Abstract
In many complex networks, such as communication networks, power grids, and transportation networks, the main task is load transmission from sources to destinations. Therefore, the transmission throughput is a very important indicator to measure the network performance, and improving the throughput becomes one of the hotspots in the research of these complex networks. Many researchers have proposed different routing algorithms to improve the network throughput. However, few of them considered the spatial location of nodes in the network. Indeed, many real-world networks can be modeled by spatial networks, where the spatial location of nodes plays a vital role in determining the structure and dynamic behaviors of such networks. Specifically, when the locations of nodes are considered, each link has a length. And the shortest path may have different meaning. Traditionally, the shortest path indicates the path which passes the least number of links from source to destination, or the least number of hops. However, when the length of link is taken into account, the least number of links does not mean the least summation of link lengths along the path. The latter can be called the shortest path length. To this end, we proposes an efficient routing strategy for spatial networks based on the shortest path length in this work. In order to test the effectiveness of the algorithm, the network throughput <inline-formula><tex-math id="M1">\begin{document}${R}_{\rm c}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20211621_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20211621_M1.png"/></alternatives></inline-formula> is used, at which the network changes from a free flow state to a congestion state, to measure the performance of the network. Simulations of homogeneous and heterogeneous spatial networks show that compared with the traditional least number of hops routing strategy, the routing algorithm based on the shortest path length proposed in this paper can effectively improve the throughput of the network. The routing algorithm proposed in this paper can be applied to many real-world spatial networks for improving their performances.
Highlights
Node i connects all nodes in its connection area
参考文献 [1] Erdös P, Rényi A 1959 Publ
Summary
20 世纪 50 年代末,Erdős 与 Rényi 提出的 ER 随机图模型[1]开辟了复杂网络 传统意义上的最短路径的策略是目前应用较为广泛的一种路由方式,即负载 从节点 A 通过最少的边数传输到节点 B,但是这种方式很容易在一些度值较大的 节点处造成拥塞现象[10]。因此,不少研究人员提出了更加高效的路由策略[10,11,12,13,14,15,16,17,18,19,20]。 Yan 等人提出了一种“the efficient path”的路由策略[18],定义任意两点i和j之间的 路径为L(P(i → j): β) = ∑ k(x ) ,以min(L)为目标选择路径,通过绕开度值 较大的节点来减少发生拥塞的可能,大大提升网络的传输性能。Huang 等人提出 了一种带记忆信息的路由策略[19],节点记录负载的传输来源,避免出现回溯现 象,使得负载在两个不同节点之间来回传输的机会大大减少,有效地提高网络吞 吐量。Wang 等人提出了一种流量模型[20],负载从节点a传输到节点b,若节点a与 b之间有边连接,则负载可直接传输至目标节点b;否则,将以Π = 的概率 本文提出一种基于最短路径长度的空间路由方式,即负载从源节点沿着最短 路径长度的方向传输到目标节点。考虑到 Zhao 等人在 2005 年发表的文章[26]中 指出,不同结构的网络出现拥塞现象的性能也不相同。因此,本文也考虑了空间 匀质网络和异质网络两种情况,在随机几何图[27]和“Local − Area and Energy − Efficient Evolution”模型[28](LAEE 模型)上进行了仿真模拟。仿真结果表明, 本文提出的路由策略能够有效提升网络的传输性能,减少拥塞现象的发生。 P(k) ∝ k ,其中k表示节点的度、γ为一常数。为了探究本文提出的路由算法在 异质网络上的适用性,我们采用 Jiang 等人在提出的具有无标度特性的空间 LAEE 演化模型[28]。 的度值,q是已经达到k 的节点的个数,f(E )是一功能函数,为了方便处理, 这里取f(E ) = 1。 Step 4.
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