Transition Matrix Study for the Max-Mean Dispersion Problem in Mobile Payment Systems

This work focuses on optimizing resource and transaction dispersion in mobile payment systems based on the Max-Mean Dispersion problem. The objective is to maximize the average distance between selected elements in order to avoid load concentration and reduce the risk of saturation. Several approaches are compared, including exact methods, heuristics, metaheuristics, and stochastic models based on Markov chains. The study shows that exact methods guarantee an optimal solution but remain limited for large network sizes. Fast heuristics offer good performance, but with sometimes suboptimal dispersion. Metaheuristic approaches, such as simulated annealing, GRASP, or genetic algorithms, offer a good compromise between quality and computation time. Stochastic modeling, on the other hand, allows the temporal variability of system states to be analyzed. The integration of Max-Mean Dispersion in mobile payment networks improves robustness, flow distribution, fault tolerance, and quality of service. Simulation results demonstrate that controlled dispersion reduces dependence on certain critical nodes and improves overall availability.