Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)5192010.22363/2658-4670-2026-34-2-175-186JEHUQUComputer ScienceИнформатика и вычислительная техникаResearch ArticleA queueing-inventory model for energy-constrained UAV base stations in non-terrestrial networksСистема массового обслуживания с запасами для беспилотных базовых станций с ограниченным энергоресурсом в неназемных сетяхhttps://orcid.org/0009-0001-7688-2527AskerovAlexander E.АскеровА. Э.

Bachelor's Student with the Department of Probability Theory and Cyber Security of RUDN University

1132226538@rudn.ruhttps://orcid.org/0009-0001-9740-2545BogolyubovSergey D.БоголюбовС. Д.

PhD Student with the Department of Probability Theory and Cyber Security of RUDN University

1142240051@rudn.ruhttps://orcid.org/0009-0000-9253-342658849959400LSI-9560-2024LeontevaKseniia A.ЛеонтьеваК. А.

Junior Researcher and PhD Student with the Department of Probability Theory and Cyber Security of RUDN University

leontyeva-ka@rudn.ruhttps://orcid.org/0000-0001-6453-814X57204395118AAC-6696-2020VlaskinaAnastasia S.ВласкинаА. С.

Candidate of Sciences in Physics and Mathematics, Senior Lecturer with the Department of Probability Theory and Cyber Security of RUDN University

vlaskina-as@rudn.ruhttps://orcid.org/0000-0002-1594-427X35332169400E-3806-2014KochetkovaIrina A.КочетковаИ. А.

Doctor of Sciences in Physics and Mathematics, Associate Professor with the Department of Probability Theory and Cyber Security of RUDN University; Senior Researcher with the Federal Research Center ``Computer Science and Control'' of the Russian Academy of Sciences

kochetkova-ia@rudn.ruRUDN UniversityРоссийский университет дружбы народовFederal Research Center "Computer Science and Control" of the Russian Academy of SciencesФедеральный исследовательский центр «Информатика и управление» Российской академии наук15082026342VOL 34, NO2 (2026)ТОМ 34, №2 (2026)17518620082026Copyright ©; 2026, Askerov A.E., Bogolyubov S.D., Leonteva K.A., Vlaskina A.S., Kochetkova I.A.Copyright ©; 2026, Аскеров А.Э., Боголюбов С.Д., Леонтьева К.А., Власкина А.С., Кочеткова И.А.2026Askerov A.E., Bogolyubov S.D., Leonteva K.A., Vlaskina A.S., Kochetkova I.A.Аскеров А.Э., Боголюбов С.Д., Леонтьева К.А., Власкина А.С., Кочеткова И.А.https://creativecommons.org/licenses/by-nc/4.0https://journals.rudn.ru/miph/article/view/51920

Unmanned aerial vehicle base stations are envisioned as key enablers of sixth-generation non-terrestrial networks, offering on-demand aerial coverage for remote areas, mass events, and emergency scenarios; however, their operational continuity is fundamentally limited by finite onboard battery capacity, a constraint that existing analytical models address inadequately by either ignoring energy dynamics or treating battery charge as a static parameter. The purpose of this study is to develop an analytical framework that jointly captures stochastic user service and discrete battery dynamics under a controlled recharging discipline. We propose a queueing-inventory model in which the unmanned aerial vehicle base station is represented as a loss system with a discrete energy resource and a threshold-based recharging policy; users arrive according to a Poisson process, service times are exponentially distributed, each served connection consumes one energy unit, and recharging is triggered when the battery level reaches a critical threshold. The system is formulated as a two-dimensional continuous-time Markov chain, and explicit expressions are obtained for the mean number of active users, the mean battery reserve, and the user blocking probability. Numerical experiments across three operational scenarios - remote area monitoring, mass event coverage, and emergency response - reveal that the threshold parameter governs a fundamental trade-off between user throughput and recharging overhead, providing a tractable tool for selecting unmanned aerial vehicle specifications at the design stage of sixth-generation communication systems.

Беспилотные базовые станции рассматриваются как ключевые элементы неназемных сетей шестого поколения, обеспечивающие мобильное покрытие в удалённых районах, при массовых мероприятиях и в чрезвычайных ситуациях; вместе с тем их операционная непрерывность принципиально ограничена конечной емкостью бортового аккумулятора - ограничение, которое существующие аналитические модели либо игнорируют, либо учитывают лишь статически. Целью исследования является разработка аналитической модели, совместно описывающей стохастическое обслуживание пользователей и дискретную динамику заряда батареи в условиях политики подзарядки. Предлагается система массового обслуживания с запасами, в которой беспилотная базовая станция представлена как система с потерями, дискретным энергетическим ресурсом и пороговой политикой подзарядки; пользователи поступают согласно пуассоновскому процессу, времена обслуживания экспоненциальны, каждое соединение потребляет одну единицу заряда, а подзарядка инициируется при достижении критического порога. Система формализована как двумерный марковский случайный процесс; получены выражения для среднего числа активных пользователей, среднего уровня заряда батареи и вероятности блокировки. Численный анализ трёх сценариев - удаленная территория, массовое мероприятие и аварийное реагирование - показывает, что параметр порога определяет компромисс между пропускной способностью и накладными расходами на подзарядку, предоставляя инструмент для выбора характеристик беспилотных станций.

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