Determining the Number of Optimum Servers in The XYZ Restaurant Queue System with Queuing Theory

Abstract

Queue is a natural phenomenon that occurs when the demand for a service at a certain time exceeds the capacity of service at the same time. In this paper, the problem is solved using the queuing theory which is an analytical tool that is very helpful in solving queuing problems. This theory includes mathematical studies that produce important information needed in decision making with the help of forecasting various characteristics of the queue line. The queuing model in this restaurant queue system is (M / G / S). The current queuing system has System utility level (p) 52.23%, average time of customers in the queue (Wq) 0.4634 minute, The average time a customer in a system (W) 2.8074 minutes, Average Number of Visitors in the Queue (Lq) = 0.2104 ≈ 1 person, and Average Number of Visitors in the System (Ls) 1.2750 ≈ 1 person. The total waiting time on server 2 is below the maximum waiting time of 15 minutes and has the greatest system utility level, thus the optimum number of servers chosen is server 2 which is already optimum.