Pemodelan Sistem Antrian Pasien RSJ Menur Menggunakan Timed Petri Net - Zumrotus Sya'diyah; Ari Maulida Intahaya (Griya Journal of Mathematics Education and Application, 2026)
Queueing systems play an important role in operational management, particularly in healthcare services. Inefficient queue management can reduce service quality and patient satisfaction. This study aims to model the outpatient queueing system at Menur Mental Hospital, Surabaya, using a Timed Petri Net approach combined with Max-Plus Algebra. The data were obtained through a literature review and an interview with one outpatient clinic nurse at Menur Mental Hospital conducted in June 2025, which provided information on the stages of service and the average duration of each service process for BPJS outpatient patients. The Petri Net model represents the service flow graphically, while the Max-Plus Algebra formulation expresses the system dynamics in a recursive form. The resulting Max-Plus matrix describes the time dependency structure among service stages. Based on the transition duration analysis, the critical path of the system is identified in the polyclinic and pharmacy services with a total service time of 56 minutes, indicating these stages as potential bottlenecks. The proposed model provides a mathematical framework to evaluate system performance and support decision-making in improving the operational efficiency of outpatient services.