RK4 Differential Equation to improve QoS in an eUTRAN LTE Network: A Deterministic vs. Stochastic Approach

Improving Quality of Service (QoS) in an eUTRAN LTE network is essential to guarantee optimal performance in the face of dynamic variations in user traffic and radio channel interference. In this context, this paper explores the use of 4^th-order Runge-Kutta differential equations (RK4) to model and optimize radio resource management, by comparing a deterministic approach, which assumes stable and predictable traffic, with a stochastic approach, which incorporates random network fluctuations. The central problem lies in the difficulty of anticipating and effectively managing network congestion, affecting resource allocation, bandwidth and transmission delay. Through a 24 h simulation, the results show that the deterministic approach predicts a resource allocation of up to 90% at peak times, a bandwidth occupancy of 80 Mbps and a maximum latency of 120ms, offering stable but limited management in the face of unforeseen events. In contrast, the stochastic approach reveals fluctuations of ±5% in resource allocation, variations of ±10 Mbps in bandwidth and a transmission delay of up to 130-140 ms, reflecting a better representation of real network conditions. These results demonstrate that the deterministic approach offers a predictable view of the network, while the stochastic approach enables better dynamic adaptation, essential for anticipating congestion and adjusting resources in real time.