h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Maybe I'm missing something. What is there to prove?

It's not totally obvious that it applies in *all* situations - it's fairly clear that it applies when the length of the queue is constant - but if the queue length is varying, and perhaps is zero for a time, then it becomes somewhat less obvious...

I keep flitting back and forth between it still being obvious and wondering if its true at all

Ok, what about this: 10 minute time period, start with 10 people in the queue, each takes a minute to serve, nobody arrives at all. Then average number of people in the system is about 5, but the average arrival rate is zero. Am I applying the result wrongly?

Hmm - I'll have to think about this one...

I think this is correct, you have just found a situation that also contains an infinity. During the time period you are correct that the arrival rate is 0, but at the very beginning there was an arrival rate of infinity (10 people are immediately in the system). I think the reason the law doesn't obviously apply in this case is that it is not a stable system (infinities tend to produce instabilities, or headaches depending on your profession

Wick