The logistic queue model: theoretical properties and performance evaluation

Abstract: The advent of digital twins (DT) for the control and management of communication networks requires accurate and fast methods to estimate key performance indicators (KPI) needed for autonomous decision-making. Among several alternatives, queuing theory can be applied to model a real network as a queue system that propagates entities representing network traffic. By using fluid flow queue simulation and numerical methods, a good trade-off between accuracy and execution time can be obtained. In this work, we present the formal derivation and mathematical properties of a continuous fluid flow queuing model called the logistic queue model. We give novel proofs showing that this queue model has all the theoretical properties one should expect such as positivity of the queue and first-in first-out (FIFO) property. Moreover, extensions are presented in order to model different characteristics of telecommunication networks, including finite buffer sizes and propagation of flows with different priorities. Numerical results are presented to validate the accuracy and improved performance of our approach in contrast to traditional discrete event simulation, using synthetic traffic generated with the characteristics of real captured network traffic. Finally, we evaluate a DT built using a queue system based on the logistic queue model and demonstrate its applicability to estimate KPIs of an emulated real network under different traffic conditions.