Routing in Multi-Commodity Sensor Networks Based on Partial Differential Equations

In this work, a method for routing in a wireless sensor network that carries the traffic of multiple commodities is introduced. A multi-commodity sensor network is an extension of a single commodity sensor network. In a single commodity sensor network, all of the packets generated by the sensors are of the same type, and it is desired that they be sent to one or more sinks in an anycast way. In a multi-commodity sensor network, the packets are categorized into several commodities, and the packets belonging to each commodity must be sent to one of the sinks of that commodity. The single commodity problem is studied in previous work, where we introduced a mathematical framework based on partial differential equations analogous to Maxwell´s equations in electrostatics. In this work we extend the single commodity methodology to multiple commodities. This extension is made by appropriate changes in the cost function of the optimization problem that gives routes. We show that under certain conditions on the cost function, the multi-commodity problem can be decomposed into multiple single commodity problems, and the solution of the multi-commodity problem can be uniquely expressed in terms of the solutions of the single-commodity problems.