Central Limit Theorem for Time to Broadcast on [o,L]

We study the problem of broadcasting in a system where n nodes are placed on a line of length L independently uniformly distributed. We assume that every node is equipped with a transmitter whose radius of transmission is 1. A message originating at the node at the origin is to be transmitted to all the nodes in the system. We prove the central limit theorem and the law of large numbers for the number of time steps required to complete a broadcast. 1 Introduction Broadcasting refers to the problem of information dessemination in systems where one node has some information that needs to be transmitted to all the other nodes. This problem has traditionally been studied in a variety of systems represented as graphs where an edge between two nodes indicates that these two nodes can communicate, [2]. The primary focus of most work has been to determine bounds and/or algorithms for the minimum time to broadcast and the minimum number of calls required to complete a broadcast 1 . Our mode..