Distributed Cross-Layer Algorithms for the Optimal Control of Multihop Wireless Networks

In this paper, we provide and study a general framework that facilitates the development of distributed mechanisms to achieve full utilization of multihop wireless networks. In particular, we describe a generic randomized routing, scheduling, and flow control scheme that allows for a set of imperfections in the operation of the randomized scheduler to account for potential errors in its operation. These imperfections enable the design of a large class of low-complexity and distributed implementations for different interference models. We study the effect of such imperfections on the stability and fairness characteristics of the system and explicitly characterize the degree of fairness achieved as a function of the level of imperfections. Our results reveal the relative importance of different types of errors on the overall system performance and provide valuable insight to the design of distributed controllers with favorable fairness characteristics. In the second part of the paper, we focus on a specific interference model, namely the secondary interference model, and develop distributed algorithms with polynomial communication and computation complexity in the network size. This is an important result given that earlier centralized throughput-optimal algorithms developed for such a model relies on the solution to an NP-hard problem at every decision. This results in a polynomial complexity cross-layer algorithm that achieves throughput optimality and fair allocation of network resources among the users. We further show that our algorithmic approach enables us to efficiently approximate the capacity region of a multihop wireless network.