Cost Comparison of a Multivariant Vacation and Working Vacation Queuing Model With Different Kind of Waiting Servers

Cost Comparison of a Multivariant Vacation and Working Vacation Queuing Model With Different Kind of Waiting Servers | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Cost Comparison of a Multivariant Vacation and Working Vacation Queuing Model With Different Kind of Waiting Servers Remya R This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5761718/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The research delves into evaluating the efficiency of different models in queueing systems with service interruptions, aiming to optimize service rates and enhance customer satisfaction. To determine the most cost-effective model for a single server serving multiple variants with working vacation periods and waiting servers. The study employs probability generating functions and MATLAB techniques to analyze and compare three queueing models.Findings: The research provides a steady-state solution and cost analysis for the examined models, shedding light on the optimal approach for managing service interruptions. The study contributes to operations management by offering insights into improving queueing systems' performance and customer service through efficient model selection. The data used in the study includes service times and vacation lengths following exponential distributions. The research involves analyzing the models' performance using probability generating functions and MATLAB simulations to compare their cost-effectiveness. The study addresses the question of which model among the three considered is the most efficient in terms of cost and service quality. The study identifies the most effective queueing model among the evaluated options for optimized service rates and enhanced customer satisfaction. Mathematics Subject Classification (2000) 60K25 . 68M20 . 90B22 Markovian queue working vacation adaptive vacations cost model optimization Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5761718","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":398322735,"identity":"a4090ca5-4332-41fd-bd6b-8052a87cf6ec","order_by":0,"name":"Remya R","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABAElEQVRIiWNgGAWjYBACfmYGAyAlwcPG3sbAzABCDCARA9xaJNsbQLI2cnw8x4jUYnDmAEg2zVhOIg1ZCz5wI3nbpxs1hxPbJJ8lfi6osE5sYG/eJsFQcAenDsYZacWzc44BtUinHZaecSY9sYHnWJkEg8EznFqYJXKMmXPYQFrSG6R52w4nNkjkmAG1HMaphQ2s5R/IYcebf/MCGQ3yb/Br4eE5Y8yc25ZmzCbBdkyatwFkCw9+LRLsbcXMuX02cmw8aWnWPMfSjdt40ootEvBosT/MvJk555sEj3z7MePbPDXWsv3shzfe+PAHtxYsvgMRCSRoGAWjYBSMglGACQAbLU7Kd1g+bgAAAABJRU5ErkJggg==","orcid":"","institution":"Karpagam Academy of Higher Education","correspondingAuthor":true,"prefix":"","firstName":"Remya","middleName":"","lastName":"R","suffix":""}],"badges":[],"createdAt":"2025-01-04 06:23:16","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5761718/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5761718/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":73962389,"identity":"50141eda-0c10-44ab-8d87-adf3469ae8b6","added_by":"auto","created_at":"2025-01-16 12:02:12","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":905331,"visible":true,"origin":"","legend":"","description":"","filename":"main.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5761718/v1_covered_2d64d63e-4721-44cd-8ee0-168551d73c91.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eCost Comparison of a Multivariant Vacation and Working Vacation Queuing Model With Different Kind of Waiting Servers\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Markovian queue, working vacation, adaptive vacations, cost model, optimization","lastPublishedDoi":"10.21203/rs.3.rs-5761718/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5761718/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe research delves into evaluating the efficiency of different models in queueing systems with service interruptions, aiming to optimize service rates and enhance customer satisfaction. To determine the most cost-effective model for a single server serving multiple variants with working vacation periods and waiting servers. The study employs probability generating functions and MATLAB techniques to analyze and compare three queueing models.Findings: The research provides a steady-state solution and cost analysis for the examined models, shedding light on the optimal approach for managing service interruptions. The study contributes to operations management by offering insights into improving queueing systems' performance and customer service through efficient model selection. The data used in the study includes service times and vacation lengths following exponential distributions. The research involves analyzing the models' performance using probability generating functions and MATLAB simulations to compare their cost-effectiveness. \u0026nbsp;The study addresses the question of which model among the three considered is the most efficient in terms of cost and service quality. The study identifies the most effective queueing model among the evaluated options for optimized service rates and enhanced customer satisfaction.\u003c/p\u003e\n\u003cp\u003eMathematics Subject Classification (2000) 60K25 . 68M20 . 90B22\u003c/p\u003e","manuscriptTitle":"Cost Comparison of a Multivariant Vacation and Working Vacation Queuing Model With Different Kind of Waiting Servers","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-01-08 03:15:53","doi":"10.21203/rs.3.rs-5761718/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"20f93ec1-1ff8-490e-8756-5d938ba32375","owner":[],"postedDate":"January 8th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-01-16T11:54:01+00:00","versionOfRecord":[],"versionCreatedAt":"2025-01-08 03:15:53","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5761718","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5761718","identity":"rs-5761718","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}