{"title":"非齐次泊松-布尔模型下线段的k覆盖","authors":"S. T. Aditya, P. Manohar, D. Manjunath","doi":"10.1109/WIOPT.2009.5291571","DOIUrl":null,"url":null,"abstract":"We consider k-coverage of a line by a twodimensional, non homogeneous Poisson-Boolean model. This has applications in sensor networks. We extend the analysis of [1] to the case for k ≫ 1. The extension requires us to define a vector Markov process that tracks the k segments that have the longest residual coverage at a point. This process is used to determine the probability of a segment of the line being completely covered by k or more sensors. We illustrate the extension by considering the case of k = 2.","PeriodicalId":143632,"journal":{"name":"2009 7th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks","volume":"545 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2009-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the k-coverage of line segments by a non homogeneous Poisson-Boolean model\",\"authors\":\"S. T. Aditya, P. Manohar, D. Manjunath\",\"doi\":\"10.1109/WIOPT.2009.5291571\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider k-coverage of a line by a twodimensional, non homogeneous Poisson-Boolean model. This has applications in sensor networks. We extend the analysis of [1] to the case for k ≫ 1. The extension requires us to define a vector Markov process that tracks the k segments that have the longest residual coverage at a point. This process is used to determine the probability of a segment of the line being completely covered by k or more sensors. We illustrate the extension by considering the case of k = 2.\",\"PeriodicalId\":143632,\"journal\":{\"name\":\"2009 7th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks\",\"volume\":\"545 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2009-06-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2009 7th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/WIOPT.2009.5291571\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2009 7th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/WIOPT.2009.5291571","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On the k-coverage of line segments by a non homogeneous Poisson-Boolean model
We consider k-coverage of a line by a twodimensional, non homogeneous Poisson-Boolean model. This has applications in sensor networks. We extend the analysis of [1] to the case for k ≫ 1. The extension requires us to define a vector Markov process that tracks the k segments that have the longest residual coverage at a point. This process is used to determine the probability of a segment of the line being completely covered by k or more sensors. We illustrate the extension by considering the case of k = 2.
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