{"title":"排队理论及一些应用说明","authors":"Carlos E. Martínez-Rodríguez","doi":"arxiv-2409.10735","DOIUrl":null,"url":null,"abstract":"This paper presents a comprehensive review of stochastic processes, with a\nparticular focus on Markov chains and jump processes. The main results related\nto queuing systems are analyzed. Additionally, conditions that ensure the\nstability, or ergodicity, of such systems are presented. The paper also\ndiscusses stability results for queuing networks and their extension to\nvisiting systems. Finally, key contributions concerning the Probability\nGenerating Function, an essential tool in the analysis of the aforementioned\nprocesses, are introduced. The review is conducted from the perspective of\nqueuing theory, grounded in the Kendall-Lee notation, emphasizing stability\nresults and the computation of performance measures based on the specific\ncharacteristics of each process.","PeriodicalId":501245,"journal":{"name":"arXiv - MATH - Probability","volume":"3 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Notas sobre Teoría de colas y algunas aplicaciones\",\"authors\":\"Carlos E. Martínez-Rodríguez\",\"doi\":\"arxiv-2409.10735\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper presents a comprehensive review of stochastic processes, with a\\nparticular focus on Markov chains and jump processes. The main results related\\nto queuing systems are analyzed. Additionally, conditions that ensure the\\nstability, or ergodicity, of such systems are presented. The paper also\\ndiscusses stability results for queuing networks and their extension to\\nvisiting systems. Finally, key contributions concerning the Probability\\nGenerating Function, an essential tool in the analysis of the aforementioned\\nprocesses, are introduced. The review is conducted from the perspective of\\nqueuing theory, grounded in the Kendall-Lee notation, emphasizing stability\\nresults and the computation of performance measures based on the specific\\ncharacteristics of each process.\",\"PeriodicalId\":501245,\"journal\":{\"name\":\"arXiv - MATH - Probability\",\"volume\":\"3 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Probability\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.10735\",\"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 - Probability","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.10735","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Notas sobre Teoría de colas y algunas aplicaciones
This paper presents a comprehensive review of stochastic processes, with a
particular focus on Markov chains and jump processes. The main results related
to queuing systems are analyzed. Additionally, conditions that ensure the
stability, or ergodicity, of such systems are presented. The paper also
discusses stability results for queuing networks and their extension to
visiting systems. Finally, key contributions concerning the Probability
Generating Function, an essential tool in the analysis of the aforementioned
processes, are introduced. The review is conducted from the perspective of
queuing theory, grounded in the Kendall-Lee notation, emphasizing stability
results and the computation of performance measures based on the specific
characteristics of each process.
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