Modeling Information Flow with a Multi-Stage Queuing Mode

Mohammad Daneshvar; Richard C. Barnard; Cory Hauck; Ilya Timofeyev

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arXiv · 2308.02703

Modeling Information Flow with a Multi-Stage Queuing Mode

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

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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. We demonstrate the validity of the closure with numerical simulations.

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BibTeX RIS

Mohammad Daneshvar, Richard C. Barnard, Cory Hauck, Ilya Timofeyev. 2023-08-04. Modeling Information Flow with a Multi-Stage Queuing Mode. https://arxiv.org/abs/2308.02703

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