Optimal Control for Uncooperative Networks

Abstract

Modern networks are complex and may include uncooperative components that cannot be fully controlled or observed. However, classic network optimization theory focuses on network models with all nodes being observable and controllable. In this thesis, we focus on developing optimal control algorithms for uncooperative networks with stochastic, non-stochastic or adversarial dynamics.

We start by stabilizing uncooperative networks with stochastic dynamics including external arrivals and uncooperative actions. Such networks can be characterized by overlay-underlay structures, where the network controller can only observe and operate on overlay nodes, and the underlay nodes are not controllable and only have limited observability. We propose the Tracking MaxWeight* (TMW*) algorithm that does not require direct observations of underlay nodes and only operates on overlay nodes. TMW* maintains virtual queues that track the dynamics of the underlay nodes using estimates of the underlay queue backlogs. The controller makes control decisions based on the virtual queues. We show that TMW* is throughput optimal. We further extend our analysis to the setting that the estimates of the underlay state are erroneous and show that as long as the errors scale sub-linearly in time, TMW* preserves throughput optimality.

We extend to uncooperative networks with non-stochastic or even adversarial dynamics. The external arrivals and underlay actions cannot be captured by any stochastic process. Even worse, there might exists an adversary that controls the underlay nodes. The adversary can observe the actions of the network controller and plan its actions accordingly to maximize disruption to the network. We first extend the existing adversarial network models by introducing a new maliciousness metric that constrains the dynamics of the adversary, and characterize the stability region. We show that TMW* is also throughput-optimal for networks with non-stochastic and adversarial dynamics. We also discuss the impact of estimation errors and show that TMW* is throughput optimal if the errors scale sub-linearly in time.

We then turn to the network utility maximization (NUM) problem for uncooperative networks. The network dynamics, such as packet admissions, external arrivals and control actions of underlay nodes, can again be stochastic, non-stochastic or adversarial. We propose the Tracking Drift-plus-Penalty (TDP*) algorithm that only operates on the overlay nodes and does not require direct observations of the underlay nodes. We rigorously analyze the tradeoffs between the average utility and queue backlog. We show that as long as the network is stabilizable, TDP* can solve the NUM, i.e., reaching the maximum utility while preserving stability.

However, application of the NUM is still limited as they require the utility to be a function of packet admissions. We finally attempt to optimize the scheduling for uncooperative networks with general objective functions. We assume that there exists a scheduling algorithm that optimizes certain metrics, but requires instantaneous access to network state information, which is not always available. A naive approach is to make decisions directly with delayed information, but we show that such methods may lead to poor performance. Instead, we propose the Universal Tracking (UT) algorithm that can mimic the actions of arbitrary scheduling algorithms under observation delay. We rigorously show that the performance gap between UT and the scheduling algorithm being tracked is bounded by constants. Our numerical experiments show that UT significantly outperforms the naive approach in various settings.