The M/M/1 queue model is a mathematical representation used in operations research and telecommunications to analyze systems with a single server. The "M" stands for "Markovian," indicating that both arrival and service times follow an exponential distribution. The "1" signifies that there is only one server handling incoming tasks or customers. This model helps in understanding key performance metrics such as average wait time, queue length, and server utilization. It is widely applied in various fields, including computer networks, call centers, and manufacturing, to optimize resource allocation and improve service efficiency.