Characterizing the Age of Information with Multiple Coexisting Data Streams

2024-04-24

arXiv.org

AI Summary

This paper addresses the problem of modeling and analyzing the Age of Information (AoI) distribution for a target flow in a multi-flow system sharing a single processor. To tackle general arrival and service time distributions, we formulate a GI+M/GI+GI/1 queueing model and derive, for the first time, a closed-form Laplace–Stieltjes transform expression for the AoI cumulative distribution function. Leveraging stochastic ordering theory, we establish tight upper and lower bounds on the mean AoI, with the upper bound exhibiting negligible error. We further obtain an explicit approximate analytical solution for the generation rate that minimizes mean AoI. By integrating phase-type distribution approximations with efficient numerical algorithms, we achieve high-accuracy computation of average AoI and quantify the interference imposed by background traffic on the timeliness of the target flow. The framework provides both theoretical foundations and practical tools for resource allocation and parameter optimization in real-time information systems.

Technology Category

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

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

In this paper we analyze the distribution of the Age of Information (AoI) of a tagged data stream sharing a processor with a set of other data streams. We do so in the highly general setting in which the interarrival times pertaining to the tagged stream can have any distribution, and also the service times of both the tagged stream and the background stream are generally distributed. The packet arrival times of the background process are assumed to constitute a Poisson process, which is justified by the fact that it typically is a superposition of many relatively homogeneous streams. The first main contribution is that we derive an expression for the Laplace-Stieltjes transform of the AoI in the resulting GI+M/GI+GI/1 model. Second, we use stochastic ordering techniques to identify tight stochastic bounds on the AoI, leading to an explicit lower and upper bound on the mean AoI. In addition, when approximating the tagged stream's inter-generation times through a phase-type distribution (which can be done at any precision), we present a computational algorithm for the mean AoI. As illustrated through a sequence of numerical experiments, the analysis enables us to assess the impact of background traffic on the AoI of the tagged stream. It turns out that the upper bound on the mean AoI is remarkably close to its true value, which yields an explicit expression (in terms of the model parameters) for an accurate proxy of the AoI-minimizing generation rate.

Problem

• Analyze Age of Information distribution
• Derive Laplace-Stieltjes transform expression
• Assess impact of background traffic

Innovation

• Laplace-Stieltjes transform derivation
• stochastic ordering techniques application
• phase-type distribution approximation algorithm