Meeting of Randomly Moving Messages in a Mobile ad-hoc Network

The mobility of ad hoc networks requires solutions that are adaptive to topological changes. Random walks offer a topology-adaptive traversal scheme that can be used in such a context. In random walk based distributed algorithms, topology changes are no fault, which leaves two major fault types (i) the absence of token in the system, (ii) the presence of more than one token in the system. In this paper, we focus on the presence of several token. When a node owns two tokens at a time, it deletes one of them and sends only one token. The purpose of this paper is to give an algorithm to compute the average time for several tokens to meet and be merged, hence the stabilization time of a random walk circulation when several tokens are present.