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DOE OSTI · 2538482

Modeling information flow in a computer processor with a multi-stage queuing model

Daneshvar, Mohammad·Barnard, Richard C.·Hauck, Cory·Timofeyev, Ilya
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Abstract

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. In conclusion, we demonstrate the validity of the closure with numerical simulations.

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97 MATHEMATICS AND COMPUTINGInformation flowMoment closureNegative binomial distributionProcessor throttlingTandem M/M/s queue

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Daneshvar, Mohammad, Barnard, Richard C., Hauck, Cory, Timofeyev, Ilya. 2024-11-22. Modeling information flow in a computer processor with a multi-stage queuing model. https://doi.org/10.1016/j.physd.2024.134446

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