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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Vydané v:	IEEE transactions on information theory Ročník 65; číslo 12; s. 8305 - 8324
Hlavní autori:	Inoue, Yoshiaki, Masuyama, Hiroyuki, Takine, Tetsuya, Tanaka, Toshiyuki
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York IEEE 01.12.2019 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:	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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Abstract	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.
AbstractList	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.
Author	Masuyama, Hiroyuki Takine, Tetsuya Inoue, Yoshiaki Tanaka, Toshiyuki
Author_xml	– sequence: 1 givenname: Yoshiaki orcidid: 0000-0002-2483-7652 surname: Inoue fullname: Inoue, Yoshiaki email: yoshiaki@comm.eng.osaka-u.ac.jp organization: Department of Information and Communications Technology, Graduate School of Engineering, Osaka University, Suita, Japan – sequence: 2 givenname: Hiroyuki surname: Masuyama fullname: Masuyama, Hiroyuki email: masuyama@i.kyoto-u.ac.jp organization: Department of Systems Science, Graduate School of Informatics, Kyoto University, Kyoto, Japan – sequence: 3 givenname: Tetsuya orcidid: 0000-0001-7499-6929 surname: Takine fullname: Takine, Tetsuya email: takine@comm.eng.osaka-u.ac.jp organization: Department of Information and Communications Technology, Graduate School of Engineering, Osaka University, Suita, Japan – sequence: 4 givenname: Toshiyuki orcidid: 0000-0001-5962-9119 surname: Tanaka fullname: Tanaka, Toshiyuki email: tt@i.kyoto-u.ac.jp organization: Department of Systems Science, Graduate School of Informatics, Kyoto University, Kyoto, Japan
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SubjectTerms	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
Title	A General Formula for the Stationary Distribution of the Age of Information and Its Application to Single-Server Queues
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