Mathematical Study of Queueing Theory

排队论的数学研究

• 批准号: 06640274
• 负责人: MIYAZAWA Masakiyo
• 金额: $ 1.28万
• 依托单位: Science University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1994
• 资助国家: 日本
• 起止时间: 1994 至 1996
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-06640274/
• 关键词: Queueing network; Traffic equation; Markov jump process; Stationary distribution; Time-reversed process; Structure reversibility; Random measure; Palm distribution; 待ち行列理論; マルコフ過程; 点過程; 非定常過程; 相互エントロピー; 位相的エントロピー; 複雑量

In this project we gave a theoretical analysis on efficiencies of queueing networks.(1) A model to represent a queueing network for aomplicated arrivals of customers was given and its mathematical representation was shown based on random measures. (2) Generalized semi-Markov Processes was extended mathematically and applied to the queueing networks in case that group service and service time for customer on each node are depended each other. (3) A new model of a queueing network was presented for the case that the stop of the service for customers and choice of path depended on the network was investigated and the analytical class of network models was characterized mathematically. (4) The analytical network models was given by the change of the conditions of the original model which is not so easy to find the stationary distribution in the network and its relation was investigated. (5) The analytic method for a queueing network which happens some change at the same time was developed.

本课题从理论上分析了嵌入式网络的效率问题。(1)给出了一个表示复杂顾客到达的排队网络的模型，并给出了基于随机测度的数学表示。(2)对广义半马尔可夫过程进行了数学推广，并将其应用于群组服务与客户在各节点上的服务时间相互依赖的排队网络。(3)针对顾客服务的停止和路径选择依赖于网络的情形，提出了一种新的排队网络模型，并对网络模型的解析类进行了数学刻画. (4)通过改变原模型中不易找到平稳分布的条件，给出了解析网络模型，并研究了其关系。(5)提出了一种同时发生变化的混沌网络的分析方法。

项目成果

M.Ohya: "Complexity and their applications to Quantum information and computer" Quantum Strucutres. (To appear).

M.Ohya：“复杂性及其在量子信息和计算机中的应用”量子结构。

大矢雅則・小嶋泉(編著),渡邉昇・須鎗弘樹(他著): "量子情報と進化の力学-研究最前線-" 牧野書店, 270 (1996)

Masanori Oya、Izumi Kojima（编辑）、Noboru Watanabe、Hiroki Sujari（等）：“量子信息和进化动力学 - 研究前沿”牧野书店，270（1996）

M.Miyazawa: "Decomposition formulas for single server queues with server vacations-A unified approach by the rate conservation law" Stochastic Models. Vol.10. 389-413 (1994)

M.Miyazawa：“带有服务器假期的单服务器队列的分解公式 - 速率守恒定律的统一方法”随机模型。

Y.Takahashi and M.Miyazawa: "Relationship between queues-length and waiting time destributions in a priority queue with batch arrivals" JORSJ.Vol.37. 48-63 (1994)

Y.Takahashi 和 M.Miyazawa：“批量到达的优先队列中队列长度与等待时间分布之间的关系”JORSJ.Vol.37。

M.Miyazawa: "Stability of discrete-time Jackson networks with batch movements, "Stochastic Networks : Stability and Rare Events"" Lecture Notes in Statistics. Vol.117. 75-94 (1996)

M.Miyazawa：“具有批量运动的离散时间杰克逊网络的稳定性，“随机网络：稳定性和稀有事件””统计讲义。