{"title":"The number of overlapping customers","authors":"Onno Boxma","doi":"10.1016/j.orl.2024.107203","DOIUrl":null,"url":null,"abstract":"<div><div>We consider the number of overlapping customers in several single- and multiserver queues, i.e., the number of customers whose visit to a service system at some point in time has an overlap with that of a tagged customer. Restricting ourself to the FCFS policy, we obtain the probability generating function and moments of the number of overlaps in the <span><math><mi>M</mi><mo>/</mo><mi>G</mi><mo>/</mo><mn>1</mn></math></span>, <span><math><mi>M</mi><mo>/</mo><mi>G</mi><mo>/</mo><mn>1</mn><mo>/</mo><mi>N</mi></math></span>, <span><math><mi>M</mi><mo>/</mo><mi>M</mi><mo>/</mo><mi>c</mi></math></span> and <span><math><mi>G</mi><mo>/</mo><mi>M</mi><mo>/</mo><mi>c</mi></math></span> queue and (as an approximation) the <span><math><mi>M</mi><mo>/</mo><mi>G</mi><mo>/</mo><mi>c</mi></math></span> queue.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"57 ","pages":"Article 107203"},"PeriodicalIF":0.8000,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Operations Research Letters","FirstCategoryId":"91","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167637724001391","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}
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Abstract
We consider the number of overlapping customers in several single- and multiserver queues, i.e., the number of customers whose visit to a service system at some point in time has an overlap with that of a tagged customer. Restricting ourself to the FCFS policy, we obtain the probability generating function and moments of the number of overlaps in the , , and queue and (as an approximation) the queue.
期刊介绍：
Operations Research Letters is committed to the rapid review and fast publication of short articles on all aspects of operations research and analytics. Apart from a limitation to eight journal pages, quality, originality, relevance and clarity are the only criteria for selecting the papers to be published. ORL covers the broad field of optimization, stochastic models and game theory. Specific areas of interest include networks, routing, location, queueing, scheduling, inventory, reliability, and financial engineering. We wish to explore interfaces with other fields such as life sciences and health care, artificial intelligence and machine learning, energy distribution, and computational social sciences and humanities. Our traditional strength is in methodology, including theory, modelling, algorithms and computational studies. We also welcome novel applications and concise literature reviews.
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