Multi-Server Chat in Node Without a Database

A few years back, I was consulting for a client who had a Node-based instant messaging feature which had worked pretty well at first. But the number of users grew, and then it didn’t.
Even though they had a number of load-balanced server instances running, they found that the Redis database they were using to track connected users was a big bottleneck. No matter how many instances they ran, they all had to talk to that database.