Little Tom Thumb Went Straight Home: Asymptotic Behavior of a Routing Protocol in Ad-hoc Networks with a Mobile Access Point

The task of routing streaming data in a sensor network is made arduous by the resource constraints imposed on each node. The control overhead of a routing protocol has to be minimized in order to preserve limited resources at the node. Furthermore, it is widely expected that the gateway of the sensor network will not be static in many application scenarios, but will be moving around the network. The gateway could move to collect data, or because it is not associated with a specific location, but with a specific mobile user. We study a simple protocol and consider the cost it imposes on the networks in terms of number of messages sent, or equivalently, bandwidth or power usage. We study the scaling behavior of the so-called bread crumbs (BC) protocol, and show that it is optimal in its scaling behavior in one-and two-dimensional graphs. The BC protocol is thus named as the mobile gateway leaves a trail in the network as it moves about, as Little Tom Thumb, or Hansel and Gretel do in the forest, in the well-known fairy tales. The BC protocol routes packets along the path followed by the mobile sink, taking short cuts whenever possible. We compare this protocol with the cost of routing on the shortest path from the sensor node to the mobile sink, and with the cost of flooding the network in the hope of finding the sink. We show that the path attained with the BC protocol is asymptotically optimal, and scales as the shortest path. We support the analysis with some simulations and also consider a one step diffusion extension of the bread crumbs protocol as well.