Numerical Flow Optimization in Dense Wireless Sensor Networks

We use a vector field model to formulate flow of information at every point of a dense wireless sensor network. The magnitude of this vector field represents the density of communication activity and its direction is toward the flow of information at each point. We present a general method for flow optimization in a wireless sensor network by minimizing the p-norm of the information flow vector field subject to the basic flow constraints, that is the flow conservation law and boundary constraints. We have called this problem the p-norm flow optimization, and use Sequential Quadratic Programming to solve it. The p-norm flow optimization shows interesting properties for different values of p. For p close to 1, the information routes resemble the geometric shortest paths while as p gets larger, there will be more load balancing effects in the flow. In this work we focus on the numerical analysis of the p-norm flow problem. For this we have to approximate the continuous flow problem by a discrete problem which adds some inaccuracy to the solutions. Therefore, we propose an algorithm to continuously compensate the error in the information flow vector field and avoid error accumulation in the system. We also discuss ways with which we can support different network geometries in the numerical analysis.