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

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 distribu...

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Vydáno v:IEEE transactions on information theory Ročník 65; číslo 12; s. 8305 - 8324
Hlavní autoři: Inoue, Yoshiaki, Masuyama, Hiroyuki, Takine, Tetsuya, Tanaka, Toshiyuki
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York IEEE 01.12.2019
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
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
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Shrnutí: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.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2019.2938171