在廣用無線通道模型上無線網路內的孤立節點數

Abstract

在大型無線隨意網路中，網路中孤立節點的存在與否，可視為網路連通性的指標。在現實生活中，隨著不同環境的影響和限制，我們須選取不同的網路通道模型來評估網路的可靠性和連通性。在此篇論文中，我們將藉由分析與推導來計算網路中的孤立節點數的期望值與機率分佈。 假設無線網路的節點是以平均值為 的普瓦松點過程分布在邊長為 的正方形區域內，每個節點都具有相同的傳輸功率，且此傳輸功率是固定的，並不會隨著 的大小而改變。若兩個節點的相對距離為 ，則令 代表此兩節點的連線機率。假設 是在 內的遞減函數。令 且 ，其中 是某個常數，並且令 。在此文中，我們證明在一個網路中的孤立節點個數的期望值是 。此外，隨著 ，網路中孤立節點個數的機率分佈將會漸近於以 為平均值的普瓦松分佈。為了驗證理論的正確性，我們模擬了數個較常使用的網路通道模型，並且觀察在不同 大小下，對於網路要達到連通性所需的網路節點數的變化比較。

In large-scale wireless ad hoc networks the exist of isolated nodes can be used as an indicated of network connectivity. In real world, we often use different network channel models to construct networks by considering the effect and restriction of different environment. Evaluating the reliability and connectivity base on the network channel model which be chosen. In this thesis, we will analysis the expected distribution of isolated nodes in networks. Assume wireless nodes are deployed by a Poisson point process with density over a deployment region , and every node has the same transmission power that is fixed and will not change with . Let be the probability of the event that two nodes have a link if they are apart from each other by . Assume is a decreasing function on with bounded supports. Let and for some constant , and let a. In our work, we proved that the expected number of isolated nodes in a network is . In addition, as , the number of isolated nodes is asymptotically Poisson with mean . In order to verity our theorem, we also simulate several popular network channel models and observe the variation of the number of network’s nodes in different while considering the connectivity property.