Scheduling in Networks With Time-Varying Channels and Reconfiguration Delay

Abstract

We consider the optimal control problem for networks subjected to time-varying channels, reconfiguration delays, and interference constraints. We show that the simultaneous presence of time-varying channels and reconfiguration delays significantly reduces the system stability region and changes the structure of optimal policies. We first consider memoryless channel processes and characterize the stability region in closed form. We prove that a frame-based Max-Weight scheduling algorithm that sets frame durations dynamically, as a function of the current queue lengths and average channel gains, is throughput-optimal. Next, we consider arbitrary Markov-modulated channel processes and show that memory in the channel processes can be exploited to improve the stability region. We develop a novel approach to characterizing the stability region of such systems using state-action frequencies, which are stationary solutions to a Markov Decision Process (MDP) formulation. Moreover, we develop a dynamic control policy using the state-action frequencies and variable frames whose lengths are functions of queue sizes and show that it is throughput-optimal. The frame-based dynamic control (FBDC) policy is applicable to a broad class of network control systems, with or without reconfiguration delays, and provides a new framework for developing throughput-optimal network control policies using state-action frequencies. Finally, we propose Myopic policies that are easy to implement and have better delay properties as compared to the FBDC policy.

A Convex Optimization Approach to Discrete Optimal Control

“…This type of constraint appears in a variety of applicationsthey are usually known in the literature as reconfiguration or switchover delays [20]-and capture the cost of selecting a "new" control action. In this wireless communication example, the requirement of selecting action y(0) every time the AP wants to change from action y(1) to y(2) and from y(2) to y(1) might be regarded as the time required for measuring Channel State Information (CSI) in order to adjust the transmission parameters.…”

Spatiotemporal Model for Uplink IoT Traffic: Scheduling and Random Access Paradox

“…However, stand-alone stochastic geometry analysis fails to account for the temporal aspects of the IoT such as traffic intensity per device and data accumulation in buffers. The temporal aspects within scheduling problems are usually captured via interacting queueing models [14]- [16], however, the work in [14]- [16] does not account for the spatial aspects (e.g., node density and mutual interference) that govern the interactions between the queues. Recently, spatiotemporal models that integrate stochastic geometry and queueing theory are proposed to jointly account for per-device traffic intensity, spatial device density, medium access control (MAC) scheme, devices' buffer states, and the mutual interference between devices [17]- [26].…”

Throughput-Optimal Scheduling for Multi-Hop Networked Transportation Systems With Switch-Over Delay

“…In B-MP, time is divided into consecutive superframes. At the beginning of a superframe, the duration of a superframe is calculated by (6). Whenever a connected intersection switches, it always switches to the phase with the maximum pressure, and therefore B-MP is max-pressure-at-switch-over.…”

“…LEMMA 2. For any max-pressure-at-switch-over scheduling policy with superframe determined by (6), if there exists some constant B0 > 0, 0 > 0 and the conditional drift satisfies that…”

“…Throughout the simulation, we assume that the fixed-time policy has perfect information about the average traffic statistics of each link and therefore is able to optimize the timing plan accordingly. For VFMW, we choose the frame size to be TS + (i,j)∈Mv Qi,j(t k ) 0.9 as suggested in [6]. For the B-MP policy, we choose α = 0.01 and β = 0.99 as discussed in Section 5.2.…”