空间相关传感器网络中贪婪路由的随机分析
A stochastic analysis of greedy routing in a spatially dependent sensor network
摘要：
针对传感器网络，提出了一种易于处理的空间相关的节点部署模型，该模型具有密度与汇聚点距离成反比的性质。一个随机模型，制定审查下贪婪路由在这样的传感器网络中的消息的进步。这项工作的目的是证明一个非齐次泊松过程可以用来模拟传感器网络与空间相关的节点密度。椭圆积分和渐近近似被用来描述跳的随机行为。影响跳跃进步的依赖类型进行了研究。我们观察到，在一个多跳路径中的连续跳跃之间的依赖性被捕获，只包括以前的转发节点的位置。我们包括一个简单的不协调的睡眠方案，并观察到，当足够的节点睡眠时，模型的复杂性降低。所有涉及多维积分的表达式推导和评估的拟蒙特卡罗方法集成方法的基础上Halton序列和最近开发的格规则。为了加快拟蒙特卡罗方法的计算速度，本文提出了一种重要抽样函数。随后的结果与模拟吻合得非常好。
英文摘要：
For a sensor network, a tractable spatially-dependent node deployment model is presented with the property that the density is inversely proportional to the sink distance. A stochastic model is formulated to examine message advancements under greedy routing in such a sensor network. The aim of this work is to demonstrate that an inhomogeneous Poisson process can be used to model a sensor network with spatially-dependent node density. Elliptic integrals and asymptotic approximations are used to describe the random behaviour of hops. Types of dependence that affect hop advancements are examined. We observe that the dependence between successive jumps in a multihop path is captured by including only the previous forwarding node location. We include a simple uncoordinated sleep scheme, and observe that the complexity of the model is reduced when enough nodes are asleep. All expressions involving multidimensional integrals are derived and evaluated with quasi-Monte Carlo integration methods based on Halton sequences and recently-developed lattice rules. An importance sampling function is derived to speed up the quasi-Monte Carlo methods. The ensuing results agree extremely well with simulations.
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