Implementation of the M/M/1 Queue System Model at Bang Mamad's Chicken Noodle Stall in the UIN Pekalongan Environment

Abstract

Mie Ayam Bang Mamad is a culinary business located near UIN K.H. Abdurrahman Wahid Pekalongan and is a popular dining destination for university members and the public. However, it remains unclear whether its single-cashier service system can accommodate customer arrivals, especially during peak hours. This study aimed to analyze the performance of the queueing system using the M/M/1 queueing model to evaluate service efficiency. A descriptive quantitative approach with a case study design was employed. Data were collected on Monday, April 13, 2026, from 12:00 to 1:00 p.m. (WIB), involving 50 customers. The research instrument consisted of an observation sheet recording customer arrival times, service start times, and service completion times. The results indicated a customer arrival rate of 8 customers per 10 minutes and a service rate of 9 customers per 10 minutes. On average, there were 8 customers in the system and 7 customers waiting in the queue. Customers spent an average of 10 minutes in the system and 9 minutes waiting in line. The cashier utilization rate reached 88%, indicating that the service system was not yet optimal. Therefore, adding an additional cashier during peak hours is recommended to improve service quality and reduce customer waiting times.