Modeling Information Flow in a Computer Processor with a Multi-Stage Queuing Model

Abstract: 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.  It is equivalent to a spatially extended version of an M/M/s queue.  The main feature of the model is a throttling function which describes the processor slowdown when the amount of information falls below a certain threshold.  We derive an ordinary differential equation (ODE) system that approximates the evolution of the mean and variance of the stochastic model, and we establish basic well-posedness properties for the ODE: existence, uniqueness, and invariant domain.  We then demonstrate the validity of the closure with numerical experiments.

Speaker’s Bio: Cory Hauck is the Group Leader of the Multiscale Methods and Dynamics Group.  He received his Ph.D. in Applied Mathematics in 2006 from the University of Maryland.  His research focuses on computational aspects of kinetic theory and hyperbolic partial differential equations, with applications in radiation transport, gas dynamics, and plasma physics.