Age Of Information Distribution Research Articles

Age Analysis of Status Updating System with Probabilistic Packet Preemption.

The age of information (AoI) metric was proposed to measure the freshness of messages obtained at the terminal node of a status updating system. In this paper, the AoI of a discrete time status updating system with probabilistic packet preemption is investigated by analyzing the steady state of a three-dimensional discrete stochastic process. We assume that the queue used in the system is , which represents that the system size is 2 and the packet in the buffer can be preempted by a fresher packet with probability . Instead of considering the system’s AoI separately, we use a three-dimensional state vector to simultaneously track the real-time changes of the AoI, the age of a packet in the server, and the age of a packet waiting in the buffer. We give the explicit expression of the system’s average AoI and show that the average AoI of the system without packet preemption is obtained by letting . When is set to 1, the mean of the AoI of the system with a queue is obtained as well. Combining the results we have obtained and comparing them with corresponding average continuous AoIs, we propose a possible relationship between the average discrete AoI with the queue and the average continuous AoI with the queue. For each of two extreme cases where and , we also determine the stationary distribution of AoI using the probability generation function (PGF) method. The relations between the average AoI and the packet preemption probability , as well as the AoI’s distribution curves in two extreme cases, are illustrated by numerical simulations. Notice that the probabilistic packet preemption may occur, for example, in an energy harvest (EH) node of a wireless sensor network, where the packet in the buffer can be replaced only when the node collects enough energy. In particular, to exhibit the usefulness of our idea and methods and highlight the merits of considering discrete time systems, in this paper, we provide detailed discussions showing how the results about continuous AoI are derived by analyzing the corresponding discrete time system and how the discrete age analysis is generalized to the system with multiple sources. In terms of packet service process, we also propose an idea to analyze the AoI of a system when the service time distribution is arbitrary.

On the Age of Information in a Two-User Multiple Access Setup.

This work considers a two-user multiple access channel in which both users have Age of Information (AoI)-oriented traffic with different characteristics. More specifically, the first user has external traffic and cannot control the generation of status updates, and the second user monitors a sensor and transmits status updates to the receiver according to a generate-at-will policy. The receiver is equipped with multiple antennas and the transmitters have single antennas; the channels are subject to Rayleigh fading and path loss. We analyze the average AoI of the first user for a discrete-time first-come-first-served (FCFS) queue, last-come-first-served (LCFS) queue, and queue with packet replacement. We derive the AoI distribution and the average AoI of the second user for a threshold policy. Then, we formulate an optimization problem to minimize the average AoI of the first user for the FCFS and LCFS with preemption queue discipline to maintain the average AoI of the second user below a given level. The constraints of the optimization problem are shown to be convex. It is also shown that the objective function of the problem for the first-come-first-served queue policy is non-convex, and a suboptimal technique is introduced to effectively solve the problem using the algorithms developed for solving a convex optimization problem. Numerical results illustrate the performance of the considered optimization algorithm versus the different parameters of the system. Finally, we discuss how the analytical results of this work can be extended to capture larger setups with more than two users.

Status Update in IoT Networks: Age-of-Information Violation Probability and Optimal Update Rate

The Internet of Things (IoT) has emerged as one of the key features of the next-generation wireless networks, where timely delivery of status update packets is essential for many real-time IoT applications. Age of Information (AoI) is a new metric to measure the freshness of update. The reduction of the violation probability that AoI of status updates exceeds a given age constraint is of great significance for guaranteeing the information freshness in IoT systems. By modeling the IoT networks as M/M/1 and M/D/1 queuing systems, this work focuses on characterizing the violation probability of peak AoI and AoI in IoT systems, where a sensor delivers updates to a monitor under M/M/1 and M/D/1 queues with first-come-first-served policy. From a time-domain perspective, we explore the correlation between interdeparture time and system time, by which the closed-form expressions of peak AoI distribution and the violation probability for any AoI constraint are derived. The obtained results induce accurate characterizations for probability distribution functions of peak AoI and AoI. Consequently, accurate characterizations of average AoI and the variance of AoI are obtained. Then, for peak AoI and AoI, the optimal generation rate of the status update that induces the minimal violation probability is also found. The numerical results show that the optimal update rate can significantly reduce the AoI violation probability for a wide range of AoI constraints. The theoretical findings and predictions are verified by numerical simulation results as well as provide guidance for the design of IoT networks.

Optimized Age of Information Tail for Ultra-Reliable Low-Latency Communications in Vehicular Networks

While the notion of age of information (AoI) has recently been proposed for analyzing ultra-reliable low-latency communications (URLLC), most of the existing works have focused on the average AoI measure. Designing a wireless network based on average AoI will fail to characterize the performance of URLLC systems, as it cannot account for extreme AoI events, occurring with very low probabilities. In contrast, this paper goes beyond the average AoI to improve URLLC in a vehicular communication network by characterizing and controlling the AoI tail distribution. In particular, the transmission power minimization problem is studied under stringent URLLC constraints in terms of probabilistic AoI for both deterministic and Markovian traffic arrivals. Accordingly, an efficient novel mapping between AoI and queue-related distributions is proposed. Subsequently, extreme value theory (EVT) and Lyapunov optimization techniques are adopted to formulate and solve the problem considering both long and short packets transmissions. Simulation results show over a two-fold improvement, in shortening the AoI distribution tail, versus a baseline that models the maximum queue length distribution, in addition to a tradeoff between arrival rate and AoI.

Statistical Guarantee Optimization for AoI in Single-Hop and Two-Hop FCFS Systems With Periodic Arrivals

Age of Information (AoI) has proven to be a useful metric in networked systems where timely information updates are of importance. In the literature, minimizing “average age” has received considerable attention. However, various applications pose stricter age requirements on the updates which demand knowledge of the AoI distribution. Furthermore, the analysis of AoI distribution in a multi-hop setting, which is important for the study of Wireless Networked Control Systems (WNCS), has not been addressed before. Toward this end, we study the distribution of AoI in a WNCS with two hops and devise a problem of minimizing the tail of the AoI distribution with respect to the frequency of generating information updates, i.e., the sampling rate of monitoring a process, under first-come-first-serve (FCFS) queuing discipline. We argue that computing an exact expression for the AoI distribution may not always be feasible; therefore, we opt for computing upper bounds on the tail of the AoI distribution. Using these upper bounds, we formulate Upper Bound Minimization Problems (UBMP), namely, Chernoff-UBMP and α-relaxed Upper Bound Minimization Problem (α-UBMP), where α > 1 is an approximation factor, and solve them to obtain “good” heuristic rate solutions for minimizing the tail. We demonstrate the efficacy of our approach by solving the proposed UBMPs for three service distributions: geometric, exponential, and Erlang. Simulation results show that the rate solutions obtained are near optimal for minimizing the tail of the AoI distribution for the considered distributions.