Stability and sensitivity for congestion control in wireless networks with time varying link capacities

While extensive efforts have been devoted to providing optimization based, distributed congestion control schemes for efficient bandwidth utilization and fair allocation in both wireline and wireless networks, a common assumption therein is fixed link capacities. This unfortunately will limit the application scope in multi-hop wireless networks where channels are ever changing. In this paper, we explicitly model link capacities to be time varying and investigate congestion control problems in multi-hop wireless networks. In particular we propose a primal-dual congestion control algorithm which is proved to be trajectory stable in the absence of feedback delay. Different from system stability around a single equilibrium point, trajectory stability Guarantees the system is stable around a time varying reference trajectory. Moreover, we obtain sufficient conditions for the scheme to be locally stable in the presence of delay. Our key technique is to model time variations of capacities as perturbations to a constant link. Furthermore, to study the robustness of the algorithm against capacity variations, we investigate the sensitivity of the control scheme and through simulations to study the tradeoff between stability and sensitivity.