Scaling laws for reliable data dissemination in shared loss multicast trees

The completion time for the dissemination of information to all nodes in a network plays a critical role in the design and analysis of communication systems. In this work, we analyse the completion time of data dissemination in a shared loss (i.e., unreliable links) multicast tree, at the limit of large number of nodes. Specifically, analytic expressions for upper and lower bounds on the expected completion time are provided, and, in particular, it is shown that both these bounds scale as α log n, where n is the number of nodes. Clearly, the completion time is determined by the last end user who receives the message, that is, a maximum over all arrival times. We derive asymptotic bounds on the expectation of this maximum and use them to obtain tight bounds on the completion time. The results are validated by simulations and numerical analysis.