Probability Analysis of Age of Information in Multi-hop Networks

Age-of-information (AoI) is a metric quantifying information freshness at the receiver. It captures the delay together with packet loss and packet generation rate. However, the existing literature focuses on average or peak AoI and neglects the complete distribution. In this work, we consider a N-hop network with time-invariant packet loss probabilities on each link. We derive closed form equations for the probability mass function of AoI. We verify our findings with simulations. Our results show that the performance indicators considered in the literature such as average or peak AoI may give misleading insights into the real AoI performance

Spatial Distribution of the Mean Peak Age of Information in Wireless Networks

This paper considers a large-scale wireless network consisting of source-destination (SD) pairs, where the sources send time-sensitive information, termed status updates, to their corresponding destinations in a time-slotted fashion. We employ Age of information (AoI) for quantifying the freshness of the status updates measured at the destination nodes for two different queuing disciplines, namely Type I and II queues. Type I queue is assumed to transmit the status updates in a first-come-first-served (FCFS) fashion with no storage facility. However, Type I queue may not necessarily minimize AoI because a new update will not be allowed to enter a server until the current update has been successfully transmitted. To overcome this shortcoming, we consider Type II queue in which the most recent status update available at a given transmission slot is transmitted in order to minimize the AoI. As the update delivery rate for a given link is a function of the interference field seen from the receiver, the temporal mean AoI can be treated as a random variable over space. Our goal in this paper is to characterize the spatial distribution of the mean AoI observed by the SD pairs by modeling them as a Poisson bipolar process. Towards this objective, we first derive accurate bounds on the moments of success probability while efficiently capturing the interference-induced coupling in the activities of the SD pairs. Using this result, we then derive tight bounds on the moments as well as the spatial distribution of peak AoI. Our numerical results verify our analytical findings and demonstrate the impact of various system design parameters on the mean peak AoI

Age of Information: An Introduction and Survey

We summarize recent contributions in the broad area of age of information (AoI). In particular, we describe the current state of the art in the design and optimization of low-latency cyberphysical systems and applications in which sources send time-stamped status updates to interested recipients. These applications desire status updates at the recipients to be as timely as possible; however, this is typically constrained by limited system resources. We describe AoI timeliness metrics and present general methods of AoI evaluation analysis that are applicable to a wide variety of sources and systems. Starting from elementary single-server queues, we apply these AoI methods to a range of increasingly complex systems, including energy harvesting sensors transmitting over noisy channels, parallel server systems, queueing networks, and various single-hop and multi-hop wireless networks. We also explore how update age is related to MMSE methods of sampling, estimation and control of stochastic processes. The paper concludes with a review of efforts to employ age optimization in cyberphysical applications