In large-scale sensor networks with monitoring applications, sensor nodes are responsible to send periodic reports to the destination which is located far away from the area to be monitored. We model this area (referred to as the distributed source) with a positive load density function which determines the total rate of traffic generated inside any closed contour within the area.

With tight limitations in energy consumption of wireless sensors and the many-to-one nature of communications in wireless sensor networks, the traditional definition of connectivity in graph theory does not seem to be sufficient to satisfy the requirements of sensor networks. In this work, a new notion of connectivity (called implementability) is defined which represents the ability of sensor nodes to relay traffic along a given direction field, referred to as information flow vector field $\vec{D}$. The magnitude of information flow is proportional to the traffic flux (per unit length) passing through any point in the network, and its direction is toward the flow of traffic. The flow field may be obtained from engineering knowledge or as a solution to an optimization problem. In either case, information flow flux lines represent a set of abstract paths (not constrained by the actual location of sensor nodes) which can be used for data transmission to the destination. In this work, we present conditions to be placed on $\vec{D}$ such that the resulting optimal vector field generates a desirable set of paths.

In a sensor network with a given irrotational flow field $\vec{D}(x,y)$, we show that a density of $n(x,y)=O(|\vec{D}(x,y)|^2)$ sensor nodes is not sufficient to implement the flow field as $|\vec{D}|$ scales linearly to infinity. On the other hand, by increasing the density of wireless nodes to $n(x,y)=O(|\vec{D}(x,y)|^2 \log |\vec{D}(x,y)|)$, the flow field becomes implementable. Implementability requires more nodes than simple connectivity. However, results on connectivity are based on the implicit assumption of exhaustively searching all possible routes which contradicts the tight limitation of energy in sensor networks. We propose a joint MAC and routing protocol to forward traffic along the flow field. The proposed tier-based scheme can be further exploited to build lightweight protocol stacks which meet the specific requirements of dense sensor networks.

We also investigate buffer scalability of sensor nodes routing along flux lines of a given irrotational vector field, and show that nodes distributed according to the sufficient bound provided above can relay traffic from the source to the destination with sensor nodes having limited buffer space. This is particularly interesting for dense wireless sensor networks where nodes are assumed to have very limited resources.