论文简报
cs.IT 2605.26247v1 必读

Age of Information in Time-Varying Multi-Priority Queues

Burak Karasakal, Aimin Li, Elif Uysal

发布日期：2026-05-25 18:14 相关性：1.0000 价值：0.8400 分类：cs.IT
arXiv 摘要 PDF 原文 网页正文

摘要

In networks with intermittent connectivity, such as mobile, aerial, and space systems, maintaining information freshness is complicated by time-varying arrivals, service disruptions, and interactions among traffic classes with different priorities. To capture these effects, we study a multi-priority single-server queue with time-varying arrivals and service rates under intermittent connectivity. Our main result shows that an appropriately selected collection of state-conditioned first moments closes exactly, leading to a finite-dimensional linear time-periodic Ordinary Differential Equation (ODE) system for the mean Age of Information (AoI) and mean Peak Age of Information (PAoI) of each priority class. For periodic arrival and service rates, we define a one-period state map by propagating the ODE over a single period, and use the periodicity condition to formulate the periodic steady state as a fixed point of this map. We then propose a fixed-point iteration algorithm and prove its convergence to the unique periodic steady state (PSS). Numerical results reveal that high-priority traffic can strongly reshape the service process seen by lower-priority classes.

相关性判断

high
相关方向
age_of_information queueing_theory communications_networks stochastic_processes
判断依据

Directly on AoI/PAoI in time-varying multi-priority queues with periodic steady-state analysis, ODE dynamics, and service processes under intermittent connectivity; squarely in communications/information-theory adjacent queueing literature.

价值判断

High relevance to AoI/PAoI and queueing theory, with explicit time-varying multi-priority intermittent-connectivity setting. Structure analysis indicates a concrete technical contribution: exact first-moment closure into finite-dimensional linear time-periodic ODEs. Includes convergence proof for periodic steady-state fixed-point iteration and interpretable numerical findings for priority interactions.

核心问题与主要方法

核心问题

Characterize class-wise AoI and PAoI in time-varying multi-priority queues with intermittent connectivity.

场景：Periodic single-server multi-class queue with strict priority, latest-only buffers, and time-varying arrivals/service under outages.

主要方法

Models the queue as a finite CTMC over service state J and per-class buffer occupancies B_i, with strict priority scheduling and latest-only replacement encoded in state transitions. Introduces auxiliary age variables for packet age in service Y(t), waiting packet ages Z_i(t), and state-conditioned moment vectors a_i(t), y(t), z_i(t) to make AoI/PAoI analysis tractable. Uses sparse transition-rate matrices for completion and next-service events so priority coupling and residual service opportunities enter the ODE through state-dependent transition structure. Defines a one-period map F by integrating the ODE over period T; the periodic steady state is the fixed point x*(0)=F(x*(0)). Uses Floquet/periodic linear-system analysis and a Lyapunov-style argument in the appendix to support uniqueness and exponential convergence of the periodic steady state. Derives a structural relation for the PAoI-AoI gap through the service probability pi_i(t), showing that peak age is not necessarily an upper bound on average age.

关键贡献与后续阅读

关键贡献

Provides an exact finite-dimensional linear time-periodic ODE characterization for class-wise mean AoI and completion-conditioned mean PAoI in a time-varying multi-priority queue with intermittent connectivity. Handles priority-induced residual service explicitly: lower-priority freshness depends on service opportunities left after higher-priority traffic, rather than on the nominal physical service process alone. Combines CTMC state probabilities with state-conditioned first moments for monitor age, in-service packet age, and waiting-buffer packet age, enabling exact first-moment closure under the stated Markovian assumptions. Formulates periodic steady-state computation as a fixed point of a one-period ODE propagation map and gives a relaxed fixed-point iteration with convergence to the unique PSS. Identifies and formalizes a nontrivial AoI/PAoI separation: for low-priority traffic under outages and starvation, time-average AoI can exceed completion-sampled PAoI.

研究启发

How robust is the moment-closure and convergence argument if service times are not exponential or arrivals are not Poisson? How does computational cost scale with the number of classes, given the state vector dimension d=(2N+2)|Q| and per-class buffer state expansion? Do the numerical results compare against simpler stationary or decoupled approximations to quantify when the full periodic priority model materially changes design decisions? Are the closest prior SHS, PDE, or nonstationary AoI models clearly separated in the full related-work comparison beyond the excerpted claims?

限制与不确定性

Assessment relies only on abstract and structure analysis, not full proof quality or comparison against closest prior AoI queueing work. Model assumptions are fairly specific, including exponential service, Poisson arrivals, strict non-preemptive priority, and latest-only buffers.

参考文献

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