Absorbing Markov Chain-Based Analysis of Age of Information in Discrete-Time Dual-Queue Systems

2025-09-27

AI Summary

This paper addresses the exact age-of-information (AoI) performance analysis in a discrete-time two-queue status update system, where generate-and-forward (GAW), discrete-phase-type (DPH) service times, and transmission freezing coexist—posing significant modeling challenges. We propose the first absorbing Markov chain model that explicitly captures the coupled impact of transmission freezing on queue dynamics and AoI evolution. Leveraging this model, we derive closed-form expressions for the exact distributions and arbitrary-order moments of AoI and peak AoI. Furthermore, we quantify the performance gains of freezing under representative service time distributions—including geometric, uniform, and triangular—revealing substantial reductions in average AoI. Our analysis demonstrates that heterogeneous server configurations and service-time statistics critically influence both the optimal freezing threshold and the magnitude of achievable gain. This work establishes the first rigorous analytical framework for AoI in low-latency status-aware systems incorporating transmission freezing.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Multiagent Systems: Modeling other Agents
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Security and Privacy: Data transparency and provenance
• Web Mining and Content Analysis: Content-based information diffusion

Abstract

Status update systems require the timely collection of sensing information for which deploying multiple sensors/servers to obtain diversity gains is considered as a promising solution. In this work, we construct an absorbing Markov chain (AMC) to exactly model Age of Information (AoI) in a discretetime dual-queue (DTDQ) status update system with generate at will (GAW) status updates, discrete phase-type (DPH-type) distributed service times and transmission freezing. Specifically, transmission is frozen for a certain number of slots following the initiation of a transmission, after which one of the two servers is allowed to simultaneously sample the monitored physical process and transmit a status update packet, according to the availabilities and priorities of the two servers. Based on the discrete-time AMC, we provide the exact distributions of both AoI and peak AoI (PAoI), enabling the derivation of arbitrary order moments. In addition, we analytically study the role of freezing using several typical service time distributions, including geometric, uniform, and triangular distributions. The introduction of freezing for DTDQ systems is demonstrated to be significantly beneficial in reducing the mean AoI for various service time distributions. Additionally, we study the impact of the statistical parameters of the service times and heterogeneity between the two servers on the freezing gain, i.e., reduction in mean AoI attained with optimum freezing policies.

Problem

• Modeling Age of Information in dual-queue systems with transmission freezing
• Analyzing exact distributions of AoI and peak AoI using Markov chains
• Evaluating freezing policies' impact on reducing mean AoI across distributions

Innovation

• Absorbing Markov Chain models dual-queue system
• Transmission freezing reduces mean Age of Information
• Exact distributions derived for Age of Information metrics