{"title":"有限容量处理器共享队列中的逗留时间","authors":"S. Borst, O. Boxma, N. Hegde","doi":"10.1109/NGI.2005.1431647","DOIUrl":null,"url":null,"abstract":"Motivated by the need to develop simple parsimonious models for evaluating the performance of wireless data systems, we consider finite-capacity processor-sharing systems. For such systems, we analyze the sojourn time distribution, which presents a useful measure for the transfer delay of documents such as Web pages. The service rates are allowed to be state-dependent, to capture the fact that the throughput in wireless data systems may vary with the number of active users due to scheduling gains or channel collisions. We derive a set of linear equations for the Laplace-Stieltjes transforms of the sojourn time distributions, conditioned on the number of users upon arrival. This set of equations is solved, and the resulting LST's are inverted, resulting in a phase-type distribution for the unconditional sojourn time. Numerical results are provided, and two types of approximations are proposed that substantially reduce the computational effort.","PeriodicalId":435785,"journal":{"name":"Next Generation Internet Networks, 2005","volume":"3 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2005-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"35","resultStr":"{\"title\":\"Sojourn times in finite-capacity processor-sharing queues\",\"authors\":\"S. Borst, O. Boxma, N. Hegde\",\"doi\":\"10.1109/NGI.2005.1431647\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Motivated by the need to develop simple parsimonious models for evaluating the performance of wireless data systems, we consider finite-capacity processor-sharing systems. For such systems, we analyze the sojourn time distribution, which presents a useful measure for the transfer delay of documents such as Web pages. The service rates are allowed to be state-dependent, to capture the fact that the throughput in wireless data systems may vary with the number of active users due to scheduling gains or channel collisions. We derive a set of linear equations for the Laplace-Stieltjes transforms of the sojourn time distributions, conditioned on the number of users upon arrival. This set of equations is solved, and the resulting LST's are inverted, resulting in a phase-type distribution for the unconditional sojourn time. Numerical results are provided, and two types of approximations are proposed that substantially reduce the computational effort.\",\"PeriodicalId\":435785,\"journal\":{\"name\":\"Next Generation Internet Networks, 2005\",\"volume\":\"3 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2005-04-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"35\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Next Generation Internet Networks, 2005\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/NGI.2005.1431647\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Next Generation Internet Networks, 2005","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/NGI.2005.1431647","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Sojourn times in finite-capacity processor-sharing queues
Motivated by the need to develop simple parsimonious models for evaluating the performance of wireless data systems, we consider finite-capacity processor-sharing systems. For such systems, we analyze the sojourn time distribution, which presents a useful measure for the transfer delay of documents such as Web pages. The service rates are allowed to be state-dependent, to capture the fact that the throughput in wireless data systems may vary with the number of active users due to scheduling gains or channel collisions. We derive a set of linear equations for the Laplace-Stieltjes transforms of the sojourn time distributions, conditioned on the number of users upon arrival. This set of equations is solved, and the resulting LST's are inverted, resulting in a phase-type distribution for the unconditional sojourn time. Numerical results are provided, and two types of approximations are proposed that substantially reduce the computational effort.