Optimal forwarding ratio on dynamical networks with heterogeneous mobility

As the discovery of non-Poissonian statistics of human mobility trajectories, more attention has been paid to understanding the role of these patterns in different dynamics. In this study, we first introduce the heterogeneous mobility of mobile agents into dynamical networks, and then investigate the forwarding strategy on the heterogeneous dynamical networks. We find that the faster speed and the higher proportion of high-speed agents can enhance the network throughput and reduce the mean traveling time in the case of random forwarding. A hierarchical structure in the dependence of high-speed is observed: the network throughput remains unchanged in small and large high-speed value. It is interesting to find that the slightly preferential forwarding to high-speed agents can maximize the network capacity. Through theoretical analysis and numerical simulations, we show that the optimal forwarding ratio stems from local structural heterogeneity of low-speed agents. Introduction. – The notion of mobile agent is really important in the study of many dynamical systems, such as collective motion in biology [1], information transmission on wireless ad-hoc network [2], and traffic congestion in city transportation system [3]. In all of these dynamical systems, each mobile agent is free to move independently in any direction, and locally interacts with current nearby agents. Take wireless ad-hoc network for example [2]. The continuous movement of mobile devices would frequently change their links to other devices due to limited forwarding range. Thus, these dynamical systems can be treated primitively as dynamical networks, in which connections between nodes always change temporarily. Network theory provides therefore a natural framework to study the emergence of structural and dynamical properties of these systems [4–8]. Physicists recently became increasingly fascinated by the dynamics on dynamical networks, such as epidemic spreading of mobile individuals [9–13], synchronization of mobile oscillators [14–16], and consensus of communicat(a)E-mail:[email protected] ing agents [17]. Especially for packet forwarding of mobile devices, how to enhance transmission efficiency has become a crucial problem due to the rapid development of wireless communication technology. Considering costs and technology limitations, more efforts should be made to improve the routing strategy [2,18–23]. Yang et al. first studied transportation dynamics on dynamical networks [24], and compared random routing with greedy routing [25]. However, the previous researches have only focused on the case of identical mobile agents, which can not reflect the diversity of mobile individuals. Since the discovery of non-Poissonian statistics of human behaviors such as human interaction activities [26] and mobility trajectories [27, 28], more and more scientists have been paying attention to the role of these patterns in different dynamics. Most recent research results showed that both time and space activities have significant impacts on spreading dynamics [29–36]. In this letter, we introduce the heterogeneous mobility of mobile agents into dynamical networks, and then propose an optimal forwarding strategy on the dynamical networks with heterogeneous mobility.