In this paper, we introduce a nonlinear stochastic model to describe the propagation of information inside a computer processor. In this model, a computational task is divided into stages, and information can flow from one stage to another. The model is formulated as a spatially-extended, continuous-time Markov chain where space represents different stages. This model is equivalent to a spatially-extended version of the M/M/s queue. The main modeling feature is the throttling function which describes the processor slowdown when the amount of information falls below a certain threshold. We derive the stationary distribution for this stochastic model and develop a closure for a deterministic ODE system that approximates the evolution of the mean and variance of the stochastic model. We demonstrate the validity of the closure with numerical simulations.

翻译：摘要：本文提出一个非线性随机模型，用于描述计算机处理器内部的信息传播过程。在该模型中，计算任务被划分为多个阶段，信息可在不同阶段之间流动。该模型被构建为一个空间扩展的连续时间马尔可夫链，其中空间维度表示不同阶段。该模型等价于空间扩展版本的M/M/s排队系统。模型的核心特征在于节流函数，该函数描述了当信息量降至特定阈值以下时处理器的降速机制。我们推导了该随机模型的稳态分布，并建立了一个确定性常微分方程系统的闭合形式，该闭合形式可近似描述随机模型均值与方差的演化。通过数值模拟验证了该闭合方法的有效性。