  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.
