Comparative analysis of M/G/K queueing model with artificial neural networks for service system dynamics

Queues emerge when the demand for service exceeds the available capacity to provide it. The M/G/K queuing model is the typical and theoretical framework to model and analyze the system when arrival rates are not in constant mode and service rate follow exponential distribution. This study investigates traffic congestion at fuel stations, focusing on queue length, customer waiting time distribution, and operational efficiency. A system with four servers were modelled to evaluate the system's behavior. The governing differential equations using M/G/K model were developed and solve by Runge–Kutta (RK4) method to derive initial state probabilities. Additionally, an Artificial Neural Network (ANN) was implemented to predict these state probabilities using simulated data. A comparison of results revealed a close approximation between the RK4 solutions and ANN predictions, demonstrating the ANN's robustness and accuracy in replicating traditional queuing dynamics These findings emphasize the potential of artificial neural networks (ANNs) as a practical tool for planning and optimizing fuel station operations, allowing for better congestion management and customer experience. Future applications may involve the extension of this methodology to other service-oriented systems.