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

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arxiv 1804.06139 v2 pith:MQHRBMXX submitted 2018-04-17 cs.PF cs.ITmath.IT

Yoshiaki Inoue , Hiroyuki Masuyama , Tetsuya Takine , Toshiyuki Tanaka This is my paper · ORCID
classification cs.PFcs.ITmath.IT
keywords disciplinesqueuesservicestationarydistributioninformationlcfsformula
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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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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A Whittle Index Approach to Minimizing Functions of Age of Information

    cs.IT 2019-08 conditional novelty 6.0 of 10

    For two status-update sources with reliable channels, the Whittle index policy exactly minimizes the time-average of any non-decreasing cost function of Age of Information.

  2. Context-Aware Information Lapse for Timely Status Updates in Remote Control Systems

    cs.IT 2019-08 conditional novelty 6.0 of 10

    A context-aware timeliness metric multiplies estimation error by a context weight, and a Lyapunov scheduling policy that minimizes it cuts threshold violations and improves CartPole control versus Age-of-Information s...

  3. Towards AoI-aware Smart IoT Systems

    cs.NI 2019-08 conditional novelty 5.0 of 10

    Measured Age of Information on real Internet and local Wi-Fi IoT testbeds and derived how synchronization bias shifts average age under linear, exponential, and logarithmic penalties.

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