MATLAB Simulation of M/M/1 Queueing System

This paper presents a MATLAB simulation of the M/M/1 queueing system. Initially, we comprehensively explain queueing system concepts and their real-world applications. Subsequently, we conduct in-depth analysis of the M/M/1 system and establish simulation assumptions based on practical scenarios, including server processing capacity, customer arrival rates, and service time parameters. The simulation employs discrete-event system methodology to accurately model real-world conditions, utilizing event scheduling algorithms and time-advance mechanisms.

Through analysis of simulation results, we obtain system steady-state distributions, average queue length, waiting time distributions, and mean waiting time values. The implementation involves statistical tracking of queue states using counter variables and time-weighted averages. We generate and analyze statistical curves through MATLAB's plotting functions (plot, hist) to better understand system performance and behavioral patterns. Comparison with theoretical results demonstrates close alignment with practical scenarios, validating simulation reliability and accuracy.

In summary, this paper details queueing system concepts and their practical applications through MATLAB simulation of the M/M/1 system. The simulation code incorporates event list management using priority queues and statistical collection mechanisms. Results analysis provides insights into system performance and behavioral patterns, offering valuable references for practical implementations.