# probability paradox with two queues

If @Harald is right, then the "paradox" should be stated differently: If you pick some point in time uniformly from all time intervals that you spend standing in such queues, then the probability is $\gt0.5$ that you're standing in the slower queue. In the situation as described in the current version of the question, the probability of picking the slower queue is exactly $0.5$. –  joriki Jul 12 '12 at 20:39
This reminds me of an annoying fact I observed many years ago. Suppose you are stuck in stop-and-go traffic on a two-lane road. Being greedy, if you see the other lane moving faster than yours, you start changing lanes. But this is not instantaneous; it takes some finite time $T$. Now if the difference between the speeds of the lanes goes as $\sin(\pi t/T)$, you will spend 100% of your time in the slower lane. –  Rahul Jul 13 '12 at 1:05