If the teller takes 10 min (on average) to serve someone and people arrive less often that 1 in every 10 minute, the average wait time is going to be finite. If people arrive more often than 1 in every 10 minutes, the queue is going to grow infinity large, and the average wait time is infinite.

So as the frequency with which people arrive approaches 1 in 10 minute (from above), the average wait time will increase dramatically, reaching infinity at 1 person / 10 min.