We study multi-hop data-dissemination in a wireless network from one source to multiple nodes where some of the nodes of the network act as re-transmitting nodes and help the source in data dissemination. In this network, we study two scenarios; i) the transmitting nodes do not need an incentive for transmission and ii) they do need an incentive and are paid by their corresponding receiving nodes by virtual tokens. We investigate two problems; P1) network power minimization for the first scenario and P2) social cost minimization for the second scenario, defined as the total cost paid by the nodes of the network for receiving data. In this paper, to address P1 and P2, we propose centralized and decentralized approaches that determine which of the nodes of the network should act as transmitting nodes, find their transmit powers and their corresponding receiving nodes. For the sake of energy efficiency, in our model, we employ maximal-ratio combining (MRC) at the receivers so that a receiver can be served by multiple transmitters. The proposed decentralized approach is based on a non-cooperative cost-sharing game (CSG). In our proposed game, every receiving node chooses its respective transmitting nodes and consequently, a cost is assigned to it according to the power imposed on its chosen transmitting nodes. We discuss how the network is formed in a decentralized way, find the action of the nodes in the game and show that, despite being decentralized, the proposed game converges to a stable solution. To find the centralized global optimum, which is a benchmark to our decentralized approach, we use a mixed-integer-liner-program (MILP). Simulation results show that our proposed decentralized approach outperforms the conventional algorithms in terms of energy efficiency and social cost while it can address the need for an incentive for collaboration.

中文翻译：

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无线网络中数据传播的能源和社会成本最小化：集中式和分散式方法

我们研究了无线网络中从一个源到多个节点的多跳数据传播，其中网络的一些节点充当转发节点并帮助源进行数据传播。在这个网络中，我们研究了两种场景；i) 传输节点不需要激励传输和 ii) 他们确实需要激励并且由其相应的接收节点通过虚拟代币支付。我们调查了两个问题；P1）第一个场景的网络功率最小化和 P2）第二个场景的社会成本最小化，定义为网络节点为接收数据支付的总成本。在本文中，为了解决 P1 和 P2，我们提出了集中式和分散式方法，以确定网络的哪个节点应该充当传输节点，找到它们的发射功率和它们对应的接收节点。出于能源效率的考虑，在我们的模型中，我们在接收器处采用了最大比合并 (MRC)，以便一个接收器可以由多个发射器提供服务。提议的分散方法基于非合作成本分摊游戏 (CSG)。在我们提出的游戏中，每个接收节点选择其各自的发送节点，因此，根据对其选择的发送节点施加的功率为其分配成本。我们讨论了网络如何以去中心化的方式形成，找到游戏中节点的动作，并表明尽管是去中心化的，但所提出的游戏收敛到一个稳定的解决方案。为了找到集中式全局最优，这是我们分散式方法的基准，我们使用混合整数线性程序（MILP）。