Predictability of Performance in Communication Networks Under Markovian Dynamics

2024-08-23

arXiv.org

AI Summary

Quantifying predictability in latency-sensitive communication networks remains an open challenge. Method: This paper formally defines system performance predictability and establishes a theoretical framework based on total variation distance. Predictability is measured as the total variation between the optimal predictive distribution and the marginal distribution. Modeling multi-hop networks under Markov dynamics, we integrate the Geo/Geo/1 queuing model with spectral analysis of Markov chains to derive exact and approximate closed-form predictability expressions—along with tight spectral upper bounds—for both single-hop and multi-hop scenarios. Contribution/Results: We quantitatively characterize how observation granularity and system dynamism jointly affect prediction capability. This work provides the first theoretical foundation for Quality-of-Service (QoS) proactive prediction and deterministic network adaptive design, enabling principled predictability-aware network optimization.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• 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

Abstract

With the emergence of time-critical applications in modern communication networks, there is a growing demand for proactive network adaptation and quality of service (QoS) prediction. However, a fundamental question remains largely unexplored: how can we quantify and achieve more predictable communication systems in terms of performance? To address this gap, this paper introduces a theoretical framework for defining and analyzing predictability in communication systems, with a focus on the impact of observations for performance forecasting. We establish a mathematical definition of predictability based on the total variation distance between forecast and marginal performance distributions. A system is deemed unpredictable when the forecast distribution, providing the most comprehensive characterization of future states using all accessible information, is indistinguishable from the marginal distribution, which depicts the system's behavior without any observational input. This framework is applied to multi-hop systems under Markovian conditions, with a detailed analysis of Geo/Geo/1 queuing models in both single-hop and multi-hop scenarios. We derive exact and approximate expressions for predictability in these systems, as well as upper bounds based on spectral analysis of the underlying Markov chains. Our results have implications for the design of efficient monitoring and prediction mechanisms in future communication networks aiming to provide deterministic services.

Problem

• Quantify predictability in communication systems performance
• Analyze impact of observations on performance forecasting
• Develop framework for multi-hop systems under Markovian conditions

Innovation

• Theoretical framework for predictability in communication systems
• Mathematical definition based on total variation distance
• Spectral analysis of Markov chains for upper bounds