An Analysis of Single waiting line with multiple parallel servers

Increasing customer happiness and improving operational efficiency are two of the most important goals that may be accomplished by optimizing queue systems in today's fast-paced service settings. A single waiting line system that is handled by many simultaneous servers is a design that is often seen in settings such as banks, contact centers, and hospital emergency rooms. This paper gives a complete examination of such a system. The research makes use of queuing theory to represent the system, with a specific emphasis on the M/M/c queue. In this queue, arrivals are arranged according to a Poisson process, service durations are exponentially dispersed, and there are c servers that are similar to one another. The average waiting time, the length of the queue, the percentage of servers that are being used, and the chance of a client being delayed are some of the performance metrics that are calculated and assessed under different system parameters. The theoretical conclusions are validated using simulation and numerical tests, which also give insights into optimum server allocation, cost-efficiency trade-offs, and system stability. The findings highlight the significance of balancing service capacity with demand in order to reduce congestion and waiting time. As a consequence, this model is very relevant to situations that occur in the real world and include significant service demand.