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