{"title":"Queueing Inventory System with Multiple Service Nodes and Addressed Retrials from a Common Orbit","authors":"","doi":"10.1007/s11009-023-10071-w","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>In this paper, we consider a queueing inventory model with <em>K</em> service nodes located apart making it impossible to know the status of the other service nodes. The primary arrival of customers follows Marked Markovian Arrival Process and the service times are exponentially distributed. If a customer arriving at a node finds the server busy or the inventory level to be zero, he joins a common orbit with infinite capacity. An orbital customer shall choose a service node at random according to some predetermined probability distribution dependent on the orbit size. Each service node is assigned with a continuous review inventory replenished according to an (<em>s</em>, <em>S</em>) policy with lead time. This scenario is modeled as a level dependent quasi birth and death process which belongs to the class of asymptotically quasi-Teoplitz Markov chains. Steady-state probabilities and some important performance measures are obtained. A cost function is introduced and employed for computing the optimal values of reorder levels and replenishment rates.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11009-023-10071-w","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we consider a queueing inventory model with K service nodes located apart making it impossible to know the status of the other service nodes. The primary arrival of customers follows Marked Markovian Arrival Process and the service times are exponentially distributed. If a customer arriving at a node finds the server busy or the inventory level to be zero, he joins a common orbit with infinite capacity. An orbital customer shall choose a service node at random according to some predetermined probability distribution dependent on the orbit size. Each service node is assigned with a continuous review inventory replenished according to an (s, S) policy with lead time. This scenario is modeled as a level dependent quasi birth and death process which belongs to the class of asymptotically quasi-Teoplitz Markov chains. Steady-state probabilities and some important performance measures are obtained. A cost function is introduced and employed for computing the optimal values of reorder levels and replenishment rates.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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