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首页> 外文期刊>Parallel and Distributed Systems, IEEE Transactions on >Lower and Upper Bounds for Multicasting under Distance Dependent Forwarding Cost Functions
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Lower and Upper Bounds for Multicasting under Distance Dependent Forwarding Cost Functions

机译：距离相关的转发成本函数下组播的上下界

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摘要

Assume a forwarding cost function which depends on the sender receiver separation, and assume further that noncooperative relaying is applied. What is the minimum total forwarding cost required for sending a message from source to one or more destinations when multicasting along optimal placed relaying nodes is applied? In this paper, I define and analyze cost function properties from which I derive general lower bound expressions on multicasting costs. I consider an MAC layer model which does not exploit the broadcast property of wireless communication and an MAC layer model which exploits it. For specific cost functions, I show further that in case of optimal relay positions, multicasts can be constructed whose cost always stays below the derived lower bound expression plus an additive constant depending on the number of destinations. For both, lower and upper bounds, I define a general procedure to check if—and if yes how—my findings can be used to derive the specific lower and upper bound expressions for a given cost function. I explain the procedure with three cost function examples: the euclidean distance, energy cost function, and the expected number of retransmissions under Rayleigh fading.
机译：假设一个转发成本函数取决于发送者与接收者之间的距离，并进一步假设应用了非合作中继。应用沿最佳放置的中继节点进行多播时，从源向一个或多个目标发送消息所需的最低总转发成本是多少？在本文中，我定义并分析了成本函数属性，从中可以得出关于组播成本的一般下界表达式。我考虑了不利用无线通信的广播特性的MAC层模型和利用它的MAC层模型。对于特定的成本函数，我进一步表明，在最佳中继位置的情况下，可以构造多播，其成本始终保持在派生的下界表达式之下，并取决于目的地的数量加上加性常数。对于下限和上限，我定义了一个通用过程来检查是否可以（如果可以的话）如何使用我的发现来得出给定成本函数的特定下限和上限表达式。我用三个成本函数示例来解释该过程：欧氏距离，能量成本函数以及瑞利衰落下的预期重传次数。

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