Customers are compelled to queue when a service system is at its busiest. This issue not only reduces customer pleasure, but it also causes the company to lose money. For consumer losses, this study proposes a queue model of customer queuing behavior. The goal is to reduce customer losses, hence researchers are looking at queue setup and optimization in random service systems. We developed three queuing models: MG1, GM1, and GG1 for estimating service quality control. We investigate queuing systems for predicting replies for service quality control based on queue models of customer behavior. The study found that the MG1 queue model yields the best service quality, however the GM1 and GG1 results are relatively close behind.