Collaborative Research: Study of Wireless Ad-Hoc and Sensor Networks in a Finite Regime

无线自组织和传感器网络已被确定为最近在通信领域取得重大成功的故事。今天，它正在成为一项具有广泛应用范围的有前途的技术。由于相关网络问题中的设计挑战，这些网络的全部潜力尚未实现。这项研究试图发展一个跨越边界的研究领域，涉及随机图理论、概率方法、通信和网络。这项工作着眼于有限无线网络(即节点数量较少或中等数量的网络)的分析和设计，现有的基于无限节点数的渐近分析或基于模拟的方法都不能满足有限无线网络的分析和设计，这项工作有可能促进几个相关领域的知识和理解。无线网络的数学研究是这一领域的理论基础。在过去的十年中，对网络的连通性、覆盖率、可靠性、时延、寿命、休眠调度、吞吐量和容量等各种网络特性进行了一定程度的分析研究。这些分析研究的大多数集中在渐近场景，即当节点数量趋于无穷大时。为了研究有限(小型或中等规模)网络，研究人员通常求助于计算机模拟和算法方法(例如线性规划)。因此，对有限网络的数学分析可能会产生实用的公式，但在很大程度上被忽视了。这项研究的目标是开发一个通用的框架来设计、研究和优化有限的无线自组网和传感器网络。

Wireless ad hoc and sensor networking has been identified as a recent major success story in the field of communications. Today, it is emerging as a promising technology with an expansive range of applications. The full potential of these networks is yet to be realized as a result of design challenges in the related networking issues. This research seeks to develop a research area crossing frontiers in random graph theory, probabilistic methods, communications and networking. Focusing on the analysis and design of finite wireless networks (i.e., networks with small or moderate number of nodes), for which both existing asymptotic analysis based on infinite number of nodes or simulation based approaches are inadequate, the work has the potential to advance knowledge and understanding across several related fields. Mathematical study of wireless networks serves as a theoretical foundation for this area. During the last ten years a variety of network properties such as network connectivity, coverage, reliability, delay, lifetime, sleep scheduling, throughput and capacity have been analytically studied to some extent. The majority of these analytical studies have concentrated on asymptotic scenarios, i.e., when the number of nodes tends to infinity. To study finite (small or moderate-size) networks researchers often resort to computer simulations and algorithmic approaches (such as linear programming). Thus, mathematical analysis of finite networks that could result in practically-useful formulas has been largely ignored. The goal of this research is to develop a general framework for design, study, and optimization of finite wireless ad hoc and sensor networks.