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

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

doi:10.1016/j.physd.2024.134446

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

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

Multiscale Methods

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	134446
Journal	Physica D: Nonlinear Phenomena
Volume	471
DOIs	https://doi.org/10.1016/j.physd.2024.134446
State	Published - Jan 2025

Funding

This research has been supported, in part, by the NSF grant DMS-1620278 and, in part, by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research (ASCR) , as part of their Applied Mathematics Research Program. Work supported by ASCR was performed at the Oak Ridge National Laboratory, which is managed by UT-Battelle, LLC under Contract No. De-AC05-00OR22725. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for the United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan ( http://energy.gov/downloads/doe-public-access-plan ).

Funders	Funder number
United States Government
DOE Public Access Plan
U.S. Department of Energy
Office of Science
National Science Foundation	DMS-1620278
National Science Foundation
Advanced Scientific Computing Research	De-AC05-00OR22725
Advanced Scientific Computing Research

Keywords

Information flow
Moment closure
Negative binomial distribution
Processor throttling
Tandem M/M/s queue

Access to Document

10.1016/j.physd.2024.134446

Cite this

@article{2d4a9a40f92e4520aff6067492c9a372,

title = "Modeling information flow in a computer processor with a multi-stage queuing model",

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.",

keywords = "Information flow, Moment closure, Negative binomial distribution, Processor throttling, Tandem M/M/s queue",

author = "Mohammad Daneshvar and Barnard, {Richard C.} and Cory Hauck and Ilya Timofeyev",

note = "Publisher Copyright: {\textcopyright} 2024",

year = "2025",

month = jan,

doi = "10.1016/j.physd.2024.134446",

language = "English",

volume = "471",

journal = "Physica D: Nonlinear Phenomena",

issn = "0167-2789",

publisher = "Elsevier",

}

TY - JOUR

T1 - Modeling information flow in a computer processor with a multi-stage queuing model

AU - Daneshvar, Mohammad

AU - Barnard, Richard C.

AU - Hauck, Cory

AU - Timofeyev, Ilya

PY - 2025/1

Y1 - 2025/1

N2 - 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.

AB - 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.

KW - Information flow

KW - Moment closure

KW - Negative binomial distribution

KW - Processor throttling

KW - Tandem M/M/s queue

UR - http://www.scopus.com/inward/record.url?scp=85209990763&partnerID=8YFLogxK

U2 - 10.1016/j.physd.2024.134446

DO - 10.1016/j.physd.2024.134446

M3 - Article

AN - SCOPUS:85209990763

SN - 0167-2789

VL - 471

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

M1 - 134446

ER -

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

Abstract

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Cite this