| 具有工作故障及有限容量的MAP/M/1排队系统性能分析 |
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| 引用本文： | 张晓亮,叶晴晴,庞钰滢.具有工作故障及有限容量的MAP/M/1排队系统性能分析[J].数学的实践与认识,2021(5):162-168. |
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| 作者姓名： | 张晓亮 叶晴晴 庞钰滢 |
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| 作者单位： | 南京信息工程大学数学与统计学院 |
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| 基金项目： | 国家自然科学基金(11901307);江苏省自然科学基金(BK20180783);江苏省高校自然科学研究面上项目(18KJB110021);国家级大学生创新训练计划项目(201910300037);江苏省大学生创新训练计划项目(No.201910300027Z)。 |
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| 摘 要： | 为了拓展随机排队理论,在具有工作故障的MAP/M/1排队的基础上,引入有限容量策略建立起一个新的排队模型.通过Uniformization Technique将连续时间排队模型转化成对应的离散时间排队模型,运用矩阵几何组合解给出系统中的顾客数量和服务器状态的联合稳态概率表达式,并给出基于稳态概率的性能指标.最后通过一些数值例子展示参数对性能指标的影响.
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| 关 键 词： | 马尔可夫到达过程 矩阵组合几何解 工作故障 Uniformization Technique变换 |
Performance Analysis of MAP/M/1 Queueing System with Working Breakdown and Finite Capacity |
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| ZHANG Xiao-liang,YE Qing-qing,PANG Yu-ying.Performance Analysis of MAP/M/1 Queueing System with Working Breakdown and Finite Capacity[J].Mathematics in Practice and Theory,2021(5):162-168. |
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| Authors: | ZHANG Xiao-liang YE Qing-qing PANG Yu-ying |
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| Institution: | (School of Mathematics and Statistics,Nanjing University of Information Science and Technology,Nanjing 210044,China) |
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| Abstract: | In order to extend the stochastic queuing theory,Based on the MAP/M/1 queue with working breakdowns,we introduce the finite capacity policy,and describe a new queueing system.Through the Uniformization Technique,we transform this continuous time queue to the corresponding discrete time queue,and obtain the steady-state probability for this discrete time queue by Matrix Geometric Combination solution,further,all kinds of performance measures in steady state are given.At last,we present several numerical examples to discuss the relationships between the performance measures and system parameters. |
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| Keywords: | markov arrival process matrix geometric combination solution working breakdowns uniformization technique |
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