A Probabilistic Approach to Growth Networks

Predrag Jelenković (), Jané Kondev (), Lishibanya Mohapatra () and Petar Momčilović ()
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Predrag Jelenković: Department of Electrical Engineering, Columbia University, New York, New York 10027
Jané Kondev: Martin A. Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02453
Lishibanya Mohapatra: School of Physics and Astronomy, College of Science, Rochester Institute of Technology, Rochester, New York 14623
Petar Momčilović: Department of Industrial and Systems Engineering, Texas A&M University, College Station, Texas 77843

Operations Research, 2022, vol. 70, issue 6, 3386-3402

Abstract: Widely used closed product-form networks have emerged recently as a primary model of stochastic growth of subcellular structures, for example, cellular filaments. The baseline bio-molecular model is equivalent to a single-class closed queueing network, consisting of single-server and infinite-server queues. Although this model admits a seemingly tractable product-form solution, explicit analytical characterization of its partition function is difficult due to the large-scale nature of bio-molecular networks. To this end, we develop a novel methodology, based on a probabilistic representation of product-form solutions and large-deviations concentration inequalities, which identifies distinct operating regimes and yields explicit expressions for the marginal distributions of queue lengths. The parameters of the derived distributions can be computed from equations involving large-deviations rate functions, often admitting closed-form algebraic expressions. From a methodological perspective, a fundamental feature of our approach is that it provides exact results for order-one probabilities, even though our analysis involves large-deviations rate functions, which characterize only vanishing probabilities on a logarithmic scale.

Keywords: Stochastic Models; closed network; product-form solution; large-scale network; large deviations (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:70:y:2022:i:6:p:3386-3402

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