Spatially Embedded Networks

近年来，无线通信网络的复杂性显著增长。这在一定程度上是由学术研究驱动的，学术研究已经开始定义某些复杂网络拓扑和协议的信息理论边界和优势。另一方面，消费者和行业的需求推动无线网络走向更复杂的架构和解决方案，主要是为了确保使用通用基础设施可以提供广泛的服务。对于4/5G技术来说尤其如此，许多人认为4/5G技术应该为所有人提供所有东西，包括语音，数据，公共安全，分布式传感和监控等。然而，在其他领域也可以找到类似的信念和趋势，例如智能电网网络甚至卫星网络。工程师了解复杂网络的全球属性非常重要，以及这些特性是如何从局部结构中产生的。这些信息可以被输入到模型和优化程序中，这样实际的网络就可以被设计得尽可能好。解决复杂问题的一种常见方法是利用底层系统的随机性和统计特性。网络建模的概率方法并非没有困难，研究人员多年来一直在努力解决的一些主要问题来自网络是具有物理边界的有限实体这一事实。最近的研究主要集中在当网络嵌入到有限的空间域中时，边界对连通性的影响。得到了总连接概率的解析表达式。这些公式量化了边界附近的节点更有可能断开连接的直观现象，从而解释了网络中断概率在高节点密度下的表现。这项工作已经大大扩展到探索弹性的概念（k-连通性）、节点方向性、多样性和幂标度律的影响、复杂的几何边界域（凸和非凸），甚至更高层信任协议与物理网络设置和空间域之间的相互作用。在该项目中，将进一步利用上面提到的概率形式来研究影响空间嵌入网络结构的几个关键概念。以下四个主题将被处理：-空间嵌入式网络的连续模型，包括随机网络的频谱和中心属性的调查; -空间嵌入式网络中的移动模型，包括随机航点和Levy飞行过程; -空间嵌入式网络中的信任模型，包括信任动力学和协议设计;- 空间嵌入网络的时间模型，包括动态节点和链接（边）模型。这项工作将采取数学方法，但将始终保持对实际影响和设计的重点。

The complexity of wireless communication networks has grown considerably in recent years. This has been driven in part by academic research that has started to define the information theoretic boundaries and advantages of certain complex networking topologies and protocols. On the other hand, the demands from consumers and industry have pushed wireless networks towards more sophisticated architectures and solutions, primarily in order to ensure a broad range of services can be delivered using a common infrastructure. This is particularly true of 4/5G technologies, which many believe should support all things for all people, including voice, data, public safety, distributed sensing and monitoring, etc. However, similar beliefs and trends can be found in other sectors, such as smart grid networks and even satellite networks.It is important that engineers understand the global properties of complex networks, and how these properties arise from local structure. Such information can be fed into models and optimisation routines so that practical networks can be designed to perform as well as possible. A common approach to tackling complex problems is to exploit randomness and statistical properties of the underlying system. Probabilistic approaches to network modelling are not without their difficulties, and some of the main problems that researchers have struggled with over the years arise from the fact that networks are finite entities with physical boundaries. Recent research by the investigators has focused on the effects that boundaries have on connectivity when networks are embedded in some finite spatial domain. Analytic expressions for the overall connection probability have been obtained. These formulae quantify the intuitive phenomenon that nodes near the boundary are more likely to disconnect, and thus they explain how the network outage probability behaves at high node densities. This work has been extended considerably to explore notions of resilience (k-connectivity), the effects of node directivity, diversity and power scaling laws, complicated geometric bounding domains (both convex and non-convex), and even the interplay between higher layer trust protocols and the physical network set-up and spatial domain.In this project, the probabilistic formalism alluded to above will be exploited further to study several key concepts that influence the structure of spatially embedded networks. The following four topics will be treated: - continuum models of spatially embedded networks, including the investigation of spectral and centrality properties of random networks; - mobility models in spatially embedded networks, including random waypoint and Levy flight processes; - trust models in spatially embedded networks, including trust dynamics and protocol design; - temporal models of spatially embedded networks, including dynamical node and link (edge) models.The work will take a mathematical approach, but will always maintain a focus on practical implications and designs.