That's the "steady state" issue. You have to imagine a bank that has been open an infinite amount of time with people arriving at an average of 5.8 times an hou

That's the "steady state" issue. You have to imagine a bank that has been open an infinite amount of time with people arriving at an average of 5.8 times an hour during that entire period. It will eventually reach an equilibrium with a very high wait time (most specifically, the expected value of the wait time approaches 5 hours as the queuing process continues). The key insight here is that clusters of people coming in within a short time (which will happen) propagate into future wait times, while clusters of nobody coming in do not -- if the line is empty, it doesn't matter for your wait how long it has been empty, but if the line is clogged, it matters for your wait time how long it has been clogged. That's kind of a silly model for a bank, but it makes more sense for a server (which, given the time span of most network requests, might as well have been up for an infinitely long time).