{"title":"密集无线多跳网络中的近最优负载均衡","authors":"E. Hyytia, J. Virtamo","doi":"10.1109/NGI.2008.31","DOIUrl":null,"url":null,"abstract":"We consider the load balancing problem in wireless multi-hop networks. In the limit of a dense network, there is a strong separation between the macroscopic and microscopic scales, and the load balancing problem can be formulated as finding continuous curves (\"routes\") between all source-destination pairs that minimize the maximum of the so-called scalar packet flux (\"traffic load\"). In this paper we re-formulate the problem by focusing entirely on the so-called d-flows (vector flow field of packets with a common destination x) and by looking at the equation these flows have to satisfy. The general solution to this equation can be written in terms of a single unknown scalar function, psi(r, x), related to the circulation density of the d-flow, for which function the optimization task can be presented as a problem of variational calculus. In this approach, we avoid completely dealing with systems of paths and calculating the load distribution resulting from the use of a given set of paths. Once the optimal solution for psi(r, x) is found the corresponding paths are obtained as the flow lines of the d-flows. In the example of a unit disk with uniform traffic demands we are able to find a set of paths which is considerably better than any previously published results, yielding a low maximal scalar flux and an extraordinarily flat load distribution. We further illustrate the methodology for a unit square with comparable improvements achieved.","PeriodicalId":182496,"journal":{"name":"2008 Next Generation Internet Networks","volume":"5 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2008-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":"{\"title\":\"Near-Optimal Load Balancing in Dense Wireless Multi-Hop Networks\",\"authors\":\"E. Hyytia, J. Virtamo\",\"doi\":\"10.1109/NGI.2008.31\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider the load balancing problem in wireless multi-hop networks. In the limit of a dense network, there is a strong separation between the macroscopic and microscopic scales, and the load balancing problem can be formulated as finding continuous curves (\\\"routes\\\") between all source-destination pairs that minimize the maximum of the so-called scalar packet flux (\\\"traffic load\\\"). In this paper we re-formulate the problem by focusing entirely on the so-called d-flows (vector flow field of packets with a common destination x) and by looking at the equation these flows have to satisfy. The general solution to this equation can be written in terms of a single unknown scalar function, psi(r, x), related to the circulation density of the d-flow, for which function the optimization task can be presented as a problem of variational calculus. In this approach, we avoid completely dealing with systems of paths and calculating the load distribution resulting from the use of a given set of paths. Once the optimal solution for psi(r, x) is found the corresponding paths are obtained as the flow lines of the d-flows. In the example of a unit disk with uniform traffic demands we are able to find a set of paths which is considerably better than any previously published results, yielding a low maximal scalar flux and an extraordinarily flat load distribution. We further illustrate the methodology for a unit square with comparable improvements achieved.\",\"PeriodicalId\":182496,\"journal\":{\"name\":\"2008 Next Generation Internet Networks\",\"volume\":\"5 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2008-04-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2008 Next Generation Internet Networks\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/NGI.2008.31\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2008 Next Generation Internet Networks","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/NGI.2008.31","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Near-Optimal Load Balancing in Dense Wireless Multi-Hop Networks
We consider the load balancing problem in wireless multi-hop networks. In the limit of a dense network, there is a strong separation between the macroscopic and microscopic scales, and the load balancing problem can be formulated as finding continuous curves ("routes") between all source-destination pairs that minimize the maximum of the so-called scalar packet flux ("traffic load"). In this paper we re-formulate the problem by focusing entirely on the so-called d-flows (vector flow field of packets with a common destination x) and by looking at the equation these flows have to satisfy. The general solution to this equation can be written in terms of a single unknown scalar function, psi(r, x), related to the circulation density of the d-flow, for which function the optimization task can be presented as a problem of variational calculus. In this approach, we avoid completely dealing with systems of paths and calculating the load distribution resulting from the use of a given set of paths. Once the optimal solution for psi(r, x) is found the corresponding paths are obtained as the flow lines of the d-flows. In the example of a unit disk with uniform traffic demands we are able to find a set of paths which is considerably better than any previously published results, yielding a low maximal scalar flux and an extraordinarily flat load distribution. We further illustrate the methodology for a unit square with comparable improvements achieved.