GPenSIM-Based Modular Petri Net for Generic Queuing Systems

Queuing systems are ubiquitous in social and economic domains, but traditional analytical methods like queuing theory face limitations due to rigid assumptions and inability to model heterogeneous or interconnected systems. This paper presents a generic Petri Module for queuing systems, developed using GPenSIM, to overcome these challenges. The proposed module can model G/G/C/K systems with arbitrary service disciplines (e.g., FCFS, LCFS, priority-based) and complex behaviors (e.g., balking, reneging). Unlike queuing theory, our approach supports heterogeneous servers (each with distinct scheduling policies) and seamless integration into larger discrete-event models. Leveraging GPenSIM's modular architecture and MATLAB compatibility, the module enables scalable simulations while benefiting from MATLAB's analytical tools. Key features include GPenSIM's pre-processor-driven service discipline enforcement, finite-capacity handling, and emulation of process sharing. The paper details implementations for time-based, priority-based, and partitioned-task disciplines, demonstrating flexibility for real-world applications. This work bridges gaps in queuing system modeling by combining Petri nets' expressiveness with GPenSIM's computational efficiency.