Colored Markov Modulated Fluid Queues

TL;DR

This paper introduces colored Markov modulated fluid queues, extending the classical framework to include memory via colors and fluid jumps, enabling more flexible modeling of complex queueing systems.

Contribution

It proposes a novel generalization of MMFQs by incorporating colors and fluid jumps, enhancing modeling capabilities for complex systems.

Findings

Enables analysis of systems with memory effects.

Reduces complexity in modeling high-dimensional queues.

Provides a flexible framework for jump processes.

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.