In wireless networks, link capacities are variable quantities determined by transmission powers, channel fading levels, user mobility, as well as the underlying coding and modulation schemes. In view of this, the traditional problems of routing and congestion control must now be jointly optimized with power control and rate allocation at the physical layer. To address this, we consider a multi-commodity flow model for interference-limited wireless networks in which power control and routing variables are chosen to minimize convex link costs reflecting, for instance, average queueing delay. We design a set of node-based distributed gradient projection algorithms which iteratively adjust local control variables with a limited exchange of control messages. We explicitly derive the scaling matrices required in the gradient projection algorithms for fast, guaranteed global convergence, and show how the scaling matrices can be computed in a distributed manner. Furthermore, we show that congestion control can be seamlessly incorporated into our framework.
Next, we consider two important extensions of our results. First, recent research on network coding has shown that extending the functionality of network nodes beyond simple routing may have benefits in certain situations. We show that our distributed node-based control algorithms can be extended to achieve minimum-cost multicast in interference-limited wireless networks by jointly optimizing the network coding subgraphs with power control and congestion control schemes. Second, we consider stochastic models of wireless networks where the random nature of traffic arrivals and queueing are explicitly modelled. For these networks, it is well-known that the Maximum Differential Backlog (MDB) control policy of Tassiulas and Ephremides can adaptively maximize the stable throughput. The implementation of the MDB policy in interference-limited wireless networks, however, in general requires centralized computation. For this, we show that our node-based control algorithms can be extended to achieve distributed throughput optimal control of wireless networks with random traffic and queueing.
Joint work with Yufang Xi, Yale University.