Receding Horizon Control for an Online Cross-Layer Design of Wireless Networks Over Time-Varying Stochastic Channels

In this paper, we formulate a network utility maximization (NUM) problem, targeting an optimal cross-layer network operation, while considering time-varying and random possibly non-stationary wireless channels. As indicated in the literature, this problem imposes scalability constraints when the time horizon of the network control increases, impeding an online (i.e., real-time) application of its solution during the network operation. To achieve an online network control, in this paper, we leverage on model predictive control (MPC) or receding horizon control (RHC) for the solution of the NUM problem. Furthermore, MPC/RHC allows for the adaptation of the optimal controls in dynamic and evolving network conditions, in our case with respect to the wireless channels, the modeling parameters of which are estimated in an online fashion. We present and analyze the NUM problem, while we appropriately reformulate it for applying MPC/RHC. Then, we describe the MPC/RHC-based algorithmic solution, which determines the decisions for the online network control including power control, scheduling, routing, and congestion control, while we discuss stability and optimality issues. Finally, we evaluate the proposed methodology via numerical results and we show that the performance lies very close to the optimal one even for relatively small receding horizon lengths that significantly reduce the computational time complexity.

I. Introduction

In this paper, we combine Network Utility Maximization (NUM) [1] with Model Predictive Control (MPC) or Receding Horizon Control (RHC) [2] aiming at an online and adaptive framework for the cross-layer design and operation of wireless multihop networks. NUM has been proven as a very popular tool in the communications research community, for the cross-layer optimization of wireless networks, where typically, a utility function is assigned to each network flow (source-destination pair), and the sum of all utilities over the network is maximized, subject to network capacity region constraints (including link transmission feasibility constraints) [3]. MPC/RHC on its part is applied as it allows for “online” network control, i.e., during the network operation, while being easily adaptive in dynamic and evolving network conditions, e.g., with respect to the network topology, the wireless channels, etc.¹

RHC and MPC will be used interchangeably throughout this paper.