Theoretically optimal performance and behavior of a routing protocol are very important because they can be used to guide the design of practical protocols. Motivated by the promising lifetime performance of an existing online cooperative transmission (CT) routing protocol for wireless sensor networks (WSNs), we formulate the lifetime optimization problem of cooperative routing using linear programming (LP), which requires considerations of CT's unique characteristics and sophisticated variable definitions. By using our LP, one can obtain the optimal lifetime of multi-hop WSNs that use cooperative routing, which can serve as a performance bound or a benchmark to compare to the lifetimes of existing routing protocols. Through the evaluations of our LP, we show the benefit of cooperative routing and usefulness of our LP formulation.
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