Application of Queue Theory in Cafe Services with Erlang Distribution

Abstract

As urban lifestyles evolve, culinary businesses, particularly cafes, have experienced rapid growth. This surge in popularity has led to an increase in customers and, consequently, longer queues. These extended wait times can frustrate customers and pose challenges to cafe management. To address this issue, we conducted a comprehensive eval___uation and optimization of the service system at a Samarinda cafe using the Erlang distribution queuing system. Primary data was meticulously collected over six days, amounting to a total of 12 hours of observation. Kolmogorov-Smirnov distribution fitting tests were employed, revealing that customer service times adhered to an exponential distribution. The average customer arrival rate was determined to be 0.351 per minute, while the average service time was calculated at 5.546 minutes per customer. Our analysis confirmed that the system operates in a steady state with a utility value of 0.06, indicating sufficient service capacity to handle the current customer load. Therefore, the study concludes that the cafe's service system is currently optimal.