Simulating Some Queues

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2025-01-06 14:00:05

System performance boils down to the timing behavior of various interacting queues. Queues are one of those incredibly simple but powerful concepts, but they have some unintuitive or non-obvious behavior when only thinking about them mathematically. Simulating queueing scenarios gives us a better picture about how queues operate in practice.

Let’s introduce the simplest possible queue as a reference point, which we’ll call the unit queue. Requests arrive once per second, and each request takes one second to process. There’s only one processor that services requests. Here are some quick definitions about the operations of this queue:

This queue is in an equilibrium state: as soon as a request is done being processed, a new one comes in. And before the next one comes in, the current request has enough time to complete. This means that a request never has to wait to be processed, and it begins processing as soon as it comes in. Because of this, the queue length is always 0 and never grows.

This won’t be a deep dive into discrete event simulation, but it helps to know a few things about it to understand the data that we’re generating in our simulations. You can read more in the SimPy docs.