基于近似贝叶斯计算方法的排队模型参数估计  

Approximate bayesian computation based parameter estimation for queuing models

作　　者：张岚 钱夕元[1] ZHANG Lan;QIAN Xiyuan(School of Science,East China University of Science and Technology,Shanghai 200237,China)

机构地区：[1]华东理工大学理学院,上海200237

出　　处：《上海理工大学学报》2020年第2期108-114,121,共8页Journal of University of Shanghai For Science and Technology

基　　金：国家高科技研究发展“863计划”资助项目(2015AA20107)。

摘　　要：基于贝叶斯推断对单服务台的马尔科夫与非马尔科夫系统下的4个排队模型做参数估计与效果评价,并对银行排队叫号换汇数据做实证研究。采用近似贝叶斯计算的方法有效解决复杂排队模型似然函数难解析表达的问题。利用R中queue computer包给出M/M/1,M/G/1,G/M/1,GI/GI/1这4个排队模型的到达时间与服务时间的参数估计及后验分布图。其中M/M/1:估计值(真实值)分别约为1.02(1)、 1.12(1/0.9),都与真实值接近;M/G/1:1.17(1)、1.21(1.2),对服务时间的估计效果优于到达时间;G/M/1:0.49(0.5)、0.96(1),从后验分布进一步得到对服务时间的估计更准确;GI/GI/1:1.16(1.1)、1.07(1)、0.23(0.251)、0.22(0.25),各分量的估计值与真实值相对接近。对于实际银行数据,估计得的参数所拟合的数据与Ausin的拟合数据分布接近。研究表明,近似贝叶斯的方法在排队模型的参数估计上有较大优势,在实际数据中取得了较好应用。Based on Bayesian inference, parameters and their validity of four queuing models with a single server in Markov and non-Markov system were estimated, and face-to-face currency exchange data of a bank was tested. By using approximate Bayesian computation, it is effective to solve the difficulty in analytically expressing the likelihood function in complex queuing models.Based on R package, parameters’ estimations and posterior distributions of arrival time and service time for four queuing models: M/M/1, M/G/1, G/M/1, GI/GI/1 were given. For M/M/1: estimated value(true value) is 1.02(1)、1.12(1/0.9) respectively, which are close to the true ones;for M/G/1: they are1.17(1)、1.21(1.2) and estimated parameter of service time is superior to that of arrival time;for G/M/1:they are 0.49(0.5)、0.96(1) and estimated parameter of service time is more accurate from the posterior distribution;for GI/GI/1: they are 1.16(1.1)、1.07(1)、0.23(0.251)、0.22(0.25) and estimated value of each component is relatively close to the true value. Furthermore, for real data, distribution of fitting data of estimated parameters is close to that of Ausin’s fitting data. The results show great efficiency of parameter estimation based on approximate Bayesian computation in queuing theory and great application to the real world.

关 键 词：排队论 近似贝叶斯计算 参数估计 

分 类 号：O212.1[理学—概率论与数理统计]