Estimating the Number of Nodes in a Mobile Wireless Network

Collecting information from mobile wireless networks has important civilian and military applications. One problem is to determine the number of nodes in a large wireless system. In a stationary wireless network, it can be trivially solved through a flooding-based query. However, the problem becomes much more challenging for mobile ad-hoc networks whose topologies are constantly changing. In this paper, we present two novel statistical methods, called the circled random walk and the tokened random walk, to address this interesting problem. These methods provide an estimation by involving only a small subset of the nodes. They make tradeoff between the overhead and the estimation accuracy. The estimation error can be made arbitrarily small at the expense of larger overhead.