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Dice and Queues
Introduction
One of the key insights from queuing theory is that the average queue size for an unbounded system tends to increase significantly as utilization approaches 100%. While these equations are fairly easy to use, I wanted to get a more intuitive understanding of how these models behave and decided to build a simulation based on the idea of rolling a single die many times. In this equation the average queue size is 0 if the utilization factor is 0, which makes sense as that corresponds to either 0 arrivals or an infinite service rate.
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