Simulation Implementation of M/M/1 Queueing Theory

By adjusting parameters of business flows, we can implement simulations of M/M/1 queueing theory. The simulation process employs discrete-event simulation techniques where we track key time metrics including system response time, waiting time, and service time. These metrics are typically calculated through timestamp tracking algorithms - recording arrival timestamps, service initiation times, and departure events. The statistical data helps analyze system performance and supports optimization decisions. In practical applications, queueing theory simulation has been widely adopted across manufacturing, logistics management, transportation systems and other domains. Through simulation and optimization, we can improve system efficiency, reduce resource waste, and create greater value for enterprises and society. Code implementation typically involves maintaining event queues using priority queues sorted by timestamps, and calculating performance metrics through statistical modules that aggregate time intervals between events.