具有非平稳到达和未观察到的停顿的服务系统的统计推断

Shreehari Anand Bodas, Michel Mandjes, Liron Ravner
{"title":"具有非平稳到达和未观察到的停顿的服务系统的统计推断","authors":"Shreehari Anand Bodas, Michel Mandjes, Liron Ravner","doi":"arxiv-2311.16884","DOIUrl":null,"url":null,"abstract":"We study a multi-server queueing system with a periodic arrival rate and\ncustomers whose joining decision is based on their patience and a delay proxy.\nSpecifically, each customer has a patience level sampled from a common\ndistribution. Upon arrival, they receive an estimate of their delay before\njoining service and then join the system only if this delay is not more than\ntheir patience, otherwise they balk. The main objective is to estimate the\nparameters pertaining to the arrival rate and patience distribution. Here the\ncomplication factor is that this inference should be performed based on the\nobserved process only, i.e., balking customers remain unobserved. We set up a\nlikelihood function of the state dependent effective arrival process (i.e.,\ncorresponding to the customers who join), establish strong consistency of the\nMLE, and derive the asymptotic distribution of the estimation error. Due to the\nintrinsic non-stationarity of the Poisson arrival process, the proof techniques\nused in previous work become inapplicable. The novelty of the proving mechanism\nin this paper lies in the procedure of constructing i.i.d. objects from\ndependent samples by decomposing the sample path into i.i.d.\\ regeneration\ncycles. The feasibility of the MLE-approach is discussed via a sequence of\nnumerical experiments, for multiple choices of functions which provide delay\nestimates. In particular, it is observed that the arrival rate is best\nestimated at high service capacities, and the patience distribution is best\nestimated at lower service capacities.","PeriodicalId":501330,"journal":{"name":"arXiv - MATH - Statistics Theory","volume":"82 6","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Statistical inference for a service system with non-stationary arrivals and unobserved balking\",\"authors\":\"Shreehari Anand Bodas, Michel Mandjes, Liron Ravner\",\"doi\":\"arxiv-2311.16884\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study a multi-server queueing system with a periodic arrival rate and\\ncustomers whose joining decision is based on their patience and a delay proxy.\\nSpecifically, each customer has a patience level sampled from a common\\ndistribution. Upon arrival, they receive an estimate of their delay before\\njoining service and then join the system only if this delay is not more than\\ntheir patience, otherwise they balk. The main objective is to estimate the\\nparameters pertaining to the arrival rate and patience distribution. Here the\\ncomplication factor is that this inference should be performed based on the\\nobserved process only, i.e., balking customers remain unobserved. We set up a\\nlikelihood function of the state dependent effective arrival process (i.e.,\\ncorresponding to the customers who join), establish strong consistency of the\\nMLE, and derive the asymptotic distribution of the estimation error. Due to the\\nintrinsic non-stationarity of the Poisson arrival process, the proof techniques\\nused in previous work become inapplicable. The novelty of the proving mechanism\\nin this paper lies in the procedure of constructing i.i.d. objects from\\ndependent samples by decomposing the sample path into i.i.d.\\\\ regeneration\\ncycles. The feasibility of the MLE-approach is discussed via a sequence of\\nnumerical experiments, for multiple choices of functions which provide delay\\nestimates. In particular, it is observed that the arrival rate is best\\nestimated at high service capacities, and the patience distribution is best\\nestimated at lower service capacities.\",\"PeriodicalId\":501330,\"journal\":{\"name\":\"arXiv - MATH - Statistics Theory\",\"volume\":\"82 6\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-11-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Statistics Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2311.16884\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Statistics Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2311.16884","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

研究了具有周期性到达率的多服务器排队系统,顾客的加入决策基于耐心和延迟代理。具体来说,每个客户都有一个从公共分布中抽样的耐心水平。到达后,他们在加入服务前会收到他们的延迟估计,只有当这个延迟不超过他们的耐心时,他们才会加入系统,否则他们会犹豫。主要目标是估计与到达率和耐心分布有关的参数。这里的复杂因素是,这种推断应该只基于观察到的过程来执行,也就是说,犹豫不决的客户仍然没有被观察到。我们建立了状态相关的有效到达过程(即对应于加入的顾客)的似然函数,建立了theMLE的强一致性,并推导了估计误差的渐近分布。由于泊松到达过程固有的非平稳性,在以前的工作中使用的证明技术变得不适用。本文证明机制的新颖之处在于,通过将样本路径分解为多个再生循环,从相关样本中构造i.i.d对象。通过一系列的数值实验,讨论了mle方法在提供延迟估计的多种函数选择下的可行性。特别地,我们观察到到达率在高服务容量时是最好的估计,而耐心分布在低服务容量时是最好的估计。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
Statistical inference for a service system with non-stationary arrivals and unobserved balking
We study a multi-server queueing system with a periodic arrival rate and customers whose joining decision is based on their patience and a delay proxy. Specifically, each customer has a patience level sampled from a common distribution. Upon arrival, they receive an estimate of their delay before joining service and then join the system only if this delay is not more than their patience, otherwise they balk. The main objective is to estimate the parameters pertaining to the arrival rate and patience distribution. Here the complication factor is that this inference should be performed based on the observed process only, i.e., balking customers remain unobserved. We set up a likelihood function of the state dependent effective arrival process (i.e., corresponding to the customers who join), establish strong consistency of the MLE, and derive the asymptotic distribution of the estimation error. Due to the intrinsic non-stationarity of the Poisson arrival process, the proof techniques used in previous work become inapplicable. The novelty of the proving mechanism in this paper lies in the procedure of constructing i.i.d. objects from dependent samples by decomposing the sample path into i.i.d.\ regeneration cycles. The feasibility of the MLE-approach is discussed via a sequence of numerical experiments, for multiple choices of functions which provide delay estimates. In particular, it is observed that the arrival rate is best estimated at high service capacities, and the patience distribution is best estimated at lower service capacities.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
自引率
0.00%
发文量
0
期刊最新文献
Precision-based designs for sequential randomized experiments Strang Splitting for Parametric Inference in Second-order Stochastic Differential Equations Stability of a Generalized Debiased Lasso with Applications to Resampling-Based Variable Selection Tuning parameter selection in econometrics Limiting Behavior of Maxima under Dependence
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1