Peak Age of Information Distribution for Edge Computing With Wireless Links

Abstract

Age of Information (AoI) is a critical metric for several Internet of Things (IoT) applications, where sensors keep track of the environment by sending updates that need to be as fresh as possible. The development of edge computing solutions has moved the monitoring process closer to the sensor, reducing the communication delays, but the processing time of the edge node needs to be taken into account. Furthermore, a reliable system design in terms of freshness requires the knowledge of the full distribution of the Peak AoI (PAoI), from which the probability of occurrence of rare, but extremely damaging events can be obtained. In this work, we model the communication and computation delay of such a system as two First Come First Serve (FCFS) queues in tandem, analytically deriving the full distribution of the PAoI for the M/M/1 -M/D/1 and the M/M/1 -M/M/1 tandems, which can represent a wide variety of realistic scenarios.

A Stochastic Hybrid Systems Approach to the Joint Distribution of Ages of Information in Networks

“…The process can be repeated to compute V (m1,m2) q (t) for the desired m 1 , m 2 ≥ 2 using V (m1−1,m2) q (t) and V (m1,m2−1) q (t) evaluated in previous steps. Further, by inspecting the structure of C q (t) from ( 9), we note that V (s1,s2) q (t) can be computed from v (s) q (t) and v (0) q (t), where v (s) q (t) can be evaluated from v (0) q (t) using (12).…”

“…Proof: See Appendix B. Theorem 1 is a generalized version of [16, Theorem 1] which was focused on the characterization of the stationary marginal moments and MGFs, i.e., the fixed points of (11) and (12). An interesting analogy between Theorem 1 and [16, Theorem 1] is that the existence of the stationary marginal/joint first moment guarantees the existence of the stationary marginal/joint higher order moments and MGF.…”

Information Freshness Analysis of Slotted ALOHA in Gilbert-Elliot Channels

“…1). The metric offers an important design tool in settings where relying on exceedingly stale information may not be tolerated (e.g., control systems), and captures in the special case m = 1 the peak age violation probability [14], [15]. We furthermore note that the presented analytical approach can be extended to a wider class of penalty functions [16] with minor effort, as will be discussed at the end of Sec.…”

Latency and Information Freshness in Multipath Communications for Virtual Reality

“…Initial studies focused on simple queuing systems with a single node and unicast scheduled transmissions [39], [40]. However, there is already a significant number of papers addressing more complex communication scenarios and topologies, like for instance models for random access and ALOHA [41] [42], multi-cast and broadcast [43], or multi-hop transmissions [44], [45].…”