Sensitivity Analysis of a Single-Server Fuel Queue System Using the M/M/1 Model: A Case Study of a Pertamini Station - Sinta Restuasih; Eko Widodo Gustany; Fitri Retna Wijayanti; Ananda Putri Ariyani; Nur Maulida Fitria (Jakarta Global University, 2025)
The rapid growth of motorcycle ownership in Indonesia has significantly increased the demand for fuel, particularly for daily transportation activities. This condition has encouraged the development of micro-scale refueling services, commonly known as Pertamini, which provide easier and more accessible fuel services for local communities. However, Pertamini stations generally operate with limited facilities and a single service channel, which may lead to queue formation, especially during peak hours. Long waiting times can reduce service efficiency and customer satisfaction, making queue system evaluation essential to support operational improvements. Therefore, this study aims to analyze the performance of the Pertamini service queue system using the M/M/1 queue model. This research applies a quantitative approach through direct field observation to collect data on customer arrival rates and fuel service times during a specified observation period. The collected data are used to determine the arrival rate (λ) and service rate (μ) as the main parameters in modeling the queue system. System stability is evaluated by comparing these parameters to ensure that service capacity can accommodate customer demand. Several performance indicators are analyzed, including system utilization, the average number of customers in the queue and in the system, and the average waiting time experienced by customers. The results indicate that under normal operational conditions, the queue system operates in a stable condition where the service rate exceeds the arrival rate. However, sensitivity analysis shows that an increase in arrival rate or a decrease in service rate significantly increases waiting time. Therefore, improving service efficiency is necessary to maintain system stability and reduce customer waiting time.