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Stability Analysis and Simulation of a Cellular Network with Retransmissions Policy
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Probability Theory and Combinatorics.
2023 (English)In: Computer Performance Engineering and Stochastic Modelling: 19th European Workshop, EPEW 2023, and 27th International Conference, ASMTA 2023, Florence, Italy, June 20–23, 2023, Proceedings / [ed] Iacono, M Scarpa, M Barbierato, E Serrano, S Cerotti, D Longo, F, Cham: Springer, 2023, p. 369-382Conference paper, Published paper (Refereed)
Abstract [en]

We consider an uplink cellular network with static users and unlimited retransmissions. The users are assigned to the base stations (BSs) using the shortest distance association policy. The network cells are formed according to the Voronoi tessellation, and we study stability of this model with focus on a single cell. In particular, we consider a model with non-homogeneous users where the buffer size of each user depends on the number and locations of the active users at each time slot. We obtain a basic relation between input and output rate (coverage probability) of each user in steady-state regime. Moreover, we use stochastic simulation to verify sufficient stability conditions (obtained in the paper [8] for a more general system) which are reformulated in terms of the model under consideration. In particular, we find that these conditions turn out to be quite close to stability criteria in the most realistic case of the heavily loaded cell. In this regard and because of analytical unavailability of some metrics, we empirically study the convergence of the stability zone of the lightly-loaded cell to the zone defined by the sufficient stability conditions, when the load increases.

Place, publisher, year, edition, pages
Cham: Springer, 2023. p. 369-382
Series
Lecture Notes in Computer Science, ISSN 0302-9743, E-ISSN 1611-3349 ; 14231
Keywords [en]
cellular network, performance evaluation, stability analysis, Markov process, stochastic simulation
National Category
Control Engineering Telecommunications
Identifiers
URN: urn:nbn:se:uu:diva-557518DOI: 10.1007/978-3-031-43185-2_25ISI: 001434796000025Scopus ID: 2-s2.0-85176010540ISBN: 978-3-031-43184-5 (print)ISBN: 978-3-031-43185-2 (electronic)OAI: oai:DiVA.org:uu-557518DiVA, id: diva2:1962164
Conference
27th International Conference on Analytical & Stochastic Modeling Techniques & Applications, June 20-23, 2023, Florence, Italy
Available from: 2025-05-28 Created: 2025-05-28 Last updated: 2025-11-13Bibliographically approved
In thesis
1. Modelling and Performance of Cellular Networks: Stochastic Geometry, Queuing, and Learning Approaches
Open this publication in new window or tab >>Modelling and Performance of Cellular Networks: Stochastic Geometry, Queuing, and Learning Approaches
2025 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis is based on seven papers concerning mathematical models for wireless cellular networks with retransmissions, buffering, and interference. The analysis combines stochastic geometry with queuing theory to capture complex stochastic aspects of the physical model. Paper I introduces a downlink model with transmitter buffers, providing performance measures such as coverage probability, delay, and loss probability. Paper II extends the modeling approach to quantify Shannon capacity under finite and infinite buffer regimes. Paper III studies multi-tier networks, extending the previous approach. The paper introduces biased load balancing and discusses the increase in capacity compared with single-tier systems. Pa-per IV derives a stability condition for buffered uplink traffic, for a special case of no noise and unbounded attenuation. The paper further refines the analytical stability bound through simulations. Paper V considers the network with heterogeneous users with different arrival rates and powers, and establishes user-specific stability bounds. Paper VI uses the well-known Foster criteria for two-dimensional Markov chains and extends them to derive both stability and transience criteria for Markov chains in higher dimensions with monotone drifts. Finally, Paper VII studies a model of a buffered cellular network in terms of reinforcement learning (RL) methodology. It introduces a decentralized mean-field RL method, where base stations act as agents who aim to maximize their channel capacity via dynamically adjusting the transmission intensity.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2025. p. 64
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 2615
Keywords
Cellular networks, performance evaluation, stochastic geometry, stochastic modelling, Shannon capacity, coverage probability, Markov chains, reinforcement learning.
National Category
Communication Systems Mathematical sciences
Research subject
Applied Mathematics and Statistics
Identifiers
urn:nbn:se:uu:diva-571533 (URN)978-91-513-2675-7 (ISBN)
Public defence
2026-01-14, Polhemsalen, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 17:29 (English)
Opponent
Supervisors
Available from: 2025-12-18 Created: 2025-11-13 Last updated: 2025-12-18

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