根据服务时间，具有间隔到达时间的相关队列

IF 1.1 4区管理学 Q4 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Asia-Pacific Journal of Operational Research Pub Date : 2023-06-30 DOI:10.1142/s0217595923500227

Zhenzhen Jia, Weimin Dai, Jianqiang Hu

{"title":"根据服务时间，具有间隔到达时间的相关队列","authors":"Zhenzhen Jia, Weimin Dai, Jianqiang Hu","doi":"10.1142/s0217595923500227","DOIUrl":null,"url":null,"abstract":"We consider a type of correlated queue in which the inter-arrival time between two consecutive customers linearly depends on the service time of the first customer. We first derive infinite systems of linear equations for the moments of the waiting time in two special cases, based on which we then develop several methods to calculate the moments of the waiting time by using MacLaurin series approximation, Padé approximation and truncation method. In addition, we show how the moments and covariances of the inter-departure times of the correlated queue can be calculated based on the moments of the waiting time. Finally, extensive numerical examples are provided to validate our methods.","PeriodicalId":55455,"journal":{"name":"Asia-Pacific Journal of Operational Research","volume":" ","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Correlated Queues with Inter-Arrival Times Depending on Service Times\",\"authors\":\"Zhenzhen Jia, Weimin Dai, Jianqiang Hu\",\"doi\":\"10.1142/s0217595923500227\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider a type of correlated queue in which the inter-arrival time between two consecutive customers linearly depends on the service time of the first customer. We first derive infinite systems of linear equations for the moments of the waiting time in two special cases, based on which we then develop several methods to calculate the moments of the waiting time by using MacLaurin series approximation, Padé approximation and truncation method. In addition, we show how the moments and covariances of the inter-departure times of the correlated queue can be calculated based on the moments of the waiting time. Finally, extensive numerical examples are provided to validate our methods.\",\"PeriodicalId\":55455,\"journal\":{\"name\":\"Asia-Pacific Journal of Operational Research\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2023-06-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Asia-Pacific Journal of Operational Research\",\"FirstCategoryId\":\"91\",\"ListUrlMain\":\"https://doi.org/10.1142/s0217595923500227\",\"RegionNum\":4,\"RegionCategory\":\"管理学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"OPERATIONS RESEARCH & MANAGEMENT SCIENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Asia-Pacific Journal of Operational Research","FirstCategoryId":"91","ListUrlMain":"https://doi.org/10.1142/s0217595923500227","RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"OPERATIONS RESEARCH & MANAGEMENT SCIENCE","Score":null,"Total":0}

引用次数: 1

摘要

我们考虑一种相关队列，其中两个连续客户之间的到达时间线性地取决于第一个客户的服务时间。我们首先推导了两种特殊情况下等待时间矩的无限线性方程组，在此基础上，我们发展了几种方法来计算等待时间矩，分别使用MacLaurin级数近似、Padé近似和截断方法。此外，我们还展示了如何根据等待时间的矩来计算相关队列的出发间隔时间的矩和协变。最后，提供了大量的数值例子来验证我们的方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Correlated Queues with Inter-Arrival Times Depending on Service Times

We consider a type of correlated queue in which the inter-arrival time between two consecutive customers linearly depends on the service time of the first customer. We first derive infinite systems of linear equations for the moments of the waiting time in two special cases, based on which we then develop several methods to calculate the moments of the waiting time by using MacLaurin series approximation, Padé approximation and truncation method. In addition, we show how the moments and covariances of the inter-departure times of the correlated queue can be calculated based on the moments of the waiting time. Finally, extensive numerical examples are provided to validate our methods.

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

Asia-Pacific Journal of Operational Research 管理科学-运筹学与管理科学

CiteScore

2.00

自引率

14.30%

发文量

审稿时长

14.2 months

期刊介绍： The Asia-Pacific Journal of Operational Research (APJOR) provides a forum for practitioners, academics and researchers in Operational Research and related fields, within and beyond the Asia-Pacific region. APJOR will place submissions in one of the following categories: General, Theoretical, OR Practice, Reviewer Survey, OR Education, and Communications (including short articles and letters). Theoretical papers should carry significant methodological developments. Emphasis is on originality, quality and importance, with particular emphasis given to the practical significance of the results. Practical papers, illustrating the application of Operation Research, are of special interest.