Control-theoretic Optimization of Utility over Mission Lifetimes in Multi-hop Wireless Networks

Both bandwidth and energy become important resource constraints when multi-hop wireless networks are used to transport relatively high data rate sensor flows. A particularly challenging problem involves the selection of flow data rates that maximize application (or mission) utilities over a time horizon, especially when different missions are active over different time intervals. Prior works on utility driven adaptation of flow data rates typically focus only on instantaneous utility maximization and are unable to address this temporal variation in mission durations. In this work, we derive an optimal control-based Network Utility Maximization (NUM) framework that is able to maximize the system utility over a lifetime that is known either deterministically or statistically. We first consider a static setup in which all the missions are continuously active for a deterministic duration, and show how the rates can be optimally adapted, via a distributed protocol, to maximize the total utility. Next, we develop adaptive protocols for the dynamic cases when we have (i) complete knowledge about the mission utilities and their arrivals and departures, and (ii) a varying amount of statistical information about the missions. Our simulation results indicate that our protocols are robust, efficient and close to the optimal.