基于PH服务的工作休假排队的流体模型

doi:10.15960/j.cnki.issn.1007-6093.2019.02.005

运筹学学报 ›› 2019, Vol. 23 ›› Issue (2): 57-66.doi: 10.15960/j.cnki.issn.1007-6093.2019.02.005

基于PH服务的工作休假排队的流体模型

王慧宁, 徐秀丽^*

燕山大学理学院, 河北秦皇岛 066004

收稿日期:2017-07-17 出版日期:2019-06-15 发布日期:2019-06-15
通讯作者: 徐秀丽 E-mail:xuxl@ysu.edu.cn
基金资助:
国家自然科学基金（No.11201408）

Fluid models driven by a working vacation-queue with PH-service time distribution

WANG Huining, XU Xiuli^*

School of Science, Yanshan University, Qinhuangdao 066004, Hebei, China

Received:2017-07-17 Online:2019-06-15 Published:2019-06-15

摘要/Abstract

摘要： 研究了带有单重工作休假的M/PH/1排队系统驱动的流体模型.首先，通过拟生灭过程和矩阵几何解法分别得到无穷小生成元和驱动过程的稳态队长分布.其次，建立并分析流体模型，根据平衡方程给出流体模型的稳态联合分布函数满足的矩阵微分方程组，利用Laplace变换（LT）和Laplace-Stieltjes变换（LST）的方法，推导出平稳缓冲器（库）容量的空库概率表达式和稳态条件下的缓冲器（库）容量的均值表达式.最后，给出模型在移动自组织网络（Ad Hoc）中的应用，并通过数值例子讨论系统参数对系统性能指标的影响.

关键词: 流体模型, M/PH/1排队, 工作休假, 移动自组织网络

Abstract: This paper is concerned with the fluid model which is driven by a PHservice time and single-server queue with server working vacation. To analyze the fluid model, we first establish the stationary distribution of the queue length process. Based on the steady-state distribution, then the matrix-type ordinary differential equation is obtained for the joint distribution characterizing the fluid model dynamics. With the help of the Laplace transform (LT) and the Laplace-Stieltjes transform (LST), as usual, the probability for the system empty and the average fluid level are given. An application of these obtained results to the mobile Ad Hoc networks is provided. The sensitivities about the system primitive parameters to the performance measures such as the average fluid level are discussed by some numerical experiments.

Key words: fluid model, M/PH/1 queue, working vacation, Ad Hoc network

中图分类号:

O226

王慧宁, 徐秀丽. 基于PH服务的工作休假排队的流体模型[J]. 运筹学学报, 2019, 23(2): 57-66.

WANG Huining, XU Xiuli. Fluid models driven by a working vacation-queue with PH-service time distribution[J]. Operations Research Transactions, 2019, 23(2): 57-66.

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基于PH服务的工作休假排队的流体模型

Fluid models driven by a working vacation-queue with PH-service time distribution

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