A General Formula for the Stationary Distribution of the Age of Information and Its Application to Single-Server Queues

• Published in: IEEE transactions on information theory Vol. 65; no. 12; pp. 8305 - 8324
• Main Authors: Inoue, Yoshiaki, Masuyama, Hiroyuki, Takine, Tetsuya, Tanaka, Toshiyuki
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.12.2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Age of information; Delays; FCFS; Information age; Markov analysis; Monitoring; non-preemptive LCFS; peak AoI; Preempting; preemptive LCFS; Queueing analysis; Queues; Queuing theory; Servers; single-server queues; stationary distribution; Upgrading
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2019.2938171

This paper considers the stationary distribution of the age of information (AoI) in information update systems. We first derive a general formula for the stationary distribution of the AoI, which holds for a wide class of information update systems. The formula indicates that the stationary distribution of the AoI is given in terms of the stationary distributions of the system delay and the peak AoI. To demonstrate its applicability and usefulness, we analyze the AoI in single-server queues with four different service disciplines: first-come first-served (FCFS), preemptive last-come first-served (LCFS), and two variants of non-preemptive LCFS service disciplines. For the FCFS and the preemptive LCFS service disciplines, the GI/GI/1, M/GI/1, and GI/M/1 queues are considered, and for the non-preemptive LCFS service disciplines, the M/GI/1 and GI/M/1 queues are considered. With these results, we further show comparison results for the mean AoI's in the M/GI/1 and GI/M/1 queues under those service disciplines.