On broadcasting time in the model of travelling agents

Consider the following broadcasting process run on a connected graph G=(V,E). Suppose that k≥2 agents start vertices selected from V uniformly and independently at random. One of has message she wants to communicate other agents. All perform independent random walks G, with being passed when an agent knows meets does not know message. The time ξ(G,k) is it takes spread all Our ultimate goal gain better understanding real-world networks roads large cities might shed some light behaviour future autonomous vehicles. Due complexity road networks, such phenomena have be studied using simulation in practical applications. In this paper, we study simplest scenario, i.e., family complete graphs, as case problem analytically tractable. We provide tight bounds for ξ(Kn,k) hold asymptotically almost surely whole range parameter k. These theoretical results reveal interesting relationships and, same time, are also helpful understand explain observe more realistic networks.