Colored Markov Modulated Fluid Queues

2026-01-28

AI Summary

Traditional Markov-modulated fluid queues struggle to capture complex queueing systems that require event memory or suffer from state-space explosion. This work proposes a colored Markov-modulated fluid queue model augmented with a fluid jump mechanism, where “colors” serve as an additional memory dimension to record the fluid state at specific event occurrences. By incorporating this memory-aware structure, the model significantly enhances its capacity to represent history-dependent behaviors. The approach mitigates the curse of dimensionality while establishing a novel theoretical framework capable of analytically tractable performance evaluation for previously intractable queueing systems. Consequently, it broadens the applicability of fluid queueing models in performance analysis of computer and communication systems.

Technology Category

• Cognitive Modeling & Cognitive Systems: Agent Architectures
• Planning, Routing, and Scheduling: Planning with Markov Models (MDPs, POMDPs)
• Machine Learning: Quantum Machine Learning

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Models for Web evolution
• Security and Privacy: Large-scale security measurements

Abstract

Markov-modulated fluid queues (MMFQs) are a powerful modeling framework for analyzing the performance of computer and communication systems. Their distinguishing feature is that the underlying Markov process evolves on a continuous state space, making them well suited to capture the dynamics of workloads, energy levels, and other performance-related quantities. Although classical MMFQs do not permit jumps in the fluid level, they can still be applied to analyze a wide range of jump processes. In this paper, we generalize the MMFQ framework in a new direction by introducing {\bf colored MMFQs} and {\bf colored MMFQs with fluid jumps}. This enriched framework provides an additional form of memory: the color of incoming fluid can be used to keep track of the fluid level when certain events took place. This capability greatly enhances modeling flexibility and enables the analysis of queueing systems that would otherwise be intractable due to the curse of dimensionality or state-space explosion.

Problem

• Markov-modulated fluid queues
• colored MMFQs
• fluid jumps
• state-space explosion
• curse of dimensionality

Innovation

• colored Markov-modulated fluid queues
• fluid jumps
• modeling flexibility
• state-space explosion
• memory mechanism