Modeling Information Flow with a Multi-Stage Queuing Mode
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866913583662628864 |
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| author | Daneshvar, Mohammad Barnard, Richard C. Hauck, Cory Timofeyev, Ilya |
| author_facet | Daneshvar, Mohammad Barnard, Richard C. Hauck, Cory Timofeyev, Ilya |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_02703 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Modeling Information Flow with a Multi-Stage Queuing Mode Daneshvar, Mohammad Barnard, Richard C. Hauck, Cory Timofeyev, Ilya Probability Distributed, Parallel, and Cluster Computing 60J20, 60E05 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. |
| title | Modeling Information Flow with a Multi-Stage Queuing Mode |
| topic | Probability Distributed, Parallel, and Cluster Computing 60J20, 60E05 |
| url | https://arxiv.org/abs/2308.02703 |