Age of Information: Fundamentals, Distributions, and Applications

A typical model for real-time status update systems consists of a transmitter node that generates real-time status updates about some physical process(es) of interest and sends them through a communication network to a destination node. Such a model can be used to analyze the performance of a plethora of emerging Internet of Things (IoT)-enabled real-time applications including healthcare, factory automation, autonomous vehicles, and smart homes, to name a few. The performance of these applications highly depends upon the freshness of the information status at the destination node about its monitored physical process(es). Because of that, the main design objective of such real-time status update systems is to ensure timely delivery of status updates from the transmitter node to the destination node. To measure the freshness of information at the destination node, the Age of Information (AoI) has been introduced as a performance metric that accounts for the generation time of each status update (which was ignored by conventional performance metrics, specifically throughput and delay). Since then, there have been two main research directions in the AoI research area. The first direction aimed to analyze/characterize AoI in different queueing-theoretic models/disciplines, and the second direction was focused on the optimization of AoI in different communication systems that deal with time-sensitive information. However, the prior queueing-theoretic analyses of AoI have mostly been limited to the characterization of the average AoI and the prior studies developing AoI/age-aware scheduling/transmission policies have mostly ignored the energy constraints at the transmitter node(s). Motivated by these limitations, this dissertation develops new queueing-theoretic methods that allow the characterization of the distribution of AoI in several classes of status updating systems as well as novel AoI-aware scheduling policies accounting for the energy constraints at the transmitter nodes (for several settings of communication networks) in the process of decision-making using tools from optimization theory and reinforcement learning.

The first part of this dissertation develops a stochastic hybrid system (SHS)-based general framework to facilitate the analysis of characterizing the distribution of AoI in several classes of real-time status updating systems. First, we study a general setting of status updating systems, where a set of source nodes provide status updates about some physical process(es) to a set of monitors. For this setting, the continuous state of the system is formed by the AoI/age processes at different monitors, the discrete state of the system is modeled using a finite-state continuous-time Markov chain, and the coupled evolution of the continuous and discrete states of the system is described by a piecewise linear SHS with linear reset maps. Using the notion of tensors, we derive a system of linear equations for the characterization of the joint moment generating function (MGF) of an arbitrary set of age processes in the network. Afterwards, we study a general setting of gossip networks in which a source node forwards its measurements (in the form of status updates) about some observed physical process to a set of monitoring nodes according to independent Poisson processes. Furthermore, each monitoring node sends status updates about its information status (about the process observed by the source) to the other monitoring nodes according to independent Poisson processes. For this setup, we develop SHS-based methods that allow the characterization of higher-order marginal/joint moments of the age processes in the network. Finally, our SHS-based framework is applied to derive the stationary marginal and joint MGFs for several queueing disciplines and gossip network topologies, using which we derive closed-form expressions for marginal/joint high-order statistics of age processes, such as the variance of each age process and the correlation coefficients between all possible pairwise combinations of age processes.

In the second part of this dissertation, our analysis is focused on understanding the distributional properties of AoI in status updating systems powered by energy harvesting (EH). In particular, we consider a multi-source status updating system in which an EH-powered transmitter node has multiple sources generating status updates about several physical processes. The status updates are then sent to a destination node where the freshness of each status update is measured in terms of AoI. The status updates of each source and harvested energy packets are assumed to arrive at the transmitter according to independent Poisson processes, and the service time of each status update is assumed to be exponentially distributed. For this setup, we derive closed-form expressions of MGF of AoI under several queueing disciplines at the transmitter, including non-preemptive and source-agnostic/source-aware preemptive in service strategies. The generality of our analysis is demonstrated by recovering several existing results as special cases. A key insight from our characterization of the distributional properties of AoI is that it is crucial to incorporate the higher moments of AoI in the implementation/optimization of status updating systems rather than just relying on its average (as has been mostly done in the existing literature on AoI).

In the third and final part of this dissertation, we employ AoI as a performance metric for several settings of communication networks, and develop novel AoI-aware scheduling policies using tools from optimization theory and reinforcement learning. First, we investigate the role of an unmanned aerial vehicle (UAV) as a mobile relay to minimize the average peak AoI for a source-destination pair. For this setup, we formulate an optimization problem to jointly optimize the UAV's flight trajectory as well as energy and service time allocations for packet transmissions. This optimization problem is subject to the UAV's mobility constraints and the total available energy constraints at the source node and UAV. In order to solve this non-convex problem, we propose an efficient iterative algorithm and establish its convergence analytically. A key insight obtained from our results is that the optimal design of the UAV's flight trajectory achieves significant performance gains especially when the available energy at the source node and UAV is limited and/or when the size of the update packet is large. Afterwards, we study a generic system setup for an IoT network in which radio frequency (RF)-powered IoT devices are sensing different physical processes and need to transmit their sensed data to a destination node. For this generic system setup, we develop a novel reinforcement learning-based framework that characterizes the optimal sampling policy for IoT devices with the objective of minimizing the long-term weighted sum of average AoI values in the network. Our analytical results characterize the structural properties of the age-optimal policy, and demonstrate that it has a threshold-based structure with respect to the AoI values for different processes. They further demonstrate that the structures of the age-optimal and throughput-optimal policies are different. Finally, we analytically characterize the structural properties of the AoI-optimal joint sampling and updating policy for wireless powered communication networks while accounting for the costs of generating status updates in the process of decision-making. Our results demonstrate that the AoI-optimal joint sampling and updating policy has a threshold-based structure with respect to different system state variables.