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.

在这个项目中，我们对排队网络​​的效率进行了理论分析。(1)给出了一个代表复杂顾客到达的排队网络的模型，并基于随机测量显示了其数学表示。 (2)对广义半马尔可夫过程进行了数学扩展，并将其应用于排队网络中，以解决各节点的群体服务和顾客服务时间相互依赖的情况。 (3)针对顾客服务停止和路径选择依赖于网络的情况，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)通过改变原模型的条件给出了解析网络模型，该模型不容易找到网络中的平稳分布，并研究了它们之间的关系。 (5)提出了同时发生某种变化的排队网络的解析方法。

项目成果

M.Miyazawa: "Palm calculus for a process with a stationary rardom measure and its applications to fluid queues" Queueing Systems. 17. 183-211 (1994)

M.Miyazawa：“具有固定随机测量的过程的手掌演算及其在流体队列中的应用”排队系统。

大矢 雅則,渡邉 昇: "量子系のK-S型平均相互エントロピーの新しい定式化とモデルに関する計算" The proceeding of symposium of Information theory and its applications. 18. 785-788 (1995)

Masanori Oya，Noboru Watanabe：“量子系统K-S型平均互熵的新表述及其模型计算”信息论及其应用研讨会论文集18。785-788（1995）。

M.Ohya: "Mathematical Study of Iuformation transmission in quantum communication processes" Plenum(Quantum communications and Measurement,). (to appear). (1995)

M.Ohya：“量子通信过程中信息传输的数学研究”Plenum（量子通信和测量）。

大矢 雅則: "Scrafアルゴリズムの改良による多重均衡解の探索" The proceeding of symposium of Information theory and Its applications. 18. 817-820 (1995)

Masanori Oya：“通过改进Scraf算法寻找多重均衡解”信息论及其应用研讨会论文集18。817-820（1995）。

M. Ohya, H. Suyari: "Mutual Entropy in Quantum Markor Chains" Plenum(Quantum and Measure ment). 351-358 (1995)

M. Ohya、H. Suyari：“量子标记链中的互熵”全会（量子与测量）。