Model Analysis Queue Theory in Fast Food Restaurants in Padang City - Vita Vidayati; Ayu Wulandari; Ira Selvia; Nadiyatul Ghina (Rangkiang Mathematics Journal, 2026)
Queuing systems represent service processes in which customers wait due to limited service resources. Analysing such systems is essential to ensure efficient service and minimise waiting time. This study aims to examine the queuing system applied at Hokben Sawahan Padang by analysing customer arrival and service rates to determine the appropriate model and system characteristics. A quantitative method was used, with primary data collected through direct observation of arrival and service times. The results indicate that the appropriate model is (M/M/1) with a FIFO discipline. The average number of customers waiting in line (Lq) is 0.52 customers per minute, while the average number in the system (L) is 1.03 customers per minute. The average time spent in the system (W) is 4.9 minutes, and the average waiting time before service (Wq) is 2.4 minutes. The server utilisation level is 50.62%, with an idle rate of 49.38%. These findings suggest that the queuing system is relatively efficient and can be categorised as quite ideal. However, further improvements are needed to increase server utilisation and service effectiveness. Enhancing service quality, cleanliness, comfort, and overall operational performance can improve customer satisfaction and business profitability. The study implies that queue performance indicators, such as waiting time and utilisation rate, can serve as important managerial tools for evaluating and optimising service operations.