The Age of Information in a Discrete Time Queue: Stationary Distribution and Non-Linear Age Mean Analysis
2021 (English)In: IEEE Journal on Selected Areas in Communications, ISSN 0733-8716, E-ISSN 1558-0008, Vol. 39, no 5, p. 1352-1364Article in journal (Refereed) Published
Abstract [en]
In this work, we investigate information freshness in a status update communication system consisting of a source-destination link. Initially, we study the properties of a sample path of the age of information (AoI) process at the destination. We obtain a general formula of the stationary distribution of the AoI, under the assumption of ergodicity. We relate this result to a discrete time queueing system and provide a general expression of the generating function of AoI in relation with the system time and the peak age of information (PAoI) metric. Furthermore, we consider three different single-server system models and we obtain closed-form expressions of the generating functions and the stationary distributions of the AoI and the PAoI. The first model is a first-come-first-served (FCFS) queue, the second model is a preemptive last-come-first-served (LCFS) queue, and the last model is a bufferless system with packet dropping. We build upon these results to provide a methodology for analyzing general non-linear age functions for this type of systems, using representations of functions as power series.
Place, publisher, year, edition, pages
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC , 2021. Vol. 39, no 5, p. 1352-1364
Keywords [en]
Information age; Probability distribution; Delays; Transmitters; Servers; Receivers; Random processes; Age of information; discrete time systems; non-linear age functions; stationary distribution
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-175839DOI: 10.1109/JSAC.2021.3065045ISI: 000641962200013OAI: oai:DiVA.org:liu-175839DiVA, id: diva2:1557453
Note
Funding Agencies|European UnionEuropean Commission [642743]; ELLIIT; Center for Industrial Information Technology (CENIIT); U.S. Office of Naval ResearchOffice of Naval Research [ONR 5-280542]; U.S. National Science FoundationNational Science Foundation (NSF) [CIF 5-243150, 5-245770, CIF 5-231912]; Swedish Research Council (VR)Swedish Research Council
2021-05-262021-05-262021-05-26