While at a university, I had a job answering the computer operations room telephone. The phone could handle multiple lines, and since I could talk with only one person at a time, sometimes I had to put someone on hold. When things were calm and someone called, I would listen to the request and handle the call, hang up, and then wait for the next call. That's when the job was relaxing. However, if the call arrival rate increased enough, someone would call while I was already talking to someone on the other line. As a result, someone had to wait his turn, or in forecasting terms, queued. I noticed once the rate of calls caused people to queue, it took only a slight increase in the call arrival rate before there were many people in the queue and they were waiting a long time. It was like everything was calm, and then-wham!-everyone was queuing.

You might have experienced this yourself with your computer systems. Performance is fine, yet the system is really busy. Then for any number of reasons, the system activity increases just a little, and-wham!-performance takes a dive. And you sit back and say, "What just happened? Everything was going fine, and the workload didn't increase that much."

What happened to both of us is that we hit the famous rocket-science-like term, elbow of the curve (also known as the knee of the curve). At the elbow of the curve, a small increase in the arrival rate causes a large increase in the response time. This happens in all queuing systems in some fashion, and it is our job to understand when and under what conditions the elbow of the curve will occur.