Figure 1. The number of extreme events versus velocity and mobility.

For a network of N = 1200 nodes in a square domain of size L = 10 (arbitrary unit), (a), The number of extreme events n_ex versus the agent velocity v for W = 50N, 80N, and 100N; (b), n_ex of extreme events versus velocity v when nodes execute random walk (R) or deterministic motion (D) within square, circular, and stadium-shaped domains. The areas of the circle and the stadium are chosen to be equal to the area of the square L × L. (c), Robustness of control with respect to heterogeneity in the nodal communication range: n_ex versus v for β = −1, 0, and 1, where β is a parameter characterizing the distribution of nodal communication range. (d) and (e), robustness of control with respect to packet-transportation protocol: n_ex versus velocity v when packet generation and annihilation are taken into account for two situations where (d) the total number of packets is fixed at W and (e) the number of newly generated packets at each time step is fixed to be W/N. (f), Generalization of mobility: n_ex versus mobility, defined as the probability that a node moves with velocity v, for a number of v values. All simulation results are obtained using 100 realizations in T = 1000 time steps. The error bars in n_ex from different realizations have relatively small and similar magnitude in (a–e), and it monotonously increases with velocity v, as shown in panel (a) [the error bars in (b–e) are omitted for clear visualization]. Here, the definition of an extreme event on a node is that its number of packets is at least four standard-deviations above the average.