ANALISIS SISTEM ANTRIAN M/M/1 PADA KASIR TOKO SAGA MENGGUNAKAN APLIKASI QM FOR WINDOWS

Abstract

This study aims to analyze the performance of the cashier queue system at Toko Saga using the M/M/1 queuing model and QM for Windows software. Assuming customer arrivals follow a Poisson distribution and service times are exponentially distributed, the M/M/1 model is applied to calculate system performance parameters and total operational costs. Based on observations, the average customer arrival rate is 7 customers per hour, while one cashier can serve 8 customers per hour. The simulation results show a system utilization rate of 88%, with an average of 6 customers waiting in line and an average queue time of approximately 52.5 minutes. The total operational cost per hour is recorded at Rp75,658, which includes cashier wages and customer waiting costs. The probability distribution indicates that the system most frequently operates with fewer than 10 customers, and the chance of exceeding 15 customers is low. Therefore, the current cashier system is considered efficient, although additional strategies such as cashier shifts or self-service systems are recommended to ensure continued performance and customer satisfaction.