Análise de desempenho e otimização do sistema de controle para Redes de Petri estocásticas

Abstract

This work addresses the optimization of client-server queueing systems with the possibility of abandonment, modeled through Stochastic Timed Petri Nets (STPNs). These systems allow for a structured representation of stochastic events such as customer arrival, service, and abandonment proportional to queue length, making them suitable for performance analysis in dynamic environments. To reduce the abandonment rate without compromising productivity, a deterministic control mechanism was introduced, based on queue limitation and admission timing. From this structure, optimization techniques were applied to determine the best control parameters, using Exhaustive Search (ES) and Genetic Algorithms (GAs). Objective functions were formulated to maximize system profit, taking into account the service rate and penalties associated with abandonment. The results show that while ES guarantees the optimal solution in small search spaces, GAs stand out for their ability to explore larger spaces at lower computational cost, identifying near-optimal solutions. Therefore, GAs prove to be a viable and efficient approach for optimizing control in stochastic systems with queueing and abandonment characteristics.