Queues are a typical occurrence in everyday life, particularly during peak hours in Fair Price Shops (FPS), government offices, banks, post offices, super markets, hospitals, and clinics. The arrival rate, service rate, and server usage all play a role in the queueing process of any system. We expect a balance between waiting time and server utilization in an effective system, with the ideal being less waiting time and maximum server utilization. This paper investigates efficient queue management in FPS using M/M/C queueing model. The major goal of this research is to minimize customer waiting time in the FPS with the minimal number of servers. It demonstrates the application of the simulation modelling as a method for optimizing the number of servers in a specific FPS in Kerala, India. The model was developed to provide the outcomes of system parameters like arrival rate, waiting time and server utilization.