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.

翻译：马尔可夫调制流体队列（MMFQs）是分析计算机与通信系统性能的强大建模框架。其显著特征在于底层马尔可夫过程在连续状态空间上演化，使其能很好地刻画工作负载、能量水平及其他性能相关量的动态特性。尽管经典MMFQs不允许流体水平发生跳跃，它们仍可应用于分析各类跳跃过程。本文通过引入**带色MMFQs**与**含流体跳跃的带色MMFQs**，将MMFQ框架向新方向进行推广。这一增强框架提供了额外的记忆形式：流入流体的颜色可用于追踪特定事件发生时的流体水平。该能力显著提升了建模灵活性，使得分析因维度灾难或状态空间爆炸而原本难以处理的排队系统成为可能。