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Routing and Topology Design of Hierarchical Sensor Networks
Prof. Mark Shayman

 Dr. Mark Shayman

A sensor network is a collection of low power devices that can collect data by sensing their environment and can send the data to one or more destination nodes that can process the sensor data in order to extract useful information. The communication of data from a sensor node to a destination may traverse intermediate sensor nodes that use wireless transmission to forward the messages.

In a network with high sensor node density, it may be more scalable to approximately represent the network by a continuous, rather than discrete, distribution of nodes. If this viewpoint is taken, a vector field can be associated with each point in the network. The direction of this vector field specifies how messages are routed at each point, while the magnitude represents the communication load that must be transmitted. Mathematically, this vector field is analogous to the electric displacement vector field in electrostatics. In fact, a strong analogy can be made with electrostatics in which sources of information correspond to positive charges, destinations of information to negative charges, and the network to a nonhomogeneous dielectric medium. Minimizing a quadratic functional of the communication load corresponds to minimizing electrostatic energy and leads to partial differential equations for optimal routing that are analogous to Maxwell’s equations. The solution to the partial differential equations gives a potential function whose gradient yields the routes.

When there are multiple destinations for the sensor messages, an important problem is to determine to which destination the messages generated by a particular sensor flow are directed. If the designer specifies how much message load is to be received by each destination, then the potential function specifies the routes and hence the region of attraction of each destination. It turns out that the distribution of load among the destinations is optimal when the value of the potential function is equal at every destination. By using a simple iterative procedure, the optimal load distribution can be obtained.

This research has received support from the National Science Foundation (NSF).