M.F,A Versatile Markovian point process,J.Appl.Prob,1979,Vol.16:764-779.

同被引文献40

  • 1Neuts M F. A versatile markovian point process[J]. Journal Application of Probability,1979, (16):764-779.
  • 2Ramaswami V. The N/G/1 queue and its detailed analysis[J]. Journal Application of Probability,1980, (12) :222- 261.
  • 3Lucantoni D M, Meier Hellstern K S, Neuts M F. A single server queue with server vacations and a class of non- renewal arrival proeesses[J]. Advance in Applied Probability, 1990,22(3) : 676-705.
  • 4Asmussen S, Koole G. Marked point processes as limits of Markovian arrival streams[J]. Journal Application of Probability, 1993,30 : 365-372.
  • 5Neuts M F. Matrix-Geometric Solutions in Stochastic Models An Algorithmic Approach[M]. Baltimore: Johns Hopkins University Press, 1981.
  • 6Ramaswami V. Matrix analytic methods: A tutorial overview with some extensions and new results[C]//Matrix Analytic Methods in Stochastic Models, 1996.
  • 7Latouche G, Ramaswaml V. Introduction to matrix analytic methods in stochastic modeling[C]//SIAM, 1999.
  • 8Kim J, Jun C-H. Analysis of a discrete-Time queueing system with a single server and heterogeneous markovian arrivals[J]. Queueing Systems, 2002, (42) :221-237.
  • 9Herrmann C. The complete analysis of the discrete time finite DBMAP/G/1/N queue [J]. Performance Evaluation, 2001,43:95-121.
  • 10Gupta U C, Sikdar K. Computing queue length distributions in MAP/G/1/N queue under single and multiple vacation [J]. Applied Mathematics and Computation, 2006,174 : 1498-1525.

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运筹学学报
2000年 第4期

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