Routing in Multi-Commodity Sensor NetworksBased on Partial Differential Equations

摘要

In this work,we introduce a method forrnrouting in a wireless sensor network that carries therntraffic of multiple commodities. A multi-commodity sensorrnnetwork is an extension of a single commodity sensorrnnetwork. In a single commodity sensor network,all ofrnthe packets generated by the sensors are of the same type,rnand it is desired that they be sent to one or more sinksrnin an anycast way. In a multi-commodity sensor network,rnthe packets are categorized into several commodities,andrnthe packets belonging to each commodity must be sent tornone of the sinks of that commodity. We have studied thernsingle commodity problem in our previous work [1],[2],rn[3],where we introduced a mathematical framework basedrnon partial differential equations analogous to Maxwell'srnequations in electrostatics. In this work we extend thernsingle commodity methodology to multiple commodities.rnThis extension is made by appropriate changes in the costrnfunction of the optimization problem that gives routes. Wernshow that under certain conditions on the cost function,rnthe multi-commodity problem can be decomposed intornmultiple single commodity problems,and the solution ofrnthe multi-commodity problem can be uniquely expressedrnin terms of the solutions of the single-commodity problems.