监控M/M/1排队系统的AEWMA控制图
AEWMA Control Chart for Monitoring the M/M/1 Queuing System
DOI: 10.12677/aam.2025.148386, PDF,    国家自然科学基金支持
作者: 赵 薇, 齐德全：长春理工大学数学与统计学院，吉林 长春
关键词: 自适应控制图；M/M/1系统；似然比检验；平均运行长度 ；Adaptive Control Chart； M/M/1 System； Likelihood Ratio Test； Average Run Length
摘要: 监控排队系统的到达率、服务率或系统利用率等指标，可以有针对性地增加或减少服务台，提高服务效率，预防系统拥塞，避免资源浪费。从统计过程控制的角度，给出了在线监控M/M/1排队系统的一般框架。将常用的相关的队列长度数据转化为独立的到达人数数据。基于似然比检验构建自适应的EWMA控制图(AEWMA*)，根据漂移的估计量计算权重函数，提高控制图的性能。引入相对平均指标(RMI)和平均样本量(ANOS)作为评价准则，实验结果显示：与对比方法相比，AEWMA*具有较低的RMI值，说明AEWMA*控制图在不同漂移场景下均具备较快的异常响应速度和综合检测优势。
Abstract: Monitoring the arrival rate, service rate, or system utilization of the queuing system can increase or decrease service counters in a targeted manner, improve service efficiency, prevent system congestion, and avoid resource waste. From the perspective of statistical process control, a general framework for online monitoring of M/M/1 queuing systems is presented. Convert commonly used queue length data into independent arrival count data. Constructing an adaptive EWMA control chart (AEWMA*) based on likelihood ratio test, calculating weight functions according to the estimated drift, and improving the performance of the control chart. By introducing the Relative Mean Index (RMI) and Average Sample Size (ANOS) as evaluation criteria, the experimental results show that compared with the comparative method, AEWMA* has a lower RMI value, indicating that the AEWMA* control chart has faster abnormal response speed and comprehensive detection advantages in different drift scenarios.
文章引用：赵薇, 齐德全. 监控M/M/1排队系统的AEWMA控制图[J]. 应用数学进展, 2025, 14(8): 239-245. https://doi.org/10.12677/aam.2025.148386

参考文献

[1] 薛建彬, 郁柏文, 徐小凤, 等. 边缘计算网络中基于排队论的通信和计算资源联合优化[J]. 计算机科学, 2024, 51(S2): 704-712.
[2] 曹石强. 智能排队取号系统设计与实现[J]. 工程技术研究, 2025, 10(8): 207-209.
[3] 高琦. 基于PEWMA控制图的排队系统的监测与优化[D]: [硕士学位论文]. 济南: 山东财经大学, 2024.
[4] Reed, J. and Zwart, B. (2014) Limit Theorems for Markovian Bandwidth-Sharing Networks with Rate Constraints. Operations Research, 62, 1453-1466. [Google Scholar] [CrossRef] 
[5] Narayanan, S., Arora, R.K., Gangwar, S., Kandhasamy, J.P., Ratheesh, T. and Murali, K. (2024) Ultra-Low Latency Communication Technique for Augmented Reality Application in Mobile Edge Computing. International Journal of Engineering Systems Modelling and Simulation, 15, 97-105. [Google Scholar] [CrossRef] 
[6] Bhat, U.N. and Rao, S.S. (1972) A Statistical Technique for the Control of Traffic Intensity in the Queuing Systems M/G/1 and GI/M/1. Operations Research, 20, 955-966. [Google Scholar] [CrossRef] 
[7] Shore, H. (2006) Control Charts for the Queue Length in a G/G/S System. IIE Transactions, 38, 1117-1130. [Google Scholar] [CrossRef] 
[8] Chen, N., Yuan, Y. and Zhou, S. (2011) Performance Analysis of Queue Length Monitoring of M/G/1 Systems. Naval Research Logistics (NRL), 58, 782-794. [Google Scholar] [CrossRef] 
[9] Chen, N. and Zhou, S. (2015) CUSUM Statistical Monitoring of M/M/1 Queues and Extensions. Technometrics, 57, 245-256. [Google Scholar] [CrossRef] 
[10] Qi, D.Q., Li, Z.H., Zi, X.M., et al. (2017) Weighted Likelihood Ratio Chart for Statistical Monitoring of Queueing Systems. Quality Technology & Quantitative Management, 14, 19-30. [Google Scholar] [CrossRef] 
[11] Han, D. and Tsung, F. (2006) A Reference-Free Cuscore Chart for Dynamic Mean Change Detection and a Unified Framework for Charting Performance Comparison. Journal of the American Statistical Association, 101, 368-386. [Google Scholar] [CrossRef] 
[12] 贡平邺, 郑冰静, 郭宝才. 基于加权似然比检验的自适应EWMA控制图设计[J]. 系统科学与数学, 2023, 43(6): 1587-1611.

为你推荐