Computer Simulation of Queueing Theory Implementation

This article presents methods for implementing computer simulations of queueing theory using MATLAB. Queueing theory is a mathematical discipline that studies the operational processes of stochastic service systems, while queueing models are mathematical frameworks used to describe service systems within queueing theory. In queueing models, we typically use m to represent the number of customers served during a workday, and t to denote the average customer waiting time. The simulation employs event-driven programming where customer arrivals and service completions trigger state changes in the system.

The applications of queueing theory span various domains including banking systems, healthcare facilities, airport operations, and other service-oriented environments where optimizing service processes is crucial for enhancing efficiency and quality. Through computer simulation of queueing theory, we can accurately predict system performance under different scenarios, enabling optimization of queuing strategies and resource allocation to improve service levels. Key algorithms implemented include Poisson process generators for arrival patterns and exponential distribution functions for service times.

In MATLAB, multiple toolboxes and functions are available for queueing theory simulations. For instance, the SimEvents toolbox provides building blocks for creating discrete-event queueing models, Simulink offers a graphical environment for system simulation, and the Queueing Theory Analyzer toolbox facilitates performance analysis of simulation results. Core functions include entity generation, server allocation, and statistical collection modules. By mastering these tools and methodologies, practitioners can efficiently conduct queueing theory simulations, providing robust support for service system optimization and improvement initiatives. The implementation typically involves configuring simulation parameters, running Monte Carlo simulations, and analyzing output metrics like queue length distributions and system utilization rates.