Predictability of Performance in Communication Networks Under Markovian Dynamics

TL;DR

The paper develops a principled framework to quantify and analyze the predictability of network performance under Markovian dynamics, defining predictability as the total variation distance between the forecast distribution and the marginal performance distribution. It derives exact and approximate expressions for predictability in Geo/Geo/1/K queues and extends the results to multi-hop systems, with spectral-based upper bounds that connect convergence to stationarity to predictability. The work also addresses imperfect observability—delayed and aggregated observations—and provides practical insights via numerical results on random-walk channel models and multi-hop queues. The findings offer design guidance for monitoring and predictive QoS in future networks, highlighting when and where observation resources yield meaningful predictive gains for deterministic service provisioning.

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.

Figures (18)

• Figure 1: Multi-hop communication system model with observable measures being conditions.
• Figure 2: Temporal dependencies in the performance model for each subsystem $m$, underscoring the conditions' Markov chain
• Figure 3: Geo/Geo/1/K Markov chain states and transition probabilities
• Figure 4: Posterior, marginal, and forecast distributions for a cellular connection’s downlink throughput, with evolving under a random walk model with $p=0.6$ (mobile).
• Figure 5: Predictability of a cellular connection’s downlink throughput, with CQI evolving under a random-walk model. The solid lines depict exact values at various lead times, while dotted and dashed lines represent two spectral upper bounds (1 and 2), respectively.

Theorems & Definitions (13)

• Definition 1
• Definition 2
• Lemma 1
• Theorem 1
• Lemma 2
• Lemma 3
• Lemma 4: Winkler2003sousi_mixing_2020
• Theorem 2: Spectral-Based Predictability Bound
• Remark 1
• Lemma 5: Subadditivity of Predictability