Taisiia Morozova: Modelling and Performance of Cellular Networks: Stochastic Geometry, Queuing, and Learning Approaches

Abstract

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.