Intuitive Queuing Theory: A Dice-Rolling Simulation

This article uses a dice-rolling simulation to provide an intuitive understanding of key queuing theory concepts. The author simulates an M/D/1 queueing model, where arrivals follow a Poisson distribution and service time is deterministic. By varying the service rate, the simulation demonstrates how queue length changes under different utilization factors. Results show that as utilization approaches 100%, average queue length increases significantly, even tending towards infinity. The simulation aligns well with theoretical results, and explores the reasons behind queue length fluctuations.