Локальне керування в мережах Ґордона — Ньюелла
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Date
2024
Authors
Чорней, Руслан
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Abstract
Запропоновано модифікацію мережі Ґордона — Ньюелла з локальною та синхронною взаємодією, яка обслуговує клієнтів у замкнутому режимі. Система околів задається за допомогою деякого скінченного графа вузлів системи. Запропоновано процедуру знаходження оптимальних нерандомізованих стратегій керування для систем із критерієм усереднених в одиницю часу витрат.
Description
We examine continuous-time stochastic processes with a general compact state space, which is organized by a fundamental graph defining a neighborhood structure of states. These neighborhoods establish local interactions among the coordinates of the spatial process. At any given moment, the random state of the system, as described by the stochastic process, forms a random field concerning the neighborhood graph. The process is assumed to have a semi-Markov temporal property, and its transition kernels exhibit a spatial Markov property relative to the basic graph. Additionally, a local control structure is introduced to optimize the evolution of the system over time. Here, optimality is defined in terms of the criterion of asymptotic average reward over time. Only discrete stepwise control is considered, meaning decisions are made exclusively at process jump moments. As is customary, random policies are represented by a conditionally independent structure. It is also assumed that this structure exists within the transition kernels of jump-like chains (synchronized kernels). The controlled random fields described, featuring local and synchronous component interactions, are applied to queueing systems—specifically, to the extended and generalized closed Gordon-Newell network. The modification primarily involves synchronizing customer service times at nodes. Based on the queue length at the node and its vicinity, a decision is made regarding serving the customer. If service is provided, a decision is also made regarding the customer’s next direction. Consequently, the enhanced Gordon-Newell network satisfies the conditions for synchronous and local system node interactions. A procedure is outlined for determining optimal non-randomized control strategies in the enhanced Gordon-Newell network.
Keywords
мережа Ґордона — Ньюелла, локальна та синхронна взаємодія, керовані випадкові процеси, процеси прийняття рішень, стаття, Gordon-Newell network, local and synchronous interaction, controlled stochastic processes, decision-making processes
Citation
Чорней Р. К. Локальне керування в мережах Ґордона — Ньюелла / Чорней Р. К. // Наукові записки НаУКМА. Комп'ютерні науки. - 2024. - Т. 7. - С. 120-129. - https://doi.org/10.18523/2617-3808.2024.7.120-129